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Style investing Wouters, T.

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Style Investing: Behavioral Explanations of Stock Market Anomalies

Tessa Wouters

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 2006, Tessa Wouters

Rijksuniversiteit Groningen

Style Investing: Behavioral Explanations of Stock Market Anomalies

Proefschrift

ter verkrijging van het doctoraat in de Economische Wetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr. F. Zwarts, in het openbaar te verdedigen op donderdag 14 september 2006 om 13.15 uur

door

Tessa Irene Maria Wouters

geboren op 15 november 1976 te IJsselstein

Promotor : Prof. dr. F.M. Tempelaar Copromotor : Dr. A. Plantinga

Beoordelingscommissie : Prof. dr. S. Benninga Prof. dr. W.F.M. De Bondt Prof. dr. R.A.H. van der Meer

Voorwoord

Dit proefschrift richt zich op anomalieën in aandelenmarkten en de verklaringen die uit de cognitieve psychologie in de loop van de jaren zijn ontstaan. Psychologische verklaringen voor gedrag van individuele mensen en groepen mensen hebben mij altijd zeer geboeid. Naast dat de psychologie van beleggers voor mijzelf en blijkend uit de reacties de afgelopen jaren ook voor veel andere mensen een interessant onderwerp is, is het ook een relevant onderwerp. De psychologie van beleggers en de invloed van hun gedragingen op het niveau en de volatiliteit van aandelenkoersen kunnen ernstige consequenties hebben voor de stabiliteit van financiële markten. Daarnaast is de psychologie van beleggers ook een interessant onderzoeksgebied voor wetenschappers, aangezien het vakgebied ‘behavioral finance’ nog in de kinderschoenen staat en op dit gebied nog veel onbekend is en onderzocht dient te worden. In de afgelopen vijf jaar heb ik als Assistent-in-Opleiding (AiO) heel veel geleerd. Belangrijk daarbij was de aanwezigheid van mensen die kritische vragen stelden en wilden luisteren naar je onderzoeksbevindingen. Deze mensen wil ik om die reden dan ook hartelijk bedanken. Auke Plantinga heeft me in dit traject geleerd om onderzoek te doen en heeft me weten te motiveren als ik vastzat en me vertrouwen gegeven dat ik dit onderzoek tot een goed einde kon brengen. Ik heb de jaren dat wij hebben samengewerkt als zeer waardevol ervaren. Prof.dr. F.M. Tempelaar wil ik bedanken voor de consciëntieuze wijze waarop hij me begeleid heeft in het

onderzoek. Indertijd heeft hij me aangenomen als studentassistent en me enthousiast gemaakt voor het doen van onderzoek. Gedurende mijn AiO- periode heeft hij mij geleerd kritisch te zijn naar mijn resultaten en (vooral) teksten. Ook wil ik de leden van de leescommissie bedanken, Prof.dr. S. Benninga, Prof.dr. W.F.M. De Bondt en Prof.dr. R.A.H. van der Meer, voor het feit dat ze de tijd hebben willen vrijmaken om mijn proefschrift zorgvuldig te bestuderen. Ook wil ik een aantal collegae bij de vakgroep Financiering, Belegging en Accounting bedanken. In de eerste plaats Prof.dr. L.J.R. Scholten die een aantal hoofdstukken van commentaar heeft voorzien. Verder wil ik Prof.dr. B.W. Lensink bedanken voor zijn belangstelling voor mijn onderzoek. Ook mijn overbuurman en paranimf, Nanne Brunia, ben ik erkentelijk voor zijn interesse en raadgevingen aangaande mijn proefschrift. Mijn tweede paranimf, Marije Teerling, wil ik bedanken voor het fungeren als ‘sparringpartner’ in het laatste traject van mijn onderzoek. In Gijsbert Willenborg vond ik een prettige gesprekspartner om alle gebeurtenissen binnen en buiten de universiteit te bediscussiëren. Daarnaast gaat mijn dank uit naar de overige collegae van de vakgroep Financiering, Belegging en Accounting, omdat zij plezierige collegae waren om mee op te trekken in de afgelopen vijf jaar. In het bijzonder wil ik mijn ouders bedanken. Zij hebben vanaf het begin mijn werkzaamheden met veel interesse gevolgd, al vonden ze het soms moeilijk te begrijpen waar ik precies mee bezig was. Het laatste dankwoord is bestemd voor Hendrik. Hij heeft vanaf het begin grote belangstelling getoond, mijn talloze gedachtespinsels moeten aanhoren en me gestimuleerd om dit proefschrift tot een goed einde te brengen.

Utrecht, juli 2006 Tessa Wouters

Contents

1 Introduction...... 1 1.1 Emergence of investment styles: historical perspective ...... 2 1.2 Style classifications: developments of the last two decades...... 5 1.3 Relevance of style investing ...... 8 1.4 Objective of the study ...... 12 1.5 Outline of the study...... 14

2 Review of the literature ...... 17 2.1 Introduction...... 17 2.2 Market efficiency and anomalies...... 18 2.3 Asset return models related to market anomalies ...... 24 2.3.1 Rationalists...... 24 2.3.2 Behavioralists...... 25 2.4 Rational models...... 30 2.4.1 Three-factor model...... 31 2.4.2 Model with growth options...... 34 2.4.3 Model with options to expand and to discontinue operations...... 38 2.5 Behavioral models...... 43 2.5.1 A model of investor sentiment...... 43 2.5.2 Investor psychology and security market over- and underreaction...... 48 2.5.3 Style investing...... 52

i CONTENTS ii

2.6 Summary and motivation for following chapters ...... 56

3 The value premium and changing expectations: on the growth of value stocks and the value of growth stocks ...... 61 3.1 Introduction...... 61 3.2 Sample selection...... 65 3.3 Switching- and fixed-style stocks ...... 71 3.4 Investor optimism and pessimism before and after style switching...... 78 3.5 Summary and conclusion...... 84 Appendix 3A...... 86

4 The drivers behind uncertainty and style migration...... 89 4.1 Introduction...... 89 4.2 Data...... 94 4.3 Step-wise empirical analysis of analysts’ forecast dispersion and style effects...... 97 4.3.1 Dispersion of analysts’ earnings forecasts, forecast errors, and value versus growth styles ...... 99 4.3.2 Dispersion of analysts’ earnings forecasts and the multiple of forecast errors...... 105 4.3.3 Dispersion of analysts’ earnings forecasts and style migration...... 113 4.4 Robustness tests...... 118 4.4.1 Comprehensive multivariate analysis of analysts’ forecast dispersion ...... 118 4.4.2 Probit analysis of style-switching behavior ...... 121 4.5 Summary and conclusion...... 127 Appendix 4A...... 129

5 Style popularity and the comovement of stocks...... 131 5.1 Introduction...... 131

iii CONTENTS

5.2 Fashion...... 135 5.3 Measures of style investing and style popularity...... 141 5.4 Methodology...... 146 5.4.1 Style popularity measures...... 147 5.4.2 Dispersion measure: stock or style popularity...... 148 5.4.3 Regression model...... 149 5.5 Data...... 150 5.6 Results...... 152 5.6.1 Popularity index...... 154 5.6.2 Popularity at a style or stock level ...... 158 5.7 Robustness analysis ...... 169 5.7.1 Movement in popularity...... 169 5.7.2 Popularity and the comovement in prices/returns...... 172 5.8 Conclusion ...... 175 Appendix 5A: Fashion cycle for the internet sector ...... 177

6 Conclusions...... 183 6.1 Overview...... 183 6.2 Main findings...... 184 6.3 Discussion...... 188

Bibliography...... 193

Samenvatting (Summary in Dutch)...... 207

Chapter 1

Introduction

The most elementary behavior of individuals when they have to make decisions is classifying or grouping objects into categories. These categories may provide some structure in the complex environment around them, which may simplify their decision-making processes (Mullainathan (2002)). The classification of objects into categories is also very useful in financial markets. An investor is faced with an enormous flow of information and investment opportunities. Taking into consideration the number of combinations of assets that can be held, the decision process seems overwhelming. Investors may categorize assets with similar characteristics to get grip on the overwhelming number of assets and to simplify diversification decisions. By combining assets into categories that vary as aggregates in response to market conditions, investors are able to create diversified portfolios in a simplified systematic way. There are many ways to classify assets. Asset classes can be classified in broad terms like stocks, bonds, real estate and cash, or they can subdivided further into liquid versus illiquid, old versus new economy, domestic versus foreign, and combinations of each. Through time investors

1 2 Chapter 1. Introduction

have categorized assets in order to separate them from each other. Today, the categorization of assets is called a style. A style can be defined as a classification of assets into a category with similar performance characteristics. The process where investors base their portfolio allocation on a style level rather than on an individual stock level is known as style investing (Barberis and Shleifer, 2003). Although style investing has been introduced as a new concept in the 1980s, the categorization of assets into different groups has taken place already for a long time. For example, the value style, which refers to investing in stocks that have low prices relative to their fundamentals (i.e. dividends, earnings, etc.) can be traced back to the 1930s. In the twentieth century, new styles (e.g. technology and telecommunication) have arrived and old styles have died off (railroad bonds). Barberis and Shleifer (2003) give two reasons for the emergence of new styles: financial innovation (e.g. inflation-linked bonds) and the detection of outperformance of certain sets of stocks with similar characteristics (see section 1.2). In the next section, we give an overview of style classifications that have been followed by investors in the twentieth century.

1.1 Emergence of investment styles: historical perspective

At the end of the 19th century and early 20th century railroad bonds were a very popular asset class among institutional investors. However, bonds became an unsatisfactory investment class in the period after World War I and also after the great crash in 1929. The years 1917 to 1920 were marked by a decline in all bond prices as the result of war financing followed by post-war inflation. Especially, railroad bonds fell into difficulties, because of decline in the creditworthiness of railroad companies. Other industrial

1.1 Emergence of style investing: historical perspective 3 bonds also had their disadvantages as an investment class, because many issuing companies fell into difficulties as well. Because of the negative experience with bonds as an investment class, investors moved their attention away from bonds to common stocks. Until the late 1920s, investors believed that stock prices were a reflection of present results because future results were uncertain. In the late 1920s up to the crash of 1929, the focus of investors turned away from established performance to expected future growth. Investors started to believe that the price of a stock should reflect future growth rates: stocks were invested in for their growth potentials. After the crash of October 1929, the great depression started and growth stock investing disappeared. In the 1930s and 1940s, the value stock approach started to gain attention. Graham and Dodd (1934) advocated to stay away from growth stocks. They argued that future growth was largely unpredictable, prospects in growth rates are arbitrary and inevitably subject to exaggeration. The work of Graham and Dodd remained very influential throughout most of the fifties. But during the boom after World War II, there was a revival of growth stock investing. Investors believed again that stock investments should be based on the prospects of future growth. An example of the Dutch stock market was the investment company Robeco that introduced the Rolinco Fund in the year 1965, which was a mutual fund that concentrated on growth stocks and where the focus was to obtain capital gains instead of dividends. In the first half of the 20th century, investors focused on assessing risks and rewards of individual securities in constructing their portfolios. Since the work of Markowitz (1959) in the 1950s, the introduction of an organized asset allocation framework started to gain ground among institutional investors. Because of modern portfolio theory, the emphasis moved away from asset selection to a more balanced emphasis on diversification, focusing on interrelationships of individual asset characteristics within the portfolio. As a result of diversification thinking the development of mutual funds started. In the late 1960s and in

4 Chapter 1. Introduction

the 1970s, there was a strong belief in market efficiency. Fama (1970) defines efficient markets as financial markets where all available information is incorporated in stock prices. This implies that portfolio managers cannot systematically outperform the market. The expected return of a stock is solely a function of risk, and should increase with the risk of an investment, as a compensation for the acceptance of additional risk. With the knowledge that investors cannot outperform the market, the best strategy is to hold diversified portfolios. As a result index investing emerged. An index portfolio mimics some broad based index of the market, such as the S&P500. At the end of the 1970s and during the 1980s, market efficiency was questioned and research into anomaly finding emerged. Academic research started to question whether stock returns were indeed consistent with the efficient market hypothesis or whether the market was segmented in terms of investment returns. It appeared that the efficient market theory could not account for the outperformance of certain classes of stocks with similar characteristics. Academics found anomalous abnormal returns for groups of stocks, which could not be explained in terms of risks (e.g. Banz (1981), DeBondt and Thaler (1985)). To exploit these unexplained market anomalies, differentiation between stock categories were made and the rise of specific investment funds started in the early 1990s. Although, specific investment funds (e.g. foreign stock funds) had been around for a long time, the aim now is to generate excess returns because of specific stock characteristics instead of facilitating diversification along specific lines. In order to exploit market anomalies, different style classifications have been developed over the last two decades. In the next section, we highlight some of these style classifications. In chapter 2, these style classifications are further developed.

1.2 Style classifications: developments of the last two decades 5

1.2 Style classifications: developments of the last two decades

Several style classifications have arrived over the last two decades to exploit market anomalies. Some classifications are more obvious than other classifications. Well-known classifications are those based on industries or countries. Although the style classification based on countries already existed, the objective was to facilitate diversification rather than generating excess returns. Other classifications that are used to classify stocks are less obvious and need analysis. Instances of relevant variables in such analyses are past performance, price-scaled ratios and market capitalization. The first classification that is discussed here is based on market capitalization. Investors that follow such strategy divide stocks into high market capitalization stocks, large caps, and low market capitalization stocks, small caps. Banz (1981) and Fama and French (1992) show that small-caps outperformed large-caps over different periods. Those studies demonstrate that the results held even after taking into account the higher risks that accompanied those higher returns.

Momentum and contrarian strategies require classifications of stocks based on past performance. Stocks that generated high returns in the past are called winner stocks and stocks that generated low returns in the past are called loser stocks. When an investor buys winner stocks he follows a momentum strategy and an investor that buys loser stocks follows a contrarian strategy. De Bondt and Thaler (1985) form portfolios of the best and worst performing stocks over the previous three years and find that the loser portfolio outperformed the winner portfolio over the long run. Jegadeesh and Titman (1993) form winner and loser portfolios over the previous six to twelve months. They find that winner portfolios

6 Chapter 1. Introduction

outperformed loser portfolios in the short run. This short-term momentum effect is also shown for countries outside the US, i.e. Rouwenhorst (1998). Other studies show momentum effects at an industry, country or style level. For example, Moskowitz and Grinblatt (1999) classify industries based on past performance. They divide stocks into twenty industry portfolios over the period 1963 to 1995. They sort the industry portfolios based on their past 6-month returns. The top-three winner portfolios are called the winner portfolios and the top-three loser portfolios are called the loser portfolios. Investing in a long-short combination portfolio (long in winners and short in losers) shows a historical average annual return of 9.5% during a period of twelve months after formation. An alternative strategy based on this concept is the style momentum strategy. Chen and DeBondt (2004) provide evidence of style momentum. Over the period 1976 to 2000, they group stocks from the S&P500 along three style- characteristics: market capitalization, book-to-market ratio and dividend yield. They rank the obtained style-portfolios by their past 3 to 12 month returns and find that stocks with characteristics that are currently in favor outperform stocks with characteristics that are currently out of favor. Alternative classifications on past performance that have been applied are for example the combination of past performance and analyst coverage. For example, Hong, Lim and Stein (2000) show that profitability of strategies based on past performance declines with analyst coverage.

Another classification is based on ratios of specific stock fundamentals to the stock’s market price. Examples of such stock ratio’s are: book-to-price, earnings-to-price, dividend-to-price, and cash flow-to-price. A stock with a low market price relative to the specific fundamental is called a value stock and a stock with a high market price relative to the specific fundamental is called a growth stock. Many empirical studies, i.e. Fama and French (1992), Lakonishok, Shleifer and Vishny (1994) and La Porta, Lakonishok, Shleifer

1.2 Style classifications: developments of the last two decades 7 and Vishny (1997), show the outperformance of value stocks with respect to growth stocks for the US stock market. Lakonishok, Shleifer and Vishny (1994) combine the cash flow-to-price ratio and past sales growth to classify stocks. They divide stocks based on the past 5-year sales growth and cash flow-to-price ratio into nine portfolios. The value portfolio (which is the portfolio with the highest cash flow-to-price ratio and the lowest past growth rate) outperformed the growth portfolio (portfolio with the lowest cash flow-to-price ratio and the highest past growth rate) over a 5-year period after formation. The relative outperformance of value stocks over growth stocks is referred to as a value premium in stock market returns. This value premium is also reported for countries outside the US, e.g. Chan, Hamao and Lakonishok (1991), Fama and French (1998), and Dimson, Nagel and Quigley (2003). Alternative classifications that have been made in the last decade are based on other fundamentals-related measures, such as analysts’ earnings forecasts and trading volume. La Porta (1996) classifies stocks on analysts’ earnings forecasts into ten deciles from high to low analysts’ earnings forecasts. He finds that the portfolio with the lowest forecasted earnings growth outperformed the portfolio with the highest growth forecasts with an average annual return of twenty percent the year after formation. In the above, we described style classifications based on specific stock characteristics in order to generate excess returns. In the last two decades also other methods have been developed to generate excess returns. An example of such a method is timing that can exploit anomalies such as calendar effects. Calendar effects show that certain days of the week, weeks of the month, or months of the year are more likely to produce rises and falls in share prices than others, i.e. January effect, weekend-effect, and holiday effect. Keim (1983) shows that daily abnormal return distributions have larger means in January relative to the remaining eleven months. Another calendar-effect is the weekend effect. Fridays show relatively high

8 Chapter 1. Introduction returns and Mondays tend to be relatively low. Studies that report the weekend-effect are for example French (1980), Lakonishok and Schmidt (1988) and Doukas (1996). The final calendar effect that is discussed here is the holiday effect. Lakonishok and Schmidt (1988) and Ariel (1990) provide evidence of high abnormal returns on days prior to a US holiday for US stock markets. Cadsby and Ratner (1992), Kim and Park (1994), and Arsad and Coutts (1997) provide evidence of Holiday effects for stock markets outside the US.

1.3 Relevance of style investing

Although style investing is by no means novel as has been explained in the previous sections, the attention of style investing has grown in recent years. Style investing has become an important issue for institutional as well as for private investors. Many institutional investors claim to follow a particular investment style, such as ‘value’ or ‘small-cap’. Financial advisors may have contributed to the growing importance of style investing within the institutional investment community. Financial advisors are hired to find portfolio managers that respond to the clients’ needs. To assess the skills of a portfolio manager, advisors prefer portfolio managers to follow a style instead of investing without a style discipline (Bernstein, 1995). In addition, the financial services industry has responded to this perception of discipline to cater the needs of private investors. Nowadays, many mutual fund managers identify themselves as following a particular style (Bogle, 2005). Investment styles have not only become an important marketing device, but are also important for the development, analysis and performance evaluation of investment strategies and/or mutual funds. In addition, investment styles also provide insight into the forces of underlying

1.3 Relevance of style investing 9 price movements in equity markets. In this section, we present the relevance of style investing from three different perspectives, notably from the perspective of investors, from the perspective of the functioning of financial markets and from the perspective of academic researchers.

1. Style investing is relevant to investors because it enables them to organize and simplify their portfolio allocation decisions. Transparency may increase, because the categorization leads to asset classes with the same kind of characteristics. Mutual fund managers can identify themselves with one style and fulfill the joint needs of individual investors into one fund. This leads to better diversification of investors’ portfolios and to a much more disciplined way of choosing among stocks. The classification of investment strategies also plays a role in the selection and evaluation of the portfolio manager. Portfolio managers are now able to identify themselves with a particular investment style. Investors can base their selection of active managers within style guidelines and categorize active managers by style. The evaluation and selection of portfolio managers is therefore simplified, because the performance of portfolios can be compared with standardized style benchmarks (Sharpe, 1992). However, style investing can also lead to misclassifications. As a consequence of investors applying style investing, mispricing and excessive comovement in prices (and returns) of styles is induced. Labeling stocks increases the chance for investors to make errors when they allocate funds at the level of categories. Stocks of companies with different business activities might be linked to the same asset category. An example of excessive comovement in prices is given by Cornell (2004). He shows that during the internet hype the prices of two internet companies comove more with each other than can be explained by their fundamentals. Froot and Dabora (1999) demonstrate mispricing with

10 Chapter 1. Introduction

two identical stocks, Shell and Royal Dutch, listed on different exchanges. The prices of these two stocks deviate more from each other than can be explained by their fundamentals. Also the demand shocks may lead to negative correlations among styles. Resources are withdrawn from one style into other competing styles. Consequently, the prices of the securities within the ‘neglected’ style depresses although the price decrease has nothing to do with the underlying fundamentals. 2. From a more general perspective of the proper functioning of financial markets, it is also important to understand style-based investment strategies. For example, positive feedback trading may result in destabilizing markets, because it may lead institutions to buy overpriced stocks and sell underpriced stocks, thereby moving market prices further away from fundamental values. This may eventually lead to an exacerbation of stock price volatility and momentum bubbles (De Long et al., 1990, and Cutler et al., 1990,). It is interesting to know which market participants are positive feedback traders and, if so, to what extent they influence stock prices. In addition, it is also in the concern of policymakers to understand what the impact of positive feedback trading by market participants may have on the exacerbation of stock price volatility and the increase in the fragility of the financial system. 3. Style investing is also an important phenomenon from the perspective of academics. The classical school of financial economics seeks to understand financial markets with models where investors are fully rational. The optimal combination of assets is derived within with frameworks such as modern portfolio theory (MPT) and capital asset pricing model (CAPM). These frameworks take only two dimensions of the return distributions, notably mean and variance, into considerations when making a choice between securities. To obtain the expected

1.3 Relevance of style investing 11

returns and expected variance investors are supposed to make unbiased fundamental-based predictions about the future. In the last two decades, the assumptions underlying MPT and CAPM have been questioned from the perspective of behavioral finance. A discussion is going on in the literature whether investors are capable of carrying out the dynamic optimization problems required by tenets of neo-classical finance theory. For example, Kahneman and Tversky (1974) have shown that people make judgments using rule of thumbs to deal with a deluge of information. Are investors always capable of making optimal decisions? And if investors are not fully rational, in what way are they biased? In addition, empirical researchers in finance have challenged the efficient market hypothesis. Over the last three decades researchers have found patterns in stock returns, which are inconsistent with the efficient market hypothesis, such as the value premium, the momentum-effect in the short run and the mean reversion effect in the long run (see section 1.2). These patterns can not be explained with the risk measures that are used in MPT-based models, like market beta and standard deviation. Since the basic model of risk and return, the CAPM, cannot explain observed return anomalies, new theoretical frameworks have been developed. These theoretical frameworks can be separated into two schools, rational and behavioral. The rational school explains the differences in stock returns in terms of non-diversifiable risk and the behavioral school explains it in terms of bounded-rational behavior of investors and limited arbitrage in stock markets (see chapter 2, section 2.3.1).

12 Chapter 1. Introduction

1.4 Objective of the study

As we mention in this chapter, various anomalies have been found which cannot be explained with rational models such as CAPM. Since then, new theoretical frameworks, rational and behavioral, have been developed. Our aim is to contribute to the discussion between the rational and the behavioral ‘school’. Because of the competing explanations for some of the anomalies, we believe that the assumptions of behavioral and rational models need empirical scrutiny. To contribute to the discussion, it is important to understand how beliefs of investors are measured. In what follows we have, therefore, decided to concentrate largely on the investor- based drivers behind behavioral models. In this thesis the focus is on style investing. In order to explore the mechanisms of style investing, the main purpose of this thesis is to empirically investigate the behavioral reasoning underlying empirical observations of return patterns for the US stock market. The investment styles classification that we concentrate on in most of our research is based on the distinction between value and growth stocks (see section 1.2). This thesis consists of two parts, each with an individual goal:

1 The first objective will be to find explanations for the value premium by introducing an alternative method of classification. We analyze the dynamic process underlying the behavior of value stocks and the generating of the value premium. 2 The second objective will be to find explanations for stock returns by introducing the effect of collective preferences of investors into the dynamics of stock markets. We introduce stock and style popularity as an important factor in the investment process.

1.4 Objective of the study 13

The empirical literature, e.g. Fama and French (1992), shows that in most of the times value stocks generate on average higher returns than growth stocks. The difference in returns between value and growth stocks is called the value premium. This value premium presents an interesting puzzle for researchers in finance, because the ‘traditionally’ known risk measures cannot explain this risk premium. Different explanations that try to explain the existence of a value premium can be summarized into two different schools. The rationalist school believes that the higher average returns for value stocks are a reward for additional systematic risks, which have not yet been observed. The behavioral school believes that the value premium is not the result of systematic risks, but the inability of investors to process and evaluate information correctly. The value stocks generate higher returns because of the biased behavior of the typical investor. Many of the categorizations in section 1.2 imply that an individual stock may change classes over time. For example, a stock that is classified as value stock at time t, may loose its status as value stock at a later point in time. This may lead to dynamics within and among asset classes. To pursue the first objective of this thesis we develop an alternative method of ranking for value and growth stocks. By analyzing an alternative method with a more sophisticated ranking we want to show better insights in the dynamic process underlying value stocks and the value premium. We make a distinction between switching versus fixed-style stocks. Within each style (i.e. value versus growth stock investing) we distinguish between stocks that stay within a particular style for only one period and stocks that stay for two or more periods. We analyze how stocks behave when they switch from style and what variables or factors are important to explain the style- switching behavior. We find that only a small fraction of the ‘value portfolio’ is responsible for the value premium, notably the switching-style stocks in the portfolio. Theories regarding the value premium, like the expectational error hypothesis and the information diffusion hypothesis, are

14 Chapter 1. Introduction

explored with this new classification. This leads to new insights and conclusions regarding the value premium. The subdivision of value and growth stocks into switching versus fixed-style stocks implies a critical note on style investing, because the label of value or growth stocks appears to be ‘too rough’. To profit from particular investment styles, portfolio managers may have to choose stocks that migrate from one style to another. To pursue the second objective of this thesis, we introduce stock popularity as an important driving factor of the investment process. Performance evaluation using style analysis is based on the idea that investors try to beat market indices reflecting the particular styles employed by investors. Barberis and Shleifer (2003) create a model that is based on a demand-driven process. Stock returns are determined by investors who base their asset choice on a category level instead of an individual level of stocks. The investment process is in terms of investment cycles where the demand for a particular style is based on the past performance of the style. Instead of choosing a passive benchmark and trying to beat this benchmark by over- and underweighting stocks, investors nowadays choose a particular style that did well in the past and hope that this will be a guarantee for future performance. We develop an alternative perspective on the performance of style investing.

1.5 Outline of the study

The first objective will be pursued in chapters 2, 3 and 4. Chapter 2 gives an overview of the models that try to explain return anomalies found in the last few decades. These models are categorized as ‘rational’ and ‘behavioral models. We argue that behavioral models can be improved upon in terms of how beliefs of investors are measured.

1.5 Outline of the study 15

In the chapters 3 and 4 we will present an alternative classification method to divide stocks in different categories. In chapter 3, we test the expectational error hypothesis with our newly obtained classification of stocks, and we add a new explanation to the discussion. In chapter 4, we will provide better insights into the impact of investors’ uncertainty about stock returns. We test two hypotheses, the information diffusion hypothesis and the expectational error hypothesis. Firstly, we look for evidence that uncertainty is increasing when less information about a stock is revealed. Secondly, we examine whether uncertainty is increasing because investors extrapolate past information (stock returns and forecast errors) into the future. Thirdly, we investigate whether it is more likely for a stock to migrate from style when investors are more uncertain about future earnings. The second objective (see section 1.4) of this thesis will be pursued in chapter 5. In this chapter, we describe the popularity of investment styles as being driven by collective preferences of investors and the changes of such preferences over time. In order to measure popularity, it will be necessary to construct a popularity index for different investment styles. Using different variables that reflect popularity, we create a popularity index. Having constructed a popularity index, it will be possible to check to what extent stock popularity can be attributed to style investing, as opposed to popularity of individual stocks. In addition, the time series of returns form the different investment styles will be used to test to what extent past performance in returns is related to the attractiveness of investment styles. Finally, we summarize our main findings from this thesis in chapter 6 and mention some issues that deserve further research. Chapters 3 to 5 are three chapters based on three different working papers. Therefore, the introductions and data descriptions of these chapters may show some overlap. In addition, chapter 3 and 5 are joined work with Dr. A. Plantinga.

16 Chapter 1. Introduction

Chapter 2

Review of the literature

2.1 Introduction

Academic researchers in finance are in the middle of a debate about the way people make decisions and how this should be modeled. In general, people make observations, process data and make judgments and decisions. The judgments and decisions have implications for individual portfolio compositions, the range of securities offered in the market, the character of earnings forecasts and the way in which securities are priced. In building models to study financial markets, assumptions have to be made about the decision making process of investors. In neo-classical finance, decision makers possess Von Neumann-Morgenstern preferences and use Bayesian techniques to make appropriate statistical judgments. Researchers working in the area of behavioral finance have produced evidence that people deviate from the Von Neumann-Morgenstern rationality and Bayesian rules. To reduce the amount of time and effort that is needed for the complex requirements of the decision-making process, people use rules of thumb or heuristics to simplify the decision-making process. However, relying on

17 18 Chapter 2. Review of the literature

heuristics may result in biased decisions ignoring relevant information or processing irrelevant information. In this chapter, we discuss different frameworks from the rational and behavioral school. The aim of this chapter is to give a review of the relevant literature.

2.2 Market efficiency and anomalies

Fama (1970) defines an efficient market as one in which security prices reflect all available information. To make this definition empirically testable, efficient markets are specified in more detail in the efficient market hypothesis. This hypothesis states that none of the trading systems based on only currently available information can earn excess risk-adjusted average returns. If the efficient market hypothesis holds, investors cannot consistently beat the market. This implies that an average investor is better off following a passive strategy where he or she holds the market portfolio, instead of following an active strategy where he or she is wasting money and time by analyzing, picking and trading the ‘right’ securities. Anomalies have been found over the last two decades that challenge the traditional view that securities are rationally priced and that the prices reflect all publicly available information. In the following paragraphs we outline some of the more salient findings in the literature. We first discuss two anomalies that challenge the weak form efficient market hypothesis. The weak-form efficient market hypothesis states that it is impossible to earn superior returns based on the knowledge of past returns and prices. De Bondt and Thaler (1985) give evidence of long-term return reversals. They divide stocks into losers and winners based on three year past returns. The

2.2 Market efficiency and anomalies 19 five year post-formation returns show that losers outperform winners, which cannot be explained with any rational pricing model and is clearly at odds with weak-form efficiency. De Bondt and Thaler explain this by investors overreacting to past information. The second anomaly is the momentum effect. Jegadeesh and Titman (1993) show evidence of short-term trends. Investors, who follow strategies that buy stocks with a good performance and sell stocks with a bad performance over the last three to twelve months, will generate significant positive returns over three to twelve month holding period. They explain these results by investors buying past winners and selling past losers, which causes the prices of stocks move away from their long-run values temporarily. These results are also found for stocks outside the United States. Rouwenhorst (1998) finds short-term momentum in returns in twelve European countries.

The semi-strong form efficient market hypothesis has also faced empirical challenges over the past decades. This hypothesis states that investors cannot earn superior risk-adjusted profits using any publicly available information. Banz (1981) finds that the average returns of small caps are too high given their market beta and that the average returns of large caps are too low. Fama and French (1992) report more recent findings. They classify stocks into deciles based on market capitalization and measure the average return for each decile over the first year after formation. They find that the small caps outperformed the large caps by 0.74% on average per month over the period 1963 to 1990. Those studies demonstrate that small caps earn higher average returns than is predicted by the capital asset pricing model. Evidence on corporate announcement effects also suggests a violation of the semi-strong form efficient market hypothesis. Bernard and Thomas (1989) divide stocks based on the size of the earnings surprise in the most recent earnings announcement into ten different portfolios. They

20 Chapter 2. Review of the literature

analyze the performance of each portfolio during the sixty days after the earnings announcement and find that on average the (tenth) portfolio with good news outperforms the (first) portfolio with bad news by 4%. Bernard (1993) summarizes the studies that analyze the (under)reaction of stock prices to earnings announcements. Stocks with positive earnings surprises earn relatively high returns in the period prior to the earnings announcement and stocks with negative earnings surprises earn relatively low returns. In the post announcement period, stocks with higher earnings surprises also earn higher returns. This is after the portfolios have been formed, which means that the market underreacts to new information and slowly revises the company’s stock price. This bias will be corrected in the following periods. This phenomenon is known as post-announcement drift. Other publicly available variables that predict future returns are, for example, fundamentals scaled by price. An example of a scaled-price ratio is the book-to-market ratio. Companies with high book-to-market ratio are called value stocks. Companies with low book-to-market ratio are called growth stocks. US and international empirical studies show that value stocks generate higher returns than growth stocks, which cannot be explained on the basis of risk differentials using the capital asset pricing model (see table 2.1). Fama and French (1992, 1996) classify stocks into deciles based on the book-to-market ratio and calculate the average return for each decile the year after formation. They find that the average monthly return of value stocks is 1.53% higher than the average monthly return of growth stocks. The difference between the average return between value and growth stocks is called the value premium and cannot be explained with the market beta. Other measures like the price-to-earnings ratio generate similar results; the difference in average returns is 0.68% per month. Lakonishok, Shleifer and Vishny (1994) divide stocks based on the past 5- year sales growth and cash flow-to-price ratio into nine portfolios. The value portfolio (which is the portfolio with the highest cash flow-to-price

2.2 Market efficiency and anomalies 21 ratio and the lowest past growth rate) outperformed the growth portfolio (portfolio with the lowest cash flow-to-price ratio and the highest past growth rate) with an average annual return of 10.7%. These results are also found for stocks outside the United States. Fama and French (1998) provide consistent evidence of the value premium for a broad sample of countries outside the US. In almost every country, the value portfolio generates a higher average return than the growth portfolio. These results hold up across a variety of value-growth determinants. Since the existence of the value premium is an important driver of our research, some major studies regarding this issue have been summarized in table 2.1.

Finally, the last group of anomalies shows that prices deviate from fundamental values and where mispricing can be established beyond any reasonable doubt. Froot and Dabora (1999) study Siamese twin stocks such as Royal Dutch and Shell. These two stocks are traded at different places, but should move together regarding that they have the same cash flow stream. They find that Royal Dutch is more sensitive to movements in the US market while Shell commoves with the UK market. A study by Cooper, Dimitrov and Rau (2001) shows that during the internet hype a corporate name change into dotcom related internet names lead to positive announcement returns on the order of 74% in the ten days surrounding the announcement. Their findings also indicate co-movements in stock prices that are not related to common fundamentals, since in their research also stocks of firms with non-internet related businesses highly benefited from a dotcom name change.

CF/P premium premium Value Value

0.36% per month

1.1%, 0.4% and 0.8% per month 1.53% and 0.68% per month

US:1.06%, Japan: 3.43%, UK: 1.09%, Europe: 1.30% and Global: 1.88% 6.96% per year , reflects the book-to-price ratio, ratio, book-to-price the reflects B/P , E/P , E/P

B/P

B/M CF/P B/M

B/P P/E Variable Variable the of literature 2. Review Chapter reflects the market capitalization. MV

exchange and NASDAQ

Market Market measures the price-to-earnings ratio, P/E 1957-1971 US: NYSE 1973-1984 US: NYSE 1973-1984 US: 1971-1988 stock Japan: Tokyo 1981-1992 International 1981-1992 International measures the dividend-to-price ratio and

D/P

Rosenberg, Reid and Rosenberg, Lanstein (1985)

Chan, Hamao and Lakonishok (1991)

Basu (1977) Basu

Fama Fama and French (1992) 1963-1990 US: NYSE, AMEX Capaul, Rowley and SharpeCapaul, Rowley (1993) 22 evidence for empirical the value premium Table 2.1: Summary determinants: value-growth of variety a shows table The Period

measures the cash flow-to-price ratio,

23 : B/M Based on Based US: 6.8%, Japan: 9.85%, UK: 4.62%, Netherlands: 2.3%. stocks: Small 6.5%, stocks: Large 3.3% per year 4.0% first post formation year 6.3%, 3.9% and 10.7% per year, respectively. , CF/P MV

& and , E/P , E/P D/P B/M and B/M B/M 5-year sales5-year rates growth B/M CF/P

and NASDAQ

and NASDAQ AMEX

1970-1998 US: NYSE, AMEX 1971-1992 US: NYSE, AMEX 1968-1990 US: NYSE and 1975-1995 International International 1975-1995 Chan, Karceski and Lakonishok (2000) 2.2 Market efficiency and anomalies Porta, Shleifer La Lakonishok, and Vishny (1997) French (1998) and Fama [Table 2.1 continued] Shleifer and Lakonishok, (1994)Vishny 24 Chapter 2. Review of the literature

2.3 Asset return models related to market anomalies

In section 2.2, several anomalies are described that cannot be explained by a simple model of risk and return, such as the capital asset pricing model (CAPM). These anomalies may have different explanations. Boudoukh, Richardson and Whitelaw (1994) categorize the explanations into three camps: “loyalists, “revisionists” and “heretics”. “Loyalists” defend the efficiency of stock markets by pointing to data mismeasurement or to market imperfections. “Revisionists” defend the efficient market hypothesis with time-varying risk premiums. The third group, the “heretics”, believes that the market is not rational and that psychological factors influence the pricing of securities. The heretics believe that profitable risk-adjusted trading strategies exist. In our opinion, both the loyalists and revisionists can be grouped together since they both try to defend the efficient market hypothesis. This group can be labeled as rationalists and Heretics can be called the behavioralists.

2.3.1 Rationalists

The rationalists believe that the superior performance of investment strategies, for example the difference in performance between losers versus winners and value versus growth stocks, are not an anomaly. They assume that the efficient market hypothesis holds, and that stock returns cannot be predicted. Rationalists give two explanations for the cross-sectional differences in returns. The first explanation is that superior returns are a result by chance, which cannot be found outside the sample. Researchers who support this thought are for example Black (1993) and MacKinley (1995). A second explanation is that the superior returns are a result of

2.3 Asset return models related to market anomalies 25 exposure to a common risk factor that is initially ignored in analyzing the returns of stocks. Higher average returns are a result of higher risks. Researchers who support this view are Fama and French (1993) with their three-factor model, the time-varying risk model of Berk, Green and Naik (1999) and the model of Zhang (2000). In section 2.4, we describe three rational models that explain the cross-sectional differences in returns from a rational point of view.

2.3.2 Behavioralists

Behavioralists have suggested alternative explanations for stock market anomalies. They study the observed behavior of investors and focus in particular on those elements that deviate from rational behavior. A field of finance that proposes psychology-based theories to explain stock market anomalies is behavioral finance. Shleifer and Summers (1990) suggest that behavioral finance rests on two foundations. The first foundation is investor sentiment. Investors deviate from the maxims of economic rationality. This implies irrationalities in investors’ behavior by forming beliefs, and in their preferences, or in how they make decisions, given their beliefs. This may lead to deviations between security prices and their fundamental values. Investor sentiment is an important fundament for behavioral finance. The second foundation is limited arbitrage, which explains why inefficiencies in markets remain after the market is disrupted by irrational investors (indicated as noise traders). With unlimited arbitrage markets remain efficient even when some investors are irrational. The arbitrageurs will digest the large demand shocks by noise traders and markets will become efficient again. Arbitrage is limited and the reason is that arbitrage is risky. Many securities do not have perfect substitutes, and if they have, the prices do not necessarily converge directly to their fundamental values

26 Chapter 2. Review of the literature because of the existence of “noise trader risks” (De Long et al., 1990, Shleifer and Vishny, 1997). Shleifer (2000) categorizes the deviations of investors (investor sentiment) from the standard decision-making model in three broad classes: non-Bayesian expectation formation, attitudes towards risk, and sensitivity of decision making to the framing of problems. The first class concentrates on beliefs or the way in which people process information. By predicting uncertain outcomes, investors show behavior different from Bayesian rationality. Instead, investors rely on a limited number of heuristics to assess probabilities and to evaluate sample outcomes. The heuristics may result in good decisions, but sometimes may lead to biased decisions caused by ignoring relevant information and/or processing irrelevant information. Tversky and Kahneman (1974) identify three heuristics that affect probability assessments and the evaluation of sample outcomes: representativeness, availability, anchoring and adjustment. In the next paragraphs the three heuristics are described, followed by some other sources of biases that influence the assessment of outcomes as well.

1. Representativeness suggests that people evaluate the probability of an event by the degree to which the event reflects similarities with comparable ‘known’ events. Thus when something looks the same they think that the probability of the event is also the same. This leads to errors because representativeness or similarity is influenced by other factors than that should affect the judgment of probabilities. An example is the sample size neglect (Kahneman and Tversky (1974)), which means that people fail to take the size of the sample into account. People will find the characteristics of a short sequence equally informative as the characteristics of a sequence generated by a random process. Thus they expect that the characteristics of the process that will be

2.3 Asset return models related to market anomalies 27

represented, will not only be found in the entire sequence (global level), but also locally in small parts of the entire sequence. Another example is the base rate neglect, which means that people put to much weight on salient features and to little weight on the base rate probability. For example, if a detailed description about someone’s personality matches up with the subject’s experiences with people of a particular profession, the subject tends to overestimate the actual probability that the given individual belongs to that profession. 2. The availability heuristic generates biases that arise because people base the probability of an event on the ease with which instances or occurrences can be brought to mind. The ability to recall instances or occurrences depends also on the actual frequency, familiarity, salience, recency, imaginability and prominence of the occurrences. Events that are familiar, salient, recent, easy to imagine or prominent are judged as more frequently-occurring than events that do not have these qualities. 3. The anchoring and adjustment heuristic describes that biases arise, because people make estimates from an initial starting point (anchor) and adjust insufficiently to the final value. For example, in the absence of any solid information, past earnings are likely to act as anchors for making an earnings forecast for next year. In predicting next year’s earnings it is easy to take last year’s earnings and adding two percent to the number allowing for the circumstances of the present case. Anchoring and adjustment contains conservatism in updating, “the adjustment”, in addition to the incorrect priors generated through the choice of the anchor. Conservatism implies that people fail to revise their beliefs in the face of new information to the same extent as Bayes’ theorem (Edwards (1968)). 4. Other biases that influence asset pricing are generated by overconfidence (self-attribution), optimism and cognitive dissonance. Overconfidence and optimism are two psychological errors that often

28 Chapter 2. Review of the literature

occur simultaneously. People have a tendency to be overconfident about the precision of their knowledge. Odean (1998) shows that the degree of overconfidence varies among professions. It is strongest in professions that can easily shift the blame for mistakes on others or unforeseen circumstances. Overconfidence stems from two biases; the illusion of control and self-attribution. Illusion of control implies that people believe to be in control of a situation far more often than they really are. Self-attribution means that people attribute good outcomes to good personal skills and bad outcomes to bad luck. Optimism implies that people display unrealistic views of their prospects and abilities. For example, the planning fallacy (Buehler, Griffin and Ross, 1994): people consistently underestimate the time they need to complete tasks. The combination of overconfidence and optimism leads investors to overestimate their knowledge, understate risk and overstate their ability to control the situation. People want to reduce cognitive dissonance in order to avoid mental inconsistencies. Therefore they ignore information that suggests that they have made the wrong decisions and search for information that supports their decisions. Furthermore they surround themselves with people that made the same decisions or have the same opinions.

The second class described by Shleifer (2000) deals with the evaluation of financial and non-financial outcomes and in particular the risk attitudes of decision makers. An important ingredient of any model trying to explain asset prices or trading behavior is the assumption about investors’ risk preferences. Finance theory is generally based on the expected utility model. This model assumes that investors’ preferences satisfy Von Neumann and Morgenstern (1947) rationality. Von Neumann-Morgenstern rationality implies that investors assess gambles at the level of total wealth.

2.3 Asset return models related to market anomalies 29

Kahneman and Tversky (1979) show with their prospect theory that investors look at gains and losses relative to some reference point. The reference point may change with the situation and is determined by the subjective perceptions and feelings of the individual. Another important feature is the S-shape of the utility function (in Kahneman and Tversky’s terminology: value function), which is convex below the reference point and concave above. This means that the marginal utility of both losses and gains generally decreases with their magnitude and individuals are risk seeking with losses and risk averse with gains.In addition, the utility function is steeper for losses than for gains, what means that the response of individuals to losses is more extreme than the response to gains. This is called loss aversion. The final feature of the prospect theory is that this theory treats preferences as a function of decision weights and assumes that these weights do not always correspond with probabilities. Specifically, prospect theory states that decision weights tend to overweight small probabilities and underweight moderate and high probabilities. The overweighting of small probabilities can give rise to risk seeking in choices involving sure losses and to risk aversion in choices involving sure gains. Kahneman and Tversky (1979) label the phenomenon where people place more weight on outcomes that are certain relative to outcomes that are merely probable, as the ‘certainty effect’.

Finally, the last class of Shleifer (2000) describes that individuals use framing to make decisions. The form that is used to describe a decision problem is called a frame. Framing refers to the way that a problem is presented to the decision maker. In traditional finance, framing is transparent and the form of decision information is irrelevant for the decision process: only into substance is relevant. Earlier in this section, we saw how the prospect theory could explain why people make different

30 Chapter 2. Review of the literature

decisions in situations with identical final wealth levels. According to the prospect theory, decision problems are analyzed by framing different outcomes. Kahneman and Tversky (1979) show that when people have to deal with choices in the face of risk and uncertainty, frame dependence is important. People tend to make different choices when problems are represented in different frames. For example, if a decision is framed in terms of losses, people tend to choose riskier outcomes whereas the same decision is framed in terms of gains people tend to avoid risks and choose the more certain outcome. In addition, choices are also made based on norms, habits and expectancies of the decision maker.

In summary, behavioralists study the observed behavior of investors and focus in particular on those elements that deviate from rational behavior. According to market efficiency not all participants are required to be rational. Only a small number is required to be rational, and they will drive the rest out of the market. Behavioralists argue that arbitrageurs (rational investors) cannot correct for the mistakes made by the irrational investors, because arbitrage is risky and therefore limited. This leads securities to be priced incorrectly subject to investor sentiments, which result in market inefficiencies (see list of anomalies described in section 2.2).

2.4 Rational models

Models such as CAPM cannot explain the previously discussed anomalies. As a consequence, several rational models have been developed in the last decade to explain these anomalies. In this section, we present three different rational models that are relevant for the following chapters, because they try to explain some of the most common anomalies (e.g. value premium) from a rational point of view. Both the three factor model of Fama and French

2.4 Rational models 31

(1993) and the time-varying risk model of Berk, Green and Naik (1999) provide rational explanations for size and the book-to-market ratio in determining differences in stock returns. Fama and French create an empirical three-factor model where size and book-to-market ratio are systematic risk factors. Berk, Green and Naik create a time-varying risk model where size, book-to-market ratio and the number of growth options explain stock returns. The multi-period model of Zhang (2000) shows close resemblance with the time-varying risk model of Berk, Green and Naik by using real options. This model is not only based on the number of growth options but also takes the option to abandon into account.

2.4.1 Three-factor model

The three-factor model of Fama and French (1993) explains the expected excess return on a stock or portfolio with the sensitivity of its return to three factors. The factors are the excess return of the market portfolio, the difference between the returns on portfolios of small and large stocks (SMB), and the difference between the returns on portfolios of high and low book-to-market ratio stocks (HML). The expected excess return of portfolio i is:

E(Ri )()− R f = bi [E RM − R f ]+ si E(SMB)+ hi E(HML), (2.1)

where E(RM)-Rf, E(SMB) and E(HML) are excess factor returns and the factor sensitivities bi, si and hi are the slopes obtained from a time-series regression of excess stock returns on excess factor returns,

Ri − R f = ai + bi (RM − R f )+ si SMB + hi HML + ε i , (2.2)

32 Chapter 2. Review of the literature

Fama and French (1993) interpret the market, size and book-to-market equity as risk measures. These factors represent sources of systematic risk, which means that risk requires compensation in the form of higher expected returns. Fama and French (1993) interpret the risks captured by the book-to- market ratio of equity and size as proxies for distress. Following the economic interpretation of Chan and Chen (1991), distressed firms are defined as firms which are less efficiently run, have higher financial leverage and have lower accessibility to external funds. This leads to prices to be more sensitive to changes in the economy. Distressed firms are less likely to survive unfavorable economic conditions and are therefore riskier than other firms. Because distressed firms are riskier, the cost of capital is higher, which leads to higher expected returns. For example, firms with poor past earnings and high financial leverage (high loadings on SMB and HML) may have restrictive accessibility to external funding. This leads to cash flow problems. In times when economic conditions are poor, these firms are more likely to get into financial difficulty. To explain the book-to-market ratio of equity in terms of risk Fama and French (1992) use two financial leverage measures, a measure of market leverage, A/ME, and a measure of book leverage, A/BE (where A is the book value of assets, BE is the book value of equity and ME is the market capitalization). Fama and French calculate both measures for the US stock market over the period 1963 to 1992. They show that both measures are statistically significant and close in absolute value, but with opposite signs. Both measures of leverage explain expected returns and the sum of the log of both measures, e.g. A/ME and A/BE, is expressed as the book-to- market ratio of equity, BE/ME. Weak firms with low earnings have high book-to-market ratios of equity and tend to have positive slopes on HML. Strong firms with high earnings have low book-to-market ratios of equity and negative slopes on HML.

2.4 Rational models 33

One general feature of the three-factor model is that factor loadings (estimated slope coefficients) and not firm characteristics (size and BE/ME) determine average returns. Fama and French (1993) explain this with two empirical facts: first, high book-to-market stocks and small size stocks have high returns; second, within each portfolio (e.g. high book-to-market and small size), stocks covary with each other. Fama and French argue that these two findings occur because the book-to-market ratio and size proxy for financial distress, which lead to a risk premium. Daniel and Titman (1997) question whether stock returns are driven by risk based elements (factor loadings) or by firm characteristics. They cast doubt on the prediction that value stocks earn higher returns because such stocks have higher loadings on the book-to-market factor and not because they have high book-to-market ratios. They perform double sorts of stocks on both loadings on book-to-market and book-to-market ratios, and show that stocks with different loadings but the same book-to-market ratio do not differ in average returns. Lally (2004) argues that the sensitivity coefficients in the Fama and French model must be related to the firm’s leverage as proposed by Modigliani and Miller (1958,1963). He shows that the empirical formulas developed by Fama and French (1997) to show the cost of equity through time, are inconsistent with the Modigliani and Miller propositions since they do not separate leverage from other factors that influence sensitivity coefficients. Another shortcoming of the three-factor model is that it cannot explain momentum returns in the short run as documented by Jegadeesh and Titman (1993). Carhart (1997) adds a fourth factor, momentum, to the three-factor model. He sorts mutual funds into decile portfolios on one-year past returns and shows that the momentum factor and size factor can account for most of the variation in returns. The final comment on the Fama-French model is that the three- factor model defines value and growth stocks with the book-to-market ratio

34 Chapter 2. Review of the literature

(i.e. high and low book-to-market ratios). However, value and growth stocks can be defined with a variety of value-growth determinants (e.g. cash flow-to-price, earnings-to-price). However, Fama and French (1996) show that the three-factor model also captures the returns of portfolios formed on cash flow-to-price (CF/P) and earnings-to-price (E/P). Firms with low CF/P and E/P ratios have similar slopes as low BE/ME ratio stocks (negative loadings on HML), which mean low expected returns. Firms with high CF/P and E/P have similar slopes as high BE/ME ratios stocks (positive slopes on HML), which implies high expected returns.

2.4.2 Model with growth options

Berk, Green and Naik (1999) develop a model in which the valuation of cash flows and the firm’s options to growth in the future leads to dynamically conditional expected returns. The changes in risk are related to investment opportunities. Firms that perform well tend to be firms that have exploited valuable investment opportunities. The value of the firm is based on assets in place that generate current cash flows and on options to make positive net present value investments in the future. Each period existing assets may die off and new investment opportunities may arise. If a firm exploits those opportunities, the firm’s systematic risk will change. For example, if a firm decides to invest in a low risk investment opportunity, its value will increase and the systematic risk will decrease. Because the systematic risk decreases over that period, the returns will also be lower on average. On the other hand, when the firm loses a low-risk asset, the systematic risk will increase, resulting in higher returns on average. The central issue in the Berk, Green and Naik-model is the distinction between two kinds of assets: assets in place and assets that embody future

2.4 Rational models 35

growth opportunities with positive net present values. The value of the firm is:

t * P()t = ∑V j ()t χ j ()t +V ()t , (2.3) j=0

where P(t) is the value of the firm at time t. The first term expresses the

value of future cash flows of assets in place, where χ j (t) = 0 if the project has expired and χ j (t) = 1if project j is still in operation. The second term presents the current value of future investment opportunities. Equation 2.3 can be expressed in terms of risk-adjusted discounted future cash flows of assets in place and cash flows from future investment opportunities:

P()t = b ()t eC−β ()t D[r(t)]+ IeC J * [r(t)], (2.4)

where b(t) is the book value of assets that are currently alive, C is the parameter that controls the mean of the cash flows, β(t) the systematic risk of a projects cash flows, D is the value of a perpetual, riskless consol bond, r(t) is the one-period riskless, continuously compounded interest rate, I is the investment required to undertake a new project and J* is the value of growth opportunities. The growth opportunities are in terms of European call options on pure discount bonds maturing at different dates. In this model the expected return depends on the life cycle of the firm. Mature firms have different expected returns than developing growth firms. If there are no ongoing projects, the value of the firm will only consist of growth opportunities. In this case the value of the firm depends only on the interest rate and not on systematic risk (this is in line with the Black and Scholes option pricing model). If the number of ongoing projects goes to

36 Chapter 2. Review of the literature

infinity, the growth component will become negligible. Then the expected return depends on systematic risk and interest rates. This means that changes in the systematic risk component are more important for mature firms and less important for growth firms. The firm’s expected return can be derived from equation 2.4 and is given by the following equation:

πD r t  b t   πD r t  1  e ( ( )) C ( ) C * * e ( ( )) , (2.5) Et ()1+ Rt+1 = +πe   + Ie J e []r()t − J []r()t   D ()r()t P()t   D ()r()t P()t 

where De is the expected value of a perpetual, riskless consol bond. The first term of this equation reflects the effects of changing interest rates on the value of the cash flows produced by the assets in place. The consequence of higher interest rates is that future cash flows will be discounted at a higher rate, which leads to lower prices and to higher expected returns. Furthermore, higher interest rates also affect the current expectations about future values of systematic risk. In general, when the interest rate is high, a firm will undertake fewer projects. As a consequence firms will only accept projects with low systematic risk. The second term is a proxy for the book-to-price ratio. The term πeC reflects the project’s expected cash flows which depreciate at rate π. Since, πeC is a positive constant, the firm’s expected return is positively correlated with the book-to-price ratio. Book-to-price ratio varies with changes in the systematic risk of the firm. The systematic risk of the firm changes, because each period existing cash flows can die off and new projects arrive. For example, when a firm adopts a new project with positive net present value that has low systematic risk, the firm creates value and lowers the average systematic risk of its cash flows in the next periods. From equation 2.4 it follows that if systematic risk decreases the current price will increase. Assuming that the expected cash flows are constant, a

2.4 Rational models 37

current price increase will result in lower expected returns in the future. This is consistent with classical finance where a positive relationship between systematic risk and expected returns exists. In addition, systematic risk changes with the fraction of existing assets relative to growth options, because systematic risk plays an important role in determining expected returns of mature firms, but is less important for growth firms (see explanation of equation 2.4). The last term in the equation represents the value of the growth options. This is the difference between the expected value of bond options * * J e []r()t and the current value of bond options J [r(t)] (accumulated at the risk-free rate) divided by its price. The value of the growth options depends on changes in the interest rate. Changes in the interest rate lead to changes in the value of the underlying assets. Because the risk premium of an option depends on the value of the underlying assets (out-of-the money options have higher risk premia than in-the-money options), the value of the growth options also changes with changes in the interest rates. Because of the changes in the value of the options the expected returns can change even if the assets in place of the firm remain unchanged. In a number of simulation experiments Berk et al. show that expected returns explain the important features of the cross-sectional and time series behavior of stock returns that is found in empirical research (e.g. explanatory power of book-to-market ratio, size and the momentum versus contrarian effects at different horizons). They compose an equally-weighted portfolio from simulated stock returns and run time-series regressions of the equally-weighted portfolio against the market beta, log of market value and log of book-to-market ratio. The results of the regressions show almost similar results in magnitude and direction as obtained by Fama and French (1992). Only when the market beta and market value are combined in one

38 Chapter 2. Review of the literature

regression, the model shows different signs than the results of Fama and French show. Berk et al. also test the profitability of momentum and contrarian strategies. The model reproduces the patterns of contrarian returns at shorter horizons and momentum returns at intermediate horizons. A shortcoming of the model is that it predicts excess returns at longer horizons than empirically has been shown. This model predicts that the contrarian strategy is profitable at a horizon of twelve months or less, where Conrad and Kaul (1998) show empirically that contrarian strategies are only profitable at horizons of about three months or less. Furthermore, this model predicts the maximum profitability of momentum strategies is approximately at sixty months, while Jegadeesh and Titman (1993) show that momentum strategies reaches the maximum of profitability at horizons of about nine to twelve months. The difference between this model and three-factor model is that expected returns are not only explained by size and leverage alone, but also by growth options. This model shows that two firms with identical book-to-market ratio’s and different growth potential can have different expected returns. For example, when a firm has no growth potential and its value depends only on the existing assets, the last term of equation 2.5 drops out and expected returns depend only on the book-to-market ratio. This brings the book-to-market ratio in a different perspective, because the book-to-market ratio is generally used as measure for growth potential. Daniel and Titman (2001) support empirically that only size and leverage cannot explain expected returns.

2.4.3 Model with options to expand and to discontinue operations

In section 2.4.1, we discussed the three-factor model where size and the book-to-market ratio are systematic risk factors. The model of Berk et al.

2.4 Rational models 39

(1999) (section 2.4.2) added growth options to this model. In addition to the model of Berk et al., Zhang’s (2000) model allows firms not only to make rational choices to expand their operations when it is sufficiently profitable, but also to discontinue when it is sufficiently unprofitable. Zhang’s model allows firms to make rational choices among investment or divestment alternatives (in terms of real options) whereby accounting signals are used to guide investment decisions. In addition, Zhang’s model shows equity value as a nonlinear function of accounting variables, while the model of Berk et al. shows the equity value as a nonlinear stochastic process. The options to expand and to discontinue operations are determined by profitability and growth opportunities. It is a multi-period model where the valuation is based on three scenarios.

1 E Vt = xt + Pd ()qt ast + Ce ()qt G , (2.6) R f −1

E where Rf equals one plus the risk free rate of return, xt is the net value

creation (or economic earnings), ast is the bookvalue of assets in place,

Pd(.) is the put option to discontinue the operations, Ce(.) the call option to expand the operations and G represents the growth potential. The first term in equation 2.6 shows the equity value if the firm operates at the same scale

as the year before. The cash investment required at time t+1 is cit+1=(1-γ)ast (where γ represents the durability of the assets). The decisions whether to

discontinue or to expand depend on future profitability, qt. The option to abandon (second term in equation (2.6)) becomes in-the-money if the profitability to discontinue operations (qd) are higher than the profitability

to continue operations ( qt+1 < qd ≡ (1− γcd )(R f −1). If the firm decides to discontinue operations, the value of the firm will depend on the assets in

place and will be equal to (1-cd)ast, where cd is the cost to discontinue. The option to expand (third term in equation 2.6) becomes in-the-money if the

40 Chapter 2. Review of the literature

profitability to expand operations (qe) is higher than the profitability to

continue operations at the same scale ( qt+1 > qe ≡ R f −1). Figure 2.1 visualizes the impact of profitability on the value of the firm. Under a specific level of qt+1 the put option becomes in the money which means that the value to discontinue is higher than the value to

continue at the same scale (qt+1>qd).

Figure 2.1: Value of the firm according to model of Zhang (2000)

decreasing constant expand scale scale scale ) t Value of (V firm of the Value

qt+1qe Profitability (qt+1)

= value of the firm without options = option to expand = option to discontinue

Above a specific level of qt+1 the call option becomes in the money which means that the value to expand is higher than the value to continue at the

same scale as before (qt+1>qe). In order for the firm to rationally continue at

2.4 Rational models 41

its existing scale, profitability (qt) will have to be above the profitability to

discontinue and below the profitability to expand ( qd ≤ qt ≤ qe ).

In this model investment decisions underlie value creation. Equity value is nonlinear in economic earnings and book value of assets in place. The model predicts that equity value is increasing with economic earnings for any level of book value of assets. In addition, for any level of economic earnings equity value is increasing with book value of assets for low profitable firms, equity value is insensitive for steady state firms, and equity value is decreasing with book value of assets for growth firms. The importance of book value of assets and economic earnings varies with profitability and growth potential. For low profitable firms, book value of assets is expected to dominate economic earnings, while for steady-state firms, economic earnings are predicted to dominate book value of assets. For growth firms, economic earnings and book value of assets are both important, and the impact of book value of assets increases with the magnitude of the growth potential. The model predicts that the impact of profitability and earnings growth rates on price-to-book is as follows: if profitability or growth opportunities are increasing, P/B increases. This implies that growth stocks are associated with high growth opportunities and high profitability and value stocks with low growth opportunities and low profitability. This is also shown by empirical studies, i.e. Lakonishok et al. (1994), which show that value stocks are stocks with low earnings growth rates and growth stocks are stocks with high earnings growth rates. This model introduces an additional feature to the model by Berk et al. (1999). It has not only an option to expand but also an option to discontinue operations. Zhang’s model shows that two firms with equal assets in place and equal growth potential can have different expected returns. For example, when a firm has no growth potential the last term of

42 Chapter 2. Review of the literature

equation 2.6 drops out and the firm depends only on the existing assets and the option to abandon. The main issue that merits discussion is whether the model of Zhang is able to explain anomalies such as the value premium and momentum in the short run. Chen and Zhang (2004) derive the return function from equation 2.6 and empirically test whether the model is able to explain the value premium. The return function shows that returns are explained by three factors, notably profitability-related information, capital investment and the change in growth opportunity. Chen and Zhang divide stocks into book-to-market deciles and perform regressions of each portfolio return against these three factors. They show that the difference in intercepts is of the same magnitude as the book-to-market effect found by Fama and French (1992). This implies that the book-to-market effect (value premium) is not subsumed by the model of Zhang.

In section 2.4, we have discussed three different rational models. The first two models try to explain market anomalies. The last model by Zhang is related to the model of Berk et al. in the way that he uses options to expand. In addition, Zhang adds options to abandon to the model. The first two models show that they are able to explain the value premium. Although the model by Zhang shows the relation between firm value and book-to-market ratio, it is not able to explain the value premium. The main issue in all of the three rational models is whether the models are able to explain anomalies such as the profitability of momentum strategies in the short run and contrarian strategies in the long run as is reported by empirical studies. In the next section, we present three behavioral models that are able to explain these two anomalies.

2.5 Behavioral models 43

2.5 Behavioral models

With the growing number of empirical papers supporting the anomalies, behavioral models have been developed to translate the empirical evidence into theoretical frameworks. The majority of these models describe the interaction between informed versus uninformed investors and rational versus irrational investors. This section presents three behavioral models, which focus on investors’ sentiment explicitly. These models try to explain how judgement biases of investors can produce overreaction to some events and underreaction to others. The models are based on two heuristics and two other sources of biases that influence the assessment of outcomes; representativeness, and anchoring and adjustment (conservatism), overconfidence and self-attribution bias. The general assumption in these models is that investors allocate funds based on past performance.

2.5.1 A model of investor sentiment

Barberis, Shleifer and Vishny (1998) construct a model of investor sentiment to reconcile the empirical findings of over- and underreaction with mental heuristics of investors. The overreaction evidence shows that over longer horizons security prices overreact to consistent patterns of new information pointing in the same direction. Securities with a long record of positive information tend to be overpriced. The underreaction evidence shows that new public information has a limited effect on prices. If there is a record of good information, prices keep trending up after the initial positive reaction. If there is a record of bad information, prices keep trending down after the initial negative reaction.

44 Chapter 2. Review of the literature

The model relates to two heuristics from the cognitive psychology to express under- and overreaction of new information, notably conservatism of Edwards (1968) and representativeness of Kahneman and Tversky (1974). Conservatism is a substitute for the anchoring and adjustment heuristic and means that investors slowly adjust their forecasts to new information (see section 2.2.1). Investors have prior views about a stock in question. When new information is revealed which is inconsistent with prior beliefs, investors adjust their expectations in the right direction, but by a smaller magnitude than the true normative rational Bayesian value. This implies an overweighing of the statistical base rate (probabilistic) information relative to the new statistical evidence. Because investors tend to stick to their prior beliefs, security prices are not adjusted sufficiently which results in underreaction of prices to earnings announcements. This can result in both positive and negative serial correlation in stock returns at short horizons. Overreaction is related to the representativeness heuristic where the recently perceived pattern is taken as representative for a persisting future pattern. For example, when a company has a consistent history of earnings growth over several years, investors may conclude that the past earnings growth history is representative for future growth potential. While, earnings growth may be nothing more than a random process, investors believe that the company belongs to a small distinctive population with high future growth potential. In overweighing past growth of the company, investors underweigh the statistical base rate (probabilistic) evidence of the small fraction of the population belonging to that high growth potential group. As a consequence investors tend to disregard the reality that a history of high earnings growth is unlikely to repeat itself. Therefore, investors overvalue the company and become disappointed when future information is revealed. This leads to overreaction in the long run. The model consists of a representative, risk-neutral investor with a constant discount rate. There is only one security, which pays out all

2.5 Behavioral models 45 earnings as dividends. This means that the equilibrium price is the net present value of the future earnings as forecasted by the investor. In addition, prices reflect only the information that is contained in earnings. True earnings follow a random walk. The model represents an investor who does not realize that earnings follow a random walk. This investor believes in a world with two states, and for each state a different regime. In regime 1 earnings are mean-reverting and in regime 2 earnings are trending.

Regime 1: Regime 2: 1 yt+1 = y yt+1 = −y yt+1 = y yt+1 = −y

yt = y π L 1− π L yt = y π H 1− π H

yt = − y 1− π L π L yt = − y 1− π H π H

In these matrices, π L is small, between 0 and 0.5, and π H is large, between 0.5 and 1. This implies that under regime 1 a positive shock is more likely to be reversed and under regime 2 a positive shock is more likely to be followed by another positive shock. Underreaction is caused if the investor puts more weight to regime 1 than to regime 2. In that case, when there is a positive earnings-shock the investor believes that earnings are mean- reverting in the next period. However, the positive earnings-shock is equally likely to be followed by a positive as a negative shock. Overreaction is caused if the investor puts more weight on regime 2 than regime 1. The investor believes that after a positive earnings-shock the chance of a new positive earnings-shock is higher than the chance of a negative earnings- shock. However, the investor does not realize that earnings follow a random walk and that the chance of positive or negative earnings surprises is equal.

1 Where yt is the shock to earnings at time t, which can take two values, +y and -y

46 Chapter 2. Review of the literature

A Markov model is used to specify the underlying regime switching process. The current regime depends on what the regime was perceived to be prevailing last period. To value the security the investor has to forecast future earnings and uses the regime-switching model.

st+1 = 1 st+1 = 2

st = 1 1− λ1 λ1 λ 1− λ st = 2 2 2

If st = 1 , the model is in the first regime, where the earnings shock is perceived to be generated by regime 1. If st = 2 , the model is in the second regime, where the earnings shock is generated by regime 2. The parameters

λ1 and λ2 are the transition probabilities from one state to the other state.

The parameters, λ1 and λ2 , are small which means that transitions from one state to another state in the investor’s perception, the likelihood of regime switching is not high. Furthermore, λ1 is smaller thanλ2 , which implies that the investor believes that the occurrence of regime 1 is more likely than regime 2. The investor who forecasts earnings for the next period has to decide which regime is currently governing the earnings pattern. He observes the past series of earnings to decide which regime is generating earnings in the next period. If he has decided, he will use the transition probabilities to forecast the earnings change in the next period. The transition probabilities do not change in the investor’s mind. Even after a long stream of earnings data he does not change the probabilities to a more random walk like model. At time t, he observes yt and calculates qt

( qt = Pr()st = 1| yt , yt−1 ,qt−1 ), which is the probability that yt is generated by model 1. The updating of qt+1 from qt probability is based on Bayes Rule.

2.5 Behavioral models 47

The model shows that if earnings shocks, yt+1 , have the same sign in period t+1 as period t, the probability, qt+1 , decreases. If earnings shocks have the opposite sign in period t+1 compared to period t the probability qt+1 increases. The price of the security in this regime-switching model is:

N P = t + y ()p − p q , (2.7) t δ t 1 2 t

where p1 and p2 are constants that depend onπ H ,π L , λ1 and λ2 . The first N term in the equation, t , is the stock’s fundamental value, i.e. the price that δ would obtain if the investor used the “true” random walk process to forecast earnings changes. The second term, yt (p1 − p2 qt ), is the sentiment indicator which causes the price to deviate from its fundamental value. If on average there is underreaction, the stock price does not react sufficiently to the earnings shock, leading to a price beneath or above its fundamental value (depending on the nature of the earnings shock). Suppose the earnings shock is positive, the sentiment indicator will have to be negative resulting in a low value for p1 relative to p2qt. If there is overreaction, the price is above (below) its fundamental value, which means that sentiment indicator will have to be positive (negative) resulting in a high (low) value of p1 compared to p2qt. The focus in this model is on learning about the time-series process of earnings shocks. Simulation results show that with an input of a random pattern of earnings changes, an output of a non-random pattern of stock returns is generated. This non-random pattern of returns, e.g. under- and overreaction pattern, is caused by two heuristics: representativeness and conservatism. Barberis et al. simulate for a large number of firms earnings,

48 Chapter 2. Review of the literature returns and prices. Then they form two portfolios on positive and negative earnings changes and calculate the difference in returns between the two portfolios in the year after formation. The differences in returns of the portfolios show post-earnings announcement drift and long-term reversals. In addition, they form portfolios on past performance in returns and on earnings-to-price ratios. They find momentum in the short run and cross- sectional forecasting power for scaled-price ratios. Because this model assumes that a trend arises after a string of similar changes, the model neglects to explain the price drift after isolated information events (examined by event studies) such as a dividend cut, stock splits and stock issues. To explain such findings, it would be useful to extend the model with other kinds of news. In addition, it will be interesting to examine the effect of adding risk-averse arbitrageurs to the model. When arbitrageurs know the regime and the movements of noise traders, they can take advantage of the misperceptions. Because arbitrage is risky here, inefficiency will not be eliminated completely. This raises the following interesting question; to what extent can arbitrageurs bring the price closer to the fundamental value? In addition, although the selected heuristics, representativeness and conservatism, are very plausible, they are not the only behavioral biases that can explain over- and underreaction. The next model uses other biases, cf. section 2.3.1, that can explain over- and underreaction.

2.5.2 Investor psychology and security market over- and underreaction

Daniel, Hirshleifer and Subramanyam (1998) provide a model that explains short-term momentum and long-term reversals, which is different from the approach of Barberis, Shleifer and Vishny (1998). The model by Daniel et

2.5 Behavioral models 49 al. emphasizes the roles of overconfidence and the self-attribution bias in the way investors react to private and public information. Overconfident investors are defined as investors who think that they are more able to value securities than they actually are, resulting in forecasting errors. The self- attribution bias determines the degree of overconfidence endogenously. When an investor receives a private signal, and a subsequent public signal is in agreement with initial private information, investors become even more confident. If the public signal contradicts with the initial private signal, overconfidence will fall, but not proportionally. This model describes two phases, the overreaction phase and the correction phase. The overreaction phase is the part of the impulse response prior to the peak and the correction phase is the time after the peak. In this model agents are divided into two groups. The first group represents uniformed, risk averse investors and the second group represents informed, risk neutral investors. We present the dynamic confidence model where a sequence of dates are described. At date 0 individuals begin with their endowments and identical prior beliefs, and trade solely for optimal risk-transfer purposes. At date 1 the overreaction phase starts. The informed investors receive a noisy private signal about the underlying security value and trade with the uniformed investors. The private signal is:

s1 = θ + ε , (2.8)

2 where ε is normally distributed with varianceσ ε , which is independent of the signal for the terminal value of the risky security, θ . Overconfidence in the private signal causes the price to overreact to this new information at date 1.The implication for the price at date 1 is:

50 Chapter 2. Review of the literature

2 σ θ P1 = EC []θ | θ + ε = 2 2 ()θ + ε , (2.9) σ θ + σ C

2 where Ec is the expectation of the informed traders’ confident beliefs, σ θ is

2 the variance of the risky security, and σ C reflects the investors’ assessment

2 2 of noise variance (σ C <σ ε ). At time 2, the noisy public signal arrives.

s2 = θ + ε * (2.10)

If the public signal at date 2 disconfirms the private signal, sign ()θ + ε ≠ sign(s2 ) , then confidence decreases by little or remains constant. Because the signal is uninformative, the price does not move at time 2. However, if the public signal at date 2 has the same sign, sign ()θ + ε = sign(s2 ) , and therefore confirms his trade, the investor becomes more confident. The new price, calculated using the new level of assessed variance of ε, at date 2 is:

2 σ θ P2C = EC []θ | θ + ε, s2 = 2 2 ()θ + ε , (2.11) σ θ + σ C + k where k determines the level of assessed noise variance. Because of the increase in investors’ confidence, the investors’ assessment of the noise 2 2 variance decreases to σ C -k (0 < k < σ C ). The continuing overreaction leads to positive autocorrelation during the initial overreaction phase (cov(P2-

P1,P1-P0)>0). The overreaction of dates 1 and 2 must be reversed in the long run. In the correction phase, starting at date 3, the following public signal will be revealed:

2.5 Behavioral models 51

s3 = θ +η , (2.12)

2 where η is normally distributed with varianceσ p , which is independent of the risky security,θ . For simplicity, the second public signal does not cause overconfidence to be affected. Eventually, as more information is released and the public information becomes precise enough, the price will move to the full-information value θ. This process causes positive autocorrelation during the correction phase (cov(P3-P2,P4-P3)>0). Overreaction to private information and the underreaction to public information tend to produce short-term momentum in stock returns. Long-term reversals are the result of public information, which starts to dominate private information. To explain the post-event abnormal price trends with the same sign as the average event-based return, two kinds of public events, non-selective and selective events, are distinguished. The non-selective event occurs with independence of the mispricing at date 2. The events can be characterized as news disclosed by outside sources, such as regularity events. The selective event at date 3 is an event whose occurrence depends on the mispricing at date 2. These events can be characterized as corporate events. For example, if a manager beliefs that the price of the security is undervalued, he will announce to repurchase shares. The public signal causes an intermediate price reaction that absorbs a fraction of the mispricing. This leads to the prediction of momentum for selective public events (although this is important for the model were confidence is constant, the dynamic confidence model shows that non-selective events can cause momentum). The magnitude of the mispricing (e.g. price/fundamental ratio) is positively correlated with the expected size and the probability of the selective event. For example, equity issues will tend to occur when price/fundamental ratios

52 Chapter 2. Review of the literature are high, because managers want to exploit the mispricing. When securities are underpriced, the probability of good-news selective events will increase.

A key difference with the model of Barberis et al. (1998) (section 2.5.1) concerns the basis of over- and underreaction. The model of Barberis et al. (1998) explains the drift in prices as a result of underreaction to new information. The model by Daniel et al. is different in the way, that it describes momentum as a result of overreaction to private information. Underreaction occurs at a later date, notably the correction phase. In addition, this model suggests that because of overconfidence, investors buy additional stocks when the public signal is in agreement with their private signal. Odean (1999) shows that investors are inclined to purchase additional stocks that have declined in price after their initial purchase instead of stocks that have gone up.

2.5.3 Style investing

The previous two models have focused on over- and underreaction to information as a source of momentum in stock returns. While over- and underreaction to news has been documented empirically, it may not describe some important features of momentum; for example, price bubbles, in which prices continue to drift upward without much news, can also occur because investors are simply chasing a trend. Such price bubbles, which exhibit positive autocorrelations, are not well described by over- or underreaction to news about fundamentals. In this section, we describe a model by Barberis and Shleifer (2003) that exhibits the same properties as in price bubbles, but in this model, it is simply a reflection of style level phenomena. Barberis and Shleifer develop a model that explains the impact that style investing can have on financial markets and security valuation.

2.5 Behavioral models 53

They combine style-based portfolio selection with a mechanism of how investors choose among styles. The model has two kind of investors, fundamental traders and switchers. The fundamental traders act as arbitrageurs that try to prevent the price of each asset to deviate too far from its expected final dividend. The investment policy of switchers is determined by two distinctive characteristics. Firstly, switchers classify assets into categories where they give each category a label. In this way, switchers try to simplify the information processing by making their decisions on a category level rather than an individual asset level. In this model, style investing is described as a production of life cycles of investment styles. The choice for a particular style depends on the relative past performance. Good fundamental news about the securities in a style is responsible for the start of a style 2 . When a style has a good past performance relative to other styles, switchers allocate their investments to that style and withdraw resources from other styles. If the style matures, good past performance is important to add new resources to a style. The style disappears when bad fundamental news arrives (or good news about the fundamentals of a competing style arrives) or due to arbitrage. A consequence of style investing is the emergence of life cycles in investment styles.

Barberis and Shleifer (2003) assume that each security fits to one style. There are 2n risky assets in fixed supply, and a risk free asset and cash in perfectly elastic supply with zero net return. Suppose the world has only two kind of styles, X and Y, with securities in X and securities in Y. The switcher’s demand of asset i in style X at time t is:

2 A style can be defined as a classification of assets into a category with similar performance characteristics.

54 Chapter 2. Review of the literature

t−1 S 1  k −1 (∆PX ,t−k − ∆PY ,t−k ) N i,t = AX + ∑θ  , (2.13) n  k=1 2 

where n is the number of securities in style X, AX is a constant, which represents the long run switchers target demand for style X, the parameter θ measures how far back investors look when they compare the past performance of styles, and PX,t and PY,t are the average prices of a share across all assets in style X and Y. Furthermore, the switcher’s demand of asset j in style Y at time t is

t−1 S 1  k −1 (∆PY ,t−k − ∆PX ,t−k ) N j,t = AY + ∑θ  (2.14) n  k=1 2 

The second kind of trader is the fundamental trader. The fundamental trader acts as an arbitrageur who does not want prices to diverge too far from their fundamental value. In contrast to switchers who base their expectations on past performance, fundamental traders base their expectations of the fundamental value. Assume that the fundamental traders have an amount WF to allocate and have no constraints to their allocations, then they have to solve the following:

F F ' max Et (− exp[− γ (W + N t (Pt+1 − Pt ))]), (2.15) Nt where γ is the degree of risk aversion, N is the number of shares allocated to F each risky asset, Pt is a price-vector for all assets, and Et is the fundamental traders expectations at time t. Combining the switchers’ demand for

2.5 Behavioral models 55 securities X and Y and the fundamental traders’ demand, the price function is as follows:

s Pt = Dt + γVN t , (2.16)

where Dt is the dividend to be paid at time t and V is the covariance-matrix of returns. Equation 2.16 shows that the fundamental traders are not able to push back the price to its fundamental value D. This is supported in the empirical literature. The covariance matrix of returns in equation 2.16 can be simplified with additional assumptions:

2 cov(∆Pi,t+1 ,∆Pj,t+1 ) = σ ,i = j  V ij = cov()∆P ,∆P = σ 2 ρ , i ≠ j, i, j in the same style , (2.17)  i,t+1 j,t+1 1  2 cov()∆Pi,t+1 ,∆Pj,t+1 = σ ρ 2 , i ≠ j i, j in different styles where the variance of all asset returns is the same, the return correlation between assets in the same style is the same and the correlation between assets in different styles is the same. Substituting the covariance structure 2.17 into equation 2.16, the price of an asset i in style X at time t is: 1 t−1  ∆P − ∆P  k −1  X ,t−k Y ,t−k  Pi,t = Di,t + ∑θ   , (2.18) φ k =1  2  where,

n φ = 2 γσ (1− ρ1 + n())ρ1 − ρ 2

ρ1 = correlation in the same style

ρ 2 = correlation between styles

56 Chapter 2. Review of the literature

This model of style investing has a number of empirical predictions. According to this model, investors do not distinguish between stocks within a style. It may appear that fundamentally unrelated stocks are grouped into the same category, which leads to demand shocks across all assets in that style. The demand shock across all assets leads to a comovement in prices even if this is unrelated to the underlying fundamentals. This has consequences for the return correlation between assets in the same style and the return correlation between assets in different styles. When a style becomes popular, the return correlation between stocks in the same style will increase. In addition, fund inflow by one style drives resources out of competing styles, which leads to negative correlations among styles. Furthermore, the presence of style switchers leads to positively autocorrelated returns in the short run and negatively autocorrelated returns in the long run within the style. Good performance over the last period relative to other styles pushes the prices up again in the next period, inducing positive autocorrelation. This causes momentum in the short run. Eventually, the price is reversed in the long run, inducing negative autocorrelation. This leads to contrarian effects in the long run.

2.6 Summary and motivation for following chapters

Financial researchers are in the midst of the debate whether investors act rational and consider all available information in the decision-making process. In this respect, it is important to know the drivers behind stock valuation, in order to assess whether the anomalies outlined in section 2.2 result from efficient pricing of risk or from behavioral biases, such as the ones analyzed in behavioral finance. Behavioral finance argues that a plausible reason for the anomalies found is that agents are not fully rational. This limited-rational behavior generates two complementary sources for

2.6 Summary and motivation for following chapters 57 financial market inefficiency, notably: investor sentiment, which means that investors deviate from the maxims of economic rationality; and limits of arbitrage which argues that the arbitrageurs are not able or willing (due to their risk aversion) to digest the large demand shocks by noise traders. While the patterns of aggregate stock market prices are not easy to understand from the rational point of view, different rational models have nonetheless been developed and can be tested against behavioral alternatives. In this chapter we discuss three rational and three behavioral models. The basic principal of rational models is that investors’ decisions are made from a return-risk point of view. Fama and French (1993) suggest that risk can be analyzed in terms of three factors: the market premium, size and book-to-market. The three-factor model has been criticized by Daniel and Titman (1997) who cast doubt on the prediction that value stocks earn higher returns because such stocks have higher loadings on the book-to- market factor and not because they have high book-to-market ratios. In addition, the three factor model fails to explain long-term effects and momentum returns. Berk et al. (1996) develop non-linear models where returns are explained in terms of the option to expand. This model shows through simulation, that it can explain the value premium, the size-effect and the momentum effect. However, this model cannot reproduce momentum and contrarian effects at the horizons as found in empirical research. Furthermore, this model is difficult to test empirically. Zhang (2000) develops a model where the value of a firm is explained by the option to abandon and the option to expand. This model fails to explain anomalies. Although these models assume that investors are rational, directly testing the validity of the assumption of rationality has not been general practice in economics. The rational school believes that not all participants are required to be rational in order to develop models that can explain stock returns. However, each of the three rational models described in section 2.4 58 Chapter 2. Review of the literature fails to explain the momentum and contrarian effect such as is reported in empirical studies. Therefore, it may be important to start to investigate the validity of rationality. In the meantime, we should be skeptical about models on rational behavior that have not been further documented empirically.

The behavioral models assume that investors are exposed to biases from cognitive psychology, which influence their decision process. The models by Barberis et al. (1998) and Daniel et al. (1998) both focus on over- and underreaction to information as a source of momentum in stock returns. Momentum may also be caused by investors who follow trends. Prices go up and down without news about fundamentals. Such positive autocorrelation in prices that cannot be explained by under- or overreaction to new information, is described by the model of Barberis and Shleifer (2003). In this model, momentum is simply a reflection of style level phenomena. Some critics argue that behavioral explanations for the empirical findings are (obviously) competing. For example, the models described in section 2.5 use different heuristics and biases from the cognitive psychology to explain the same phenomenon, notably momentum in the short run and mean-reversion in the long run. The model by Barberis et al. (1998) assumes that investors are exposed to representativeness and anchoring and adjustment while the model by Daniel et al. (1998) assumes that investors are exposed to overconfidence and self-attribution. In addition, Barberis and Shleifer (2003) emphasize the role of representativeness to explain momentum and contrarian effects. In addition, the models described in section 2.5 are only able to explain those anomalies that they are designed for. For example, the model by Barberis et al. fails to explain price drifts after isolated information events such as stock splits and dividends. The models by Barberis et al. and by Daniel et al. both fail to explain

2.6 Summary and motivation for following chapters 59 momentum due to investors who are chasing a trend instead of momentum as a result of the investors’ reaction to new information. Although the price pattern that is described in each model is the same, the explanations are different. In Daniel et al. the momentum phase features overreaction, as investors overreact to public signals that confirm their private information. The model of Barberis et al. (1998) works differently. Barberis et al. (1998) argue that the momentum phase reflects underreaction, as investors slowly react to new information. Barberis and Shleifer (2003) explain momentum as a result of investors who base their decisions on the style’s past performance. Fama (1998) reviews the studies of Barberis et al. (1998) and Daniel et al. (1998) and provide his view of under– and overreaction. He argues that underreaction appears as often as overreaction and that these instances cancel each other out. Therefore, market efficiency still remains. According to this view, market efficiency implies that prices coincide with fundamentals on average, but may deviate from each other due to chance. To explain the over– and underreaction evidence as a result of chance, Fama ignores that the circumstances where investors underreact differ from the circumstances where investors overreact. Notably, investors underreact to short-term information and overreact to long-term information.

The aim of this thesis is to contribute to the discussion between rationalists and behaviorists. In this chapter, we have described several models that are developed to explain anomalies. One way to compare the behavioral models is with empirical tests. The theoretical models are based on explicit and implicit assumptions about how beliefs of investors are formed. Hence, shedding some more light on these assumptions and testing the validity of these assumptions in practice is a prerequisite for evaluating these models. Based on the assessment of behavioral models, there are several directions 60 Chapter 2. Review of the literature deserving further research in order to obtain better insights in the decision- making process of investors:

1. Value premium With respect to the value premium two possibilities seem worth to investigate: first, the error-in-expectation hypothesis, and second, to examine the drivers behind investors’ uncertainty. So far, both hypotheses have been explored by several empirical researchers in order to explain the value premium. None of these empirical studies have used a different approach for the classification of value and growth stocks. This line of research will be followed in the chapters 3 and 4. 2. Style investing Barberis and Shleifer (2003) create a model that is based on a demand-driven process. Stock returns are determined by investors who base their asset choice on a group level instead of an individual stock level. The investment process is in terms of investment cycles where the demand of a particular style is based on heuristics from the cognitive psychology. This model has been tested by several researches using in- and outflows of mutual funds and portfolios of individual investors. So far, social effects such as collective preferences have been neglected in these studies. We use different variables that reflect collective preferences of investors and investors’ sentiment over time to test the popularity issue. We will pursue this direction in chapter 5.

Because of the competing behavioral explanations for some of the empirical facts, we believe that the assumptions of behavioral models need empirical scrutiny. In what follows we will therefore concentrate largely on the drivers behind behavioral models.

Chapter 3

The value premium and changing expectations: on the growth of value stocks and the value of growth stocks*

3.1 Introduction

The value premium has been subject of an extensive debate in the literature. Repeated empirical research shows that the value premium, which is the difference between the return of value and growth stocks, is positive3. The debate is on the nature of this premium. Fama and French (1992) consider the value premium as a reward for systematic risk in the context of a linear multifactor model. In their opinion, the value premium is related to firm

*This chapter is a working paper of T. Wouters and A. Plantinga (2005).

61 62 Chapter 3. The value premium and changing expectations leverage, measured by the market-to-book ratio, which can be considered as a proxy for financial distress. Another model in the rational school (see chapter 2, section 2.2) is that of Berk et al. (1999), who perform a simulation study based on a dynamic model of the firm. This model provides a rational justification for the book-to-market ratio as the relevant determinant, since it is rooted in (rational) option pricing theory, and is able to replicate many of the results found in the empirical literature, such as the findings of Fama and French. On the other hand, behaviorists (see chapter 2, section 2.3) relate the value premium to the inability of investors to process and evaluate information correctly. Lakonishok et al. (1994) suggest that the superior return of value stocks is due to expectational errors made by investors, who tend to extrapolate past growth rates too far into the future. When earnings are realized and financial results are made public, investors are faced with surprises. For value stocks, which have low implicit future growth rates, earnings realizations are systematically above expectations (investors exhibit pessimism) and result in positive stock returns. For growth stocks, the opposite happens, and earnings realizations tend to lead to negative return surprises (investors suffer from optimism). This assumed tendency to extrapolate past information too far into the future is referred to as the expectational error hypothesis (also called the extrapolation hypothesis). La Porta (1996) tests the expectational error hypothesis using financial analysts’ earnings forecasts as proxies for the expectations of investors. He defines value stocks as those having low expected earnings growth rates and growth stocks as having high-expected earnings growth

3 See for example, Fama and French (1992, 1993, 1996). Other authors use the label glamour stock as an alternative name for growth stocks.

3.1 Introduction 63 rates. He sorts stocks based on their forecasted 5-year growth rates, and finds that the realized earnings yields in the period after the initial sort is higher for value stocks than for growth stocks. La Porta et al. (1997) study the returns in the days surrounding an earnings announcement. They find that value stocks show a significant positive excess annual return of approximately 4% on the three days surrounding an earnings announcement. Growth stocks show negative returns of approximately – 0.4%. The positive announcement return for value stocks is seen as evidence supporting the extrapolation hypothesis. Using analyst earnings forecasts 8 months prior to the fiscal year end, Doukas et al. (2002) reject the expectational error hypothesis, since they find that value stocks tend to have higher forecast errors and larger downward forecast revisions than growth stocks. Initial forecasts for both value and growth stocks are too optimistic, and the optimism for value stocks exceeds the optimism for growth stocks 4 . Furthermore, they find that analysts revise forecasts downward for both value and growth stocks as time progresses towards the forecasting horizon. Based on this discussion, it seems fair to reject investor pessimism as the cause of the value premium and focus on the role of excess optimism in the longer-term forecasts as an alternative explanation for the value premium. Klein (1990), Ali et al. (1992), and Dowen (1996) provide evidence supporting the notion that investors become overly optimistic for stocks that show some good news after a period of mediocre performance. They find that analysts issue more optimistic forecasts for firms reporting recent losses than for firms reporting recent profits. Sedor (2002) suggests that this difference in optimism is related to unintentional optimism caused by the scenarios used by management to present forecasts. Scenario

4 In contrast, Chan, Karceski, and Lakonishok (2003) find that the 5-years forecasts in I/B/E/S are excessively optimistic relative to the realized rates, in particular for firms with high growth rates.

64 Chapter 3. The value premium and changing expectations thinking inflates the probability beliefs regarding the forecasted outcome. Although most value stocks do not suffer losses, investor’s expectations may suffer from the same unintentional optimism initiated after some good news regarding the performance of a value stock with a previously mediocre earnings growth. Rather than extrapolating past (low) earnings growth, investors are overly pleased with good news on future earnings. In this chapter we investigate the role of investors’ optimism in explaining the value premium. In order to attain this goal, we use forecasts of financial analysts and compare these with the final earnings realization. This allows us to draw conclusions on the level of optimism present in analysts’ forecasts. The studies of La Porta et al. (1997) and Doukas et al. (2002) focus on the bias in earnings prior to the announcement date. We focus on the bias in earnings in the next two years after portfolio formation. We assume that investors’ expectations can be proxied by analysts’ earnings forecasts. As a consequence, investor optimism/pessimism can be measured by analyst forecast precision, i.e. investors are considered to be optimistic when analysts’ earnings forecasts are higher than actual earnings realization and pessimistic when analysts’ earnings forecasts are lower than actual earnings realization. In order to relate investor optimism to the value premium, we first analyze the stocks that are responsible for realizing the value premium. The value premium is generated by a relative small group of value stocks that get reclassified as ‘medium’ or growth stock, creating large returns for the value portfolio. Similarly, growth stocks perform badly due to a small group of growth stocks that looses its classification, and creates a large negative return. Therefore, we make a distinction between switching-style stocks and fixed style stocks. For example, switching-value stocks are classified as value stock in year t but loose their status as a value

3.2 Sample selection 65 stock in year t +1. Fixed-value stocks are able to prolong their status as value stocks for two or more years. Likewise, switching-growth stocks are stocks that are reclassified after one year, and fixed-growth stocks remain in their class for two or more years. As we will show in this chapter, analyst forecasts of value stocks losing their initial classification are associated with increasing optimism, predicting an earnings yield of 14.6% whereas 10.3% is realized eventually. This chapter is organized as follows. In section 3.2 we provide a description of the data. In section 3.3 we describe differences in performance and announcement returns for switching- and fixed style stocks. In section 3.4 we study the level of optimism and pessimism present in analysts’ earnings forecasts. Section 3.5 provides a summary and a conclusion.

3.2 Sample selection

We use return data from the CRSP database, accounting data from COMPUSTAT, and earnings forecasts from I/B/E/S. The sample period covered in this study is from the beginning of January 1976 to the end of December 2003. Each stock is classified into one of three portfolios based on book-to-market value of equity (BE/ME) at the end of each year. The year after formation (t), book-to-market portfolios include all NYSE, AMEX and NASDAQ stocks for which we have market equity data and book value of equity in December of year t-1. We include stocks in our analysis with at least twenty-four months of return data and stocks with negative book-to-market values are omitted. We exclude real estate investment trusts (REITs), American Depository Receipts (ADRs), closed end mutual funds, foreign stocks, unit investment trusts and Americus

66 Chapter 3. The value premium and changing expectations trusts5. Companies should also have at least two years of data on earnings (before extraordinary items). We collect announcements returns over a three-day period (τ6-1, τ+1) surrounding each publication date in the Wall Street Journal. Returns are calculated from July at year t until June of year t+5. To ensure that the accounting variables are known before portfolio formation, we follow the same procedure as Fama and French (1992) by matching the accounting data of December t-1 with the returns of July in year t. The gap of six months between the fiscal data (December t-1) and the returns (June t) is conservative, because earlier work (e.g., Basu (1983)) reveals that most accounting data are available within three months of fiscal year ends. We collect the median annual consensus earnings forecasts from the I/B/E/S database starting from 1977. We select forecasts with a horizon of 1 and 2 years, as well as the long-term growth forecasts, which reflect the earnings growth rate for the next 5 years. Forecasts are made eight months before fiscal year-end, so that analysts have the annual reports and know the current earnings numbers before they make their forecasts. Forecast errors are defined as the earnings realization minus the consensus forecast as derived from I/B/E/S. Forecast errors are calculated at t = 0 and t = 1, by matching the forecast F0 and F1 with the relevant realized earnings number published in I/B/E/S. In order to facilitate aggregation of forecasted earnings and forecast errors, we scale both observations at t = 0 and t = 1 by the price at t = 0. We also retrieve the prices from I/B/E/S in order to be consistent with adjustments of stock dividends and stock splits. The timescale of our sample data is illustrated in figure 3.1. Where E(t) is earnings of year t. If financial analysts are too optimistic for stocks that are

5 Americus trusts are defined as sponsors of a technique to separate certain common stocks into a five-year warrant and a five-year covered call warrant writer's position at relatively low cost. 6 Where τ refers to days, whereas t refers to years.

3.2 Sample selection 67 previously classified as value stocks, we expected on average significant positive forecast errors in the forecasts posterior to the year of switching. This implies that we investigate investors’ optimism or pessimism in the forecasts (F0 and F1) of future earnings at t = 0 and t = 1, indicated by A and B in figure 3.1 for switching and fixed-style stocks.

Figure 3.1: Time scale of forecasts

Portfolio formation date

E(0) E(1) E(2) E(3)

F0 F1

t=-1 t=0 t=1 t=2 t=3

A B Next, we divide the stocks into three different categories based on their book-to-market ratio. Following Fama and French (1992), each stock is classified in three book-to-market groups based on the breakpoints of the NYSE stocks, which are available on Kenneth French’s website7. We label stocks below the 30th percent book-to-market equity (BE/ME) percentile as growth stocks and stocks above the 70th percentile as value stocks. Stocks with book-to-market values between these two classes are labeled “Medium”. Table 3.1 presents the annual buy-and-hold returns and the earnings announcement returns for value versus growth stocks from 1977 to 2003. These results correspond with the results of La Porta et al. (1997) and are consistent with Lakonishok et al. (1994). Panel A contains the annual buy- and hold returns over the 5 years after portfolio formation. The average difference in buy-and-hold returns between value and growth stocks is

7 see http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html

68 Chapter 3. The value premium and changing expectations

10.5% in the first year after formation, 10.0% in year +2 and 8.5% in year +3. The differences in returns are significant for all five post-formation years.

Table 3.1: Annual buy-and-hold returns and 12-day announcement returns from July 1977 to June 2003 for growth and value portfolios of NYSE, AMEX, NASDAQ stocks Portfolios are sorted at the end of each December (between 1976 and 1997) of year t based on the book-to-market ratio. The top 30% represents the portfolio of value stocks and the bottom 30% represents the portfolio of growth stocks. The annual returns are calculated over the period July of year t until June of the year t+5. Returns are reported for 1 to 5 years after portfolio formation. Earnings announcement returns are the average returns in the three days surrounding the earnings announcement date. To obtain aggregated annual intervals, we sum up the four quarterly earnings announcement returns for each post-formation year. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Number of Year after portfolio formation observations + 1 + 2 + 3 + 4 + 5 A: Annual returns Value 5934 0.156 0.169 0.146 0.104 0.101 Growth 10774 0.051 0.069 0.062 0.034 0.049 Difference 0.105** 0.100** 0.085** 0.070** 0.053** Value–Growth t-statistic on 4.129 4.524 4.247 4.462 3.067 difference B: Earnings announcement returns Value 0.025 0.024 0.022 0.020 0.020 Growth 0.006 0.009 0.010 0.011 0.013 Difference 0.019** 0.016** 0.012** 0.009** 0.007** Value–Growth t-statistic on 7.007 6.194 5.235 4.636 3.599 difference

Panel B reports the earnings announcement returns over the 5 years after portfolio formation. The 20-quarterly earnings announcement returns are equally weighted 3-day (τ-1, τ+1) buy-and-hold returns calculated for each stock for which data is available in that quarter. For each post formation

3.2 Sample selection 69 year, we annualize the announcement returns by summing up the four quarterly event returns. For example, table 3.1 shows the announcement returns for the first year after portfolio formation, +1, which represents the average of the 22 formation years, i.e. each of the years 1976 through 1997, in which portfolio formation has been dated in December. The difference in earnings announcement returns is 1.9% in the year after formation, 1.6% in the second year and 1.2% in the third year. These differences are 18.1%, 16.0% and 14.1% of the annual buy-and-hold return differences.

In table 3.2, we show summary statistics for earnings forecasts and forecast errors. The top panel of table 3.2 presents the earnings forecasts for value stocks and growth stocks at the time of portfolio formation scaled by their corresponding stock prices at the beginning of the year. We present the average 1-year and 2-years earnings forecasts and long-term (5 year) growth rate forecasts. We scale forecasted earnings by the stock price, because differences in the number of stocks may result in large differences in earnings per share for firms that are equal in terms of size and profitability. As expected, the forecasted earnings level is much lower for growth stocks than for value stocks, and the forecasted growth in earnings is much higher for growth stocks. The average differences in 1-year and 2-year forecasted earnings between value and growth stocks is 4.7% and 5.7%, respectively. These differences in forecasted earnings are statistically significant at a 1% level. More surprising is the remarkable growth from the 1-year forecasted earnings yield to the 2-year forecasted earnings yield for value stocks. Next year’s earnings is expected to be 9.3% of the current stock price, as compared to 12.1% for the earnings two years ahead. This increase is remarkable, since strong growth in earnings is usually associated with growth stocks. The bottom panel displays the forecast errors. Forecast errors are measures as realized earnings minus forecasted earnings. Therefore, a negative forecast error indicates analysts’ optimism. As can be

70 Chapter 3. The value premium and changing expectations seen, the forecasts for value stocks are on average more optimistic than for growth stocks.

Table 3.2: Average earnings forecasts and forecast errors for value and growth portfolios from 1977 to 2003 This table presents the average scaled earnings forecasts for value and growth stocks, and the expected long-term growth rate. This is the earnings growth rate for the next 5 years. The same classification criteria are used as in table 3.1. Earnings forecasts are reported at the moment of portfolio formation for the earnings in the first and second year after portfolio formation. Earnings forecast are reported with a 1 and a 2-year horizon. Earnings forecasts are scaled by the price at the time of portfolio formation. Long-term growth is not price-scaled and expressed in percentages. The t-statistic corresponds to the difference in means between value and growth stocks. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Values in brackets refer to medians. Forecast horizon Number of Average long-term observations 1 year 2 year growth rate (%) A: Average earnings forecast 0.093 0.121 11.689 Value 5934 (0.094) (0.114) (10.000) 0.051 0.067 16.819 Growth 10774 (0.057) (0.070) (15.000) Difference 0.047** 0.057** -5.130**

Value–Growth (0.039) (0.045) (-5.000) t-statistic on -18.777 -19.584 35.208 difference B: Average forecast error (scaled) -0.035 -0.058 Value 5934 (-0.007) (-0.018) -0.016 -0.029 Growth 10774 (-0.002) (-0.012) Difference -0.019** -0.029**

Value–Growth (-0.006) (-0.006) t-statistic on -19.233 -15.753 difference

The average differences in 1-year and 2-year forecast errors between value and growth stocks is 1.9% and 2.9%, respectively. These differences are

3.3 Switching- and fixed-style stocks 71 statistically significant at a 1% level. Furthermore, the degree of optimism for the 2-year ahead forecast is larger than for the 1-year forecast.

3.3 Switching- and fixed-style stocks

Our analysis in the previous section is based on distinguishing two style investing categories among stocks, notably growth and value (with an intermediate category labelled ‘medium’). Since stock prices and book values are variables that change over time, stocks can move from one style class to another. In order to get an impression of the probability that stocks switch from category, we report in table 3.3 the relative frequency of moving from category i at the start of year t to category j at the start of year t +1.

Table 3.3: Relative stock transitions between style categories Panel A: Relative frequency The relative frequency of stocks with portfolio classification i in year t moving to classification j in year t+1 for the period 1977 to 2003. Category j in year t+1 Category i in year t Growth Medium Value Growth 0.754 0.225 0.021 Medium 0.157 0.651 0.192 Value 0.032 0.247 0.721

Panel B: Returns The average returns in the period 1977 to 2003 from July of year t to June of year t+1 for stocks moving from category i in year t to category j in year t+1. Category j in year t+1 Category i in year 1 Growth Medium Value Growth 0.097 -0.120 -0.387 Medium 0.300 0.113 -0.084 Value 0.467 0.263 0.086

72 Chapter 3. The value premium and changing expectations

As can be seen, there are considerable year-to-year changes in the composition of value and growth portfolios. After a year, approximately 28% of the value stocks disappear from that category and 25% of the growth stocks do. These probabilities have interesting implications for the success of style investing. The most obvious implication is that maintaining a value or a growth strategy means active rebalancing. Panel B of table 3.3 shows the accompanying returns. Value stocks that migrate to the growth category earn a return of 46.7% and growth stocks that migrate to the value category earn a return of -38.7%. Given the previous observations, we make the following distinction between switching-style and fixed-style stocks. Switching stocks are stocks that lose their status in the year after initial classification. Fixed-style stocks retain their status for two or more consecutive years. Switching-value stocks are classified as value stock at the start of year t and loose their status as a value stock at the start of year t +1. Fixed-value stocks have their status as value stocks for at least two consecutive years. Likewise, switching-growth stocks are stocks that are reclassified after one year, and fixed-growth stocks remain in their class for at least two years. If we assume that the book value of equity per share is constant within a two year period (see further analysis at table 3.6), the price change should be responsible for the style-switch that stocks make. Thus, we expect that switching-value stocks have higher returns than fixed-style stocks, since the price of the switching-value stocks must have risen in the year after portfolio formation. Furthermore, we expect that switching-growth stocks experience negative returns, since their switching is caused by a fall in stock market price. In panel A of table 3.5, we present the returns for switching and fixed-style stocks. As expected, the results indicate that the returns of switching-value stocks are substantially higher than those of switching-growth stocks in the first year after portfolio formation.

3.3 Switching- and fixed-style stocks 73

Table 3.5: Analysis of annual buy-and-hold returns of growth and value stocks from 1977 to 2003 Using the initial style classification, we calculate returns (panel A) and size-adjusted returns (panel B) for switching- and fixed-style stocks. The portfolio is formed at the beginning of a new sequence. The returns presented are the averages of the (size-adjusted) returns n years after the start of a sequence. See table 3.1 for explanation of the period of the annual returns. Style Value Growth Difference (V-G) Switching Fixed Switching Fixed Switching Fixed

Years after Panel A: Annual returns formation

1 0.285 0.086 -0.156 0.097 0.440 -0.011 2 0.092 0.124 0.062 0.029 0.030 0.095 3 0.083 0.113 0.032 0.026 0.052 0.087 4 0.060 0.102 0.029 0.001 0.032 0.101 5 0.042 0.066 -0.013 -0.019 0.056 0.084 Panel B: Size-adjusted annual returns 1 0.116 -0.084 -0.304 -0.055 0.420 -0.028 2 -0.066 -0.042 -0.094 -0.112 0.028 0.070 3 -0.082 -0.051 -0.118 -0.120 0.036 0.069 4 -0.096 -0.065 -0.128 -0.136 0.032 0.071 5 -0.111 -0.088 -0.153 -0.148 0.042 0.060

Switching value stocks report a return of 28.5% in the year after portfolio formation, indicating a large change in stock prices and, therefore, a large change in the expectations of investors. For fixed-value stocks we report a return of 8.6% in the first year, which is much lower than the return for switching value stocks. Since the high returns reflect the switching event, returns for switching value stocks in the second and later years after formation are lower compared to the first year after formation, as stocks can retain their new status or can switch back to their old status at the expense of low or negative returns. On the other hand, switching-growth stocks report a return of –15.6% in the first year, whereas fixed-style growth stocks report a positive return of 9.7%. The negative return in the first year

74 Chapter 3. The value premium and changing expectations reflects the switching event. Therefore, returns for switching growth stocks in the second and later years after formation are higher compared to the first year after formation. These results suggest that the differences between the returns of fixed-style value and growth stocks are moderate, whereas the differences in the returns of the switching style stocks of the categories are much bigger. Apparently, switching stocks experience large changes in investors’ expectations regarding their future profitability. Notice that the switching- and fixed-style portfolios are based on hindsight information on the length of the classification sequence. Therefore, given our present results, it is not very likely that an investor can devise a strategy that enables him to invest only in switching-value and fixed-growth stocks. While the value premium persists even after adjusting for size (Lakonishok et al., 1994), we test whether the style-switching behavior is entirely driven by small stocks. In order to correct for potential size effects, we calculate size-adjusted annual buy-and-hold returns based on size benchmarks in the same way as La Porta et al. (1997) (see panel B of table 3.5). For each year, we divide stocks based on their market capitalization (determined at the last trading day of each year in June) in ten different size categories. The classification is based on the NYSE breakpoints8, which are determined by the market capitalization in June of each year based on all NYSE stocks on CRSP. Because deciles may contain a disproportional part of value or growth stocks, we use for the calculation of the size-benchmark returns only stocks from the intermediate category (‘medium’), which are neither value nor growth stocks based on their book-to-market ratio. The return of the resulting size benchmarks is calculated as an equally weighted average. Annual size-adjusted returns are calculated for each stock by subtracting the return of its corresponding size benchmark portfolio. The

8 The NYSE-breakpoints can be found at the website of Kenneth French (http://web.mit.edu/kfrench/www/data_library.html). The size breakpoint for year t is

3.3 Switching- and fixed-style stocks 75 results for size-adjusted returns are consistent and even stronger than the unadjusted returns, as can be seen from comparing the right-hand columns of panels A and B of table 3.5. In our explanation of the underlying cause of style-switching, so far, we have assumed that book values are constant with a two-year period. Since we attribute style switches to changes in earnings growth expectations (that underlie the changes in stock prices), it is important to check the behavior of book value. Changes in market-to-book ratios could also occur due to changes in book value, indicating realized growth, i.e. increased asset values. Furthermore, switching might be caused by a large depreciation (appreciation) or another accounting change unrelated to investors’ expectations. In order to check whether changes in book value have contributed to the switching behavior, we calculated the mean and median book value for different years after their initial classification as a switching- or fixed-style stock. The results are reported in table 3.6. From panel B of the table we observe that the average first-year growth rate in the book value of switching-value stocks is 0.4%. Given the relevant return figure from table 3.5, this indicates that the switching behavior is mainly caused by price changes. Both groups (fixed and switching) of value stocks report a low realized first-year growth in book value, thereby confirming the image of value stocks as having poor growth rates. For switching- growth stocks, we observe an average growth of equity book value of 13.7% in the first year after formation. Therefore, together with the fall in stock price the increase in book value contributes to the reclassification of switching growth stocks. Consequently, we conclude that the high returns for switching value stocks and the low returns for switching growth stocks are largely driven by

the median NYSE market equity at the end of June of year t. See p. 5 for an explanation of the BE/ME breakpoints.

76 Chapter 3. The value premium and changing expectations changes in stock prices and, therefore, by changes in investors’ expectations.

Table 3.6: The analysis of book value of equity for switching versus fixed-style stocks for the period 1977 to 2003 The top panel of this table presents the average and median book value of equity. The bottom panel presents the implied growth rates of book values. Median values are given between brackets. Value stocks Growth stocks Switching Fixed Switching Fixed Year after initial Panel A: Average book value of equity stock classification: 388.878 442.16 214.474 370.92 0 (32.697) (37.881) (29.758) (32.779) 368.425 459.127 258.184 431.862 +1 (30.669) (37.766) (35.092) (42.552) 392.759 461.969 284.798 513.354 +2 (34.078) (37.116) (35.673) (52.669) 434.087 466.504 296.871 599.419 +3 (37.136) (37.494) (36.992) (60.766) 458.243 475.499 301.979 672.775 +4 (40.111) (37.978) (39.263) (68.416) 481.474 481.963 323.897 750.426 +5 (42.861) (38.551) (39.355) (74.746) Panel B: Growth rates in book value of equity 0.40% 2.20% 13.70% 38.50% +1 (5.90%) (3.30%) (12.70%) (19.50%) 13.60% 1.50% 1.80% 30.10% +2 (10.50%) (3.50%) (6.30%) (17.10%) 13.90% 3.40% 5.10% 19.70% +3 (8.90%) (4.10%) (6.70%) (13.40%) 3.10% 5.10% 3.90% 0.60% +4 (7.40%) (4.30%) (6.00%) (11.10%) 4.60% 4.20% 5.10% 1.70% +5 (6.70%) (4.40%) (5.90%) (9.50%)

3.3 Switching- and fixed-style stocks 77

Although the book value of equity of switching-growth stocks increases with 13.7%, the book value of equity of fixed-growth stocks increases with 38.5%. Therefore, we cannot simply conclude that the style-switch is caused by an increase in the book value of equity. Given that the return on fixed-style growth stocks exceeds the return on fixed-style value stocks, the value premium is largely driven by switching stocks. Value stocks perform so well because on average 30% of them loose their status as value stocks after one year and generate generous returns. This result in itself provides evidence against the expectational error hypothesis, since reassigning value stocks to a category with a higher market-value ratio (i.e. a lower book-to- market ratio) is hard to reconcile with investors extrapolating low levels of past growth into the future. Because at the moment of portfolio formation it is not known which stocks will be switching, it is difficult to build a strategy on switching- and fixed-style stocks. Therefore, the generous returns of switching style value stocks do not provide evidence against rational asset pricing or market efficiency.

Our distinction between switching and fixed-style stocks may have an interesting implication for active portfolio management. Given the transition probabilities presented in table 3.3, the probability that a growth stock is a fixed growth stock is much higher than the probability that a value stock is a switching value stock. Consequently, it may be easier for an active manager to pursue successfully an active strategy of growth stock investing than active value strategy. This may explain the result by Daniel, Grinblatt, Titman, and Wermers (1997), who found evidence of positive forecasting ability for aggressive growth fund managers.

78 Chapter 3. The value premium and changing expectations

3.4 Investor optimism and pessimism before and after style switching

In this section we investigate the role of analysts’ optimism in explaining the value premium. The core of the optimism hypothesis is that analysts become too optimistic about the switching-value stocks and less optimistic about the switching-growth stocks. In order to test the optimism hypothesis, we use analysts’ earnings forecasts and compare these with the final earnings realization. If analysts are too optimistic for stocks that previously classified as value stocks, we expect on average significant positive forecast errors in the forecasts posterior to the year of switching. If prices reflect rational expectations, style switches should be caused by changes in unbiased expected growth rates, whereas the extrapolation hypothesis (error-in- expectation hypothesis) predicts that forecasted growth rates are systematically too low. In order to further analyze this aspect of the problem, we take a closer look at earnings growth rates with each style category. Table 3.7 presents the earnings growth rates (EG) for the switching- and fixed-style stocks. We show average and median growth rates (after having applied a filter on earning growth rates above 500%, to avoid the impact of firms with extreme growth rates. Examples of such firms are start-up firms, which have very small earnings in the beginning). We observe that the actual earnings growth rates for growth stocks are considerably larger than the growth rates for value stocks. Fixed-style value stocks show a persistent negative earnings growth, indicative of their perceived poor performance. Switching value stocks show a growth rate considerably less negative than fixed-style value stocks. More interestingly, the difference in earnings growth rates between time t=0 and t=1 for switching-value stocks is 10.3% and for switching growth stocks is -33.6%. This suggests that there is some substantial positive (negative) news on switching-value (switching-growth) stocks,

3.4 Investor optimism and pessimism before and after style switching 79 which may provide the ignition of the type of excessive optimism (pessimism) documented by Klein (1990), Ali et al. (1992), and Dowen (1996). For switching growth stocks, the growth rate becomes negative in the year of the switch, whereas the fixed growth stocks still show a positive growth in the first year.

Table 3.7: Realized earnings growth rates for switching- and fixed-style stocks, period 1977 to 2003

EG0 indicates the earnings growth rate in the year prior to portfolio formation, EG1 refers to the year after portfolio formation (median growth rates are presented between brackets). We applied a filter for earning growth rates above 500%. The subscripts sg and fg denote switching- and fixed-growth stocks, respectively, and the subscripts sv and fv denote switching- and fixed-value stocks, respectively. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Value stocks Growth stocks

EG1,sv– EG1,sg– EG0,sv EG1,sv EG0,sg EG1,sg EG0,sv EG0,sg Switching- -0.223 -0.119 0.103 0.236 -0.099 -0.336** style stocks (0.014) (0.074) (0.060) (0.223) (0.009) (-0.214**)

EG1,fv– EG1,fg– EG0,fv EG1,fv EG0,fg EG1,fg EG0,fv EG0,fg Fixed-style -0.149 -0.253 -0.104** 0.195 0.114 -0.080** stocks (-0.009) (-0.019) (-0.010) (0.191) (0.163) (-0.027**)

The next step in our analysis is to test the hypothesis that the style- switching behavior of stocks is driven by an overreaction of investors to new information. To implement this we start with focusing on F0, the forecasted earnings at the portfolio formation date and F1, the earnings forecast 1 year after the portfolio formation date. If analysts are too optimistic (pessimistic) for stocks that previously classified as value (growth) stocks, we expect on average significant positive (negative) difference between the earnings forecasts at t = 0 and t = 1. We use forecast data on the earnings in the first and second year after formation, as well as on the long-term earnings growth (see also table 3.2). Table 3.8 contains

80 Chapter 3. The value premium and changing expectations this forecast information in a derived format, limited to style-switching growth and value stocks. We test the hypothesis that analysts have raised the forecasts of next year’s earnings of switching-value stocks, as well as the forecasts of year 2 and long term growth (5-year growth rates), relative to last year’s forecast. We also test the hypothesis that analysts have lowered the earnings forecasts of switching-growth stocks.

Table 3.8: Changes in earnings forecasts This table shows the mean and median (between brackets) of the earnings forecasts scaled by the price at portfolio formation date (t = 0). We deleted stocks with prices lower than 3 dollars at the beginning of the fiscal year, and stocks with forecast errors larger than 100% of the price. F1,sv indicates the earnings forecast at time t = 1 for switching value stocks (sv). The subscripts sg denotes switching growth stocks. Long-term growth is expressed as a percentage. Tests on median (mean) 9 differences between F0 and F1 are performed with the Kruskal-Wallis test (t-test). The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Switching value stocks Switching growth stocks

Forecasts F0,sv F1,sv F1,sv–F0,sv F0,sg F1,sg F1,sg–F0,sg 0.088 0.115 0.027** 0.058 0.048 -0.009** 1-yr forecast (0.095) (0.113) (0.010**) (0.061) (0.054) (-0.008) 0.116 0.146 0.030** 0.075 0.065 -0.010** 2-yr forecast (0.114) (0.135) (0.021**) (0.075) (0.067) (-0.008) Long-term 11.603 11.915 0.312 21.387 18.611 -2.777** growth (%) (10.000) (10.000) (0.000) (19.000) (15.500) (-4.500**)

Table 3.8 shows that both 1-year and 2-year forecasts of switching value stocks increased with 2.7% and 3.0% at a statistical significant level of 1%. Furthermore, 1-year and 2-year forecasts for switching growth stocks have been lowered significantly. The 1-year and 2-year forecasts decreased with - 0.9% and -1.0% at a 1% significance level. In order to test whether these changes in expectations are too excessive, we calculate the forecast errors scaled by stock price. If the average scaled forecast errors are negative, financial analysts are too

9 We show median values because mean values can be influenced by extreme observations (outliers).

3.4 Investor optimism and pessimism before and after style switching 81 optimistic, and financial analysts are too pessimistic if the forecast errors are positive. We expect that forecast errors for firms with poor actual earnings growth are smaller than those for firms that previously experienced high earnings growth. Therefore, we test whether the average forecast error for switching-value stocks is smaller than for switching-growth stocks. If optimism by financial analysts for switching stocks is representative for the expectations of all investors, then we can conclude that the stock market may have overreacted to the good news for switching stocks, and returns may actually be “too high”. In that case, the value premium is partly driven by excessive optimism by investors. Since the errors in long-term growth forecasts are more difficult to evaluate, we omit these from the present analysis. In table 3.9, we calculate the average forecasting error at portfolio formation date (t=0) and one year after (t=1), in order to test whether the degree of optimism has increased after the style switch. The table shows that optimism is present in the forecasts for all relevant stocks. Two-year forecasts are more optimistic than 1-year forecasts (except for sv at t=0). Initially, financial analysts were less optimistic for switching value stocks. However, after the stock switched the level of optimism by analysts has increased significantly by 2.9%. In other words, in addition to high returns, the earnings forecasts of switching value stocks also experience increasing optimism. We consider this as evidence that the value premium is associated with increasing optimism of investors rather than persistent pessimism as suggested by the expectational errors hypothesis. In order to show that our outcomes are not depended on the period we chose, we show in appendix 3A in table 3A.1 the forecast errors over the period 1977 to 1989 and over the period 1990 to 2003. These results are similar to the findings of table 3.9. Switching value stocks show an increase in optimism during the year of the style switch.

82 Chapter 3. The value premium and changing expectations

Table 3.9: Changes in earnings forecast errors, indicating changes in optimism and pessimism This table shows the mean and median (between brackets) of the scaled forecast errors based on the same selection criteria used in table 3.8. To control for price-effects, forecast errors are scaled by the price at t=0. FE0 and FE1 indicates the error in earnings forecast at time t=0 and t=1, respectively. The subscripts sv, sg, fv, and fg denote respectively switching value, switching growth, fixed value and fixed growth stocks. Tests on medians are performed with the Kruskal-Wallis test. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Value stocks Growth stocks Switching- FE0,sv FE1,sv FE1,sv–FE0,sv FE0,sg FE1,sg FE1,sg–FE0,sg style stocks -0.016 -0.014 0.003 -0.021 -0.020 0.001 1-yr forecast (0.001) (0.000) (0.001) (-0.010) (-0.008) (0.003) -0.014 -0.043 -0.029** -0.050 -0.040 0.012** 2-yr forecast (0.001) (-0.010) (-0.010**) (-0.031) (-0.018) (0.013) Fixed-style FE0,fv FE1,fv FE1,fv–FE0,fv FE0,fg FE1,fg FE1,fg–FE0,fg stocks -0.031 -0.034 -0.003 -0.005 -0.009 -0.005** 1-yr forecast (-0.009) (-0.006) (0.003**) (-0.000) (-0.002) (-0.002**) -0.057 -0.054 0.003 -0.015 -0.026 -0.011** 2-yr forecast (-0.020) (-0.015) (0.005**) (-0.006) (-0.011) (-0.005**)

Finally, we directly relate our analysis to the expectational error hypothesis. Since the initial evidence on expectational error hypothesis was based on earnings announcement returns, we present in table 3.10 earnings announcement returns for fixed- and switching style stocks. The annualized (size-adjusted) earnings announcement returns are calculated similar to the (size-adjusted) raw returns in table 3.4. The benchmark portfolios for the earnings announcement returns include all stocks that are neither value nor growth stocks and where earnings announcement return data is available. The size benchmark returns are the equally weighted earnings announcement returns. The size-adjusted earnings announcement returns for each firm are calculated by subtracting its corresponding size-decile earnings announcement benchmark.

3.4 Investor optimism and pessimism before and after style switching 83

Table 3.10 shows a positive announcement return for switching value and fixed style stocks. The positive result of 3.3% for switching-value stocks after 1 year is only slightly higher than the 2.2% announcement return for fixed-style value stocks.

Table 3.10: Annual Cumulative Earnings Announcement returns from, 1977 to 2003 The quarterly earnings announcement returns are equally-weighted 3-day (τ - 1, τ + 1) buy-and-hold returns calculated for each stock for which data is available. For each post formation year we annualize the announcement returns by summing up the relevant four quarterly event returns. For example, +1 presents the cumulative quarterly event returns of the first year after portfolio formation. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Value Growth Years after Switching Switching Fixed style Differencea Fixed style Differencea formation style style Announcement returns +1 0.033 0.022 0.011** -0.004 0.012 -0.016** +2 0.016 0.027 -0.011** 0.013 0.006 0.007** Size-adjusted announcement returns +1 0.023 0.007 0.016** -0.018 -0.001 -0.017** +2 0.006 0.013 -0.007** 0.003 -0.005 0.008** a t-statistic is calculated on difference between switching- and fixed-style portfolios

Some part of this may actually be explained by the fact that the average return of switching value stocks exceeds that of fixed-style value stocks. However, the positive announcement returns for fixed-style value stocks require some discussion. Given the evidence of Doukas et al. (2002) and our evidence on the optimism in earnings forecasts, it is difficult to interpret this return as evidence in favor of pessimism in investor’s expectations. Perhaps the interpretation of Cohen et al. (2004) is more appropriate: at the earnings announcement date, the uncertainty regarding the exact number of last year’s earnings is going to be resolved, and the positive return is the risk premium for this uncertainty.

84 Chapter 3. The value premium and changing expectations

In summary, we can conclude from section 3.4 that optimism in earnings forecasts increases significantly in the year that value stocks switch from style. Switching-growth stocks show a decrease in optimism in earnings forecasts in the year that stocks switch from the growth classification to the medium or value classification. Therefore, our results support the optimism hypothesis instead of the expectational error hypothesis. Although the announcement returns show an increase the first year after portfolio formation for switching-value stocks, this result is difficult to interpret in terms of pessimism given the increase in analysts’ optimism.

3.5 Summary and conclusion

There has been an ongoing discussion in the literature on the nature of the value premium. In this chapter we investigated the role of expectational errors in the value premium. Previous studies by La Porta (1996) and La Porta et al. (1997) suggest that investors extrapolate past growth trends too far into the future. Since value stocks are by definition stocks with mediocre or poor past growth rates, naïve extrapolation implies that realizations are consistently above forecasts. In a similar way it can be argued that naive extrapolation will result in earnings realizations of growth stocks being below their forecasts. Consequently, investors are repeatedly surprised about the performance of value stocks and disappointed about the performance of growth stocks, which results in positive returns for value stocks. However, there is an abundant literature on optimism in earnings forecasts, suggesting that in general earnings forecasts are too optimistic (De Bondt and Thaler, 1990). More specifically, Doukas et al. (2002) show that earnings forecasts for value stocks are even more optimistic than for growth stocks. It remains an open question to what extent analysts’ earnings forecasts are representative

3.5 Summary and conclusion 85 for investor expectations in general. However, we assume this to be the case. In this chapter, we contribute to the discussion by focusing on changes in the style classifications of individual stocks. Changes in style classifications, such as the move from value stocks to medium or growth stocks, are associated with changes in expectations. We illustrate this by showing the differences in returns and earnings growth rates of switching stocks and fixed-style stocks. For our sample period, switching-value stocks experienced an average return of 28.5% and their forecasted earnings yield increased from 8.8% prior to switching to 11.5% after the switch. Likewise, switching growth stocks generate low returns and forecasted earnings yield decreased from 5.8% to 4.8%. Therefore, we conclude that the value premium is generated by the switching of value and growth stocks from their initial classification. Without having looked at analyst forecast errors, the returns for switching stocks may still be consistent with investors having rational expectations. However, studying the forecast errors generates our most important finding: optimism in earnings forecasts increases significantly in the year that stocks switch from the value classification to the medium or growth classification. This increase is significant on both a statistical level as well as an economic level. Analysts’ optimism, implied by the error in 2- year forecasts scaled by the price, increased from -1.4% to -4.3%. If analyst expectations are representative for investor expectations, then this implies that at least part of the value premium is the result of excessive optimism on behalf of investors. This conclusion is at odds with the expectational error hypothesis which suggests that investors tend to be pessimistic when extrapolating earnings yields of value stocks.

86 Chapter 3. The value premium and changing expectations

Appendix 3A

Table 3A.1: Changes in forecast errors This table shows the mean and median (between the brackets) of the scaled forecast errors based on the same selection criteria used in table 3.8. To control for price-effects, forecast errors are scaled by the price at t=0. FE1,sv indicates the error in earnings forecast of one year after portfolio formation (t = 1) for switching value stocks (sv). The subscripts sg, fv, and fg denote respectively switching growth, fixed value and fixed growth stocks. Tests on medians are performed with the Kruskal- Wallis test. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. A) Period 1977-1989 Value stocks Growth stocks Switching- FE0,sv FE1,sv FE1,sv–FE0,sv FE0,sg FE1,sg FE1,sg–FE0,sg style stocks -0.036 -0.023 0.013 -0.040 -0.036 0.004 1-yr forecast (-0.003) (-0.002) (-0.001) (-0.019) (-0.017) (0.001) -0.024 -0.052 -0.028** -0.068 -0.056 0.012 2-yr forecast (-0.002) (-0.013) (-0.015*) (-0.046) (-0.036) (0.011**) Fixed-style FE0,fv FE1,fv FE1,fv–FE0,fv FE0,fg FE1,fg FE1,fg–FE0,fg stocks -0.040 -0.048 -0.008 -0.008 -0.012 -0.004* 1-yr forecast (-0.013) (-0.013) (0.000) (-0.001) (-0.003) (-0.002**) -0.076 -0.077 -0.001 -0.018 -0.030 -0.012** 2-yr forecast (-0.032) (-0.026) (0.006) (-0.008) (-0.015) (-0.007**)

Appendix 3A 87

[Table 3A.1 continued]

B) Period 1990-2003 Value stocks Growth stocks Switching- FE0,sv FE1,sv FE1,sv–FE0,sv FE0,sg FE1,sg FE1,sg –FE0,sg style stocks -0.009 -0.010 -0.001 -0.017 -0.017 0.000 1-yr forecast (0.002) (0.002) (0.001*) (-0.009) (-0.006) (0.003**) -0.010 -0.039 -0.029** -0.043 -0.032 0.012** 2-yr forecast (0.001) (-0.007) (-0.008**) (-0.029) (-0.015) (0.013**) Fixed-style FE0,fv FE1,fv FE1,fv–FE0,fv FE0,fg FE1,fg FE1,fg–FE0,fg stocks -0.028 -0.029 -0.001 -0.004 -0.009 -0.005** 1-yr forecast (-0.007) (-0.004) (0.003**) (-0.000) (-0.002) (-0.002**) -0.050 -0.046 0.004 -0.015 -0.025 -0.010** 2-yr forecast (-0.016) (-0.012) (0.004**) (-0.005) (-0.010) (-0.005**)

88 Chapter 3. The value premium and changing expectations

Chapter 4

The drivers behind uncertainty and style migration

4.1 Introduction

US and international empirical evidence shows that on average value stocks outperform growth stocks (Fama and French, 1992, 1996, 1998, and Lakonishok, Shleifer and Vishny, 1994). Although it is becoming increasingly accepted that value stocks generate higher returns than growth stocks, the interpretation as to why they have done so is more controversial. Risk-based and error-in-expectation explanations have emerged as possible sources for the return differentials found (e.g. Fama and French, 1992, Doukas et al., 2003, La Porta, 1996, and La Porta et al., 1997). Various theoretical models have been constructed to explain the empirical findings, in order to understand the mechanisms of stock pricing. Hong and Stein (1999) built a unified behavioral model, where the interaction between heterogeneous investors plays a central role. The

89 90 Chapter 4. The drivers behind uncertainty and style migration investors can be divided into two groups, newswatchers and momentum traders. Newswatchers make forecasts based on private information and momentum traders make forecasts conditioned on past information on stock prices. The general assumption they make is that private information diffuses gradually across the newswatchers population. This is the so-called information diffusion hypothesis. When only newswatchers are active, prices adjust slowly to new information. This explains the underreaction phenomenon. Then momentum traders come into action and exploit the pricing underreaction with a simple arbitrage strategy. However, by making it profitable for momentum traders to enter the market, excessive momentum is created in prices that inevitably leads to overreaction. Hong, Lim and Stein (2000) test the information diffusion hypothesis empirically. They use two proxies for the speed of diffusion of information, size and analyst coverage, to classify stocks from high to low information diffusion. They find that stocks with slower information diffusion have more pronounced momentum, as the evidence shows that profitability of momentum strategies declines with firm size and analyst coverage. Barberis, Shleifer and Vishny (1998) have a different approach than Hong and Stein (1999). They emphasize the psychology of the representative investor to explain the under- and overreaction mechanisms. There is a representative investor who suffers from a conservatism bias which means that he does not update his beliefs sufficiently when new public information arrives. This gives rise to underreaction in the short run. At the same time, when the investor repeatedly receives similar information, he believes that earnings follow a trend. This gives rise to overreaction. Keastner (2005) finds empirical evidence in favor of this model. He studies current and past earnings surprises and the subsequent market reaction for US companies and finds that earning surprises have predictive power for stock returns. Stocks that have experienced a string of

4.1 Introduction 91 earnings surprises show a reversal in their stock prices when a subsequent opposite earnings surprise occurs, even when the forecast error is zero. The longer the pattern of similar earnings surprises the higher the subsequent reversal of the market. Another study that examines the string of forecast errors is by Huberts and Fuller (1995). They use the average of the absolute values of three most recent annual forecast errors to show that past forecast errors persist and that historical forecast errors have predictive power for future returns. Doukas, Kim and Pantzalis (2003) use the dispersion in analysts’ earnings forecasts as a measure of uncertainty to test whether value stocks are riskier than growth stocks. They find that the value premium reflects a compensation for uncertainty, because investors are more uncertain about future earnings of value stocks in comparison with earnings forecasts of growth stocks. Combining the information diffusion hypothesis and uncertainty, one would expect that the higher the speed of information diffusion, the lower uncertainty will be. Measures that reflect the speed of information diffusion are size and analyst coverage. Doukas, Kim and Pantzalis (2004) show that analyst coverage and book-to-market ratio are negatively related to each other. Value stocks have lower analyst coverage than growth stocks. In addition, it is reasonable to expect that the higher the speed of information diffusion across the investing public, the more accuracy of estimating future earnings will increase. Lim (2001) and Doukas, and Kim and Pantzalis (2004) show that forecast errors, which they find relatively high for value stocks, decrease with analyst coverage. In addition, when analysts’ earnings forecasts have been wrong in the period before, this, in itself, may lead to higher uncertainty among analysts. Ackert (1997) supports the positive relation between optimism and uncertainty. He finds that when firms are surrounded by more uncertainty, analysts are more likely to act on their incentives to release optimistic forecasts.

92 Chapter 4. The drivers behind uncertainty and style migration

While these studies test the information diffusion hypothesis, the error-in- expectation hypothesis (based on representativeness) or the uncertainty hypothesis separately, they do not consider a combination of the three. The first aim of this chapter is to test whether uncertainty is related to past information and to the speed of information diffusion. Firstly, we look for evidence that uncertainty is increasing when less information about a stock is revealed. Secondly, we examine if uncertainty is increasing because investors extrapolate past information into the future. This information can be in the form of stock returns but also in the form of forecast errors. The possible influence of analysts’ coverage on firm’s uncertainty stems from its ability to make stock prices more informative in the sense that they more precisely reflect their fundamental values. To the extent that analyst coverage does increase the speed of information to the investment public, it is also expected that it has a better forecasting quality. If less information is available about a company, one expects that analysts are also making larger mistakes when they forecast future earnings. However, when analysts’ earnings forecasts have been wrong a couple of times, this, in itself, may lead to higher uncertainty among analysts. Therefore, if the analyst coverage for a firm is low and the string of forecasts has been too optimistic, analysts may become more uncertain. In addition, when stocks have a bad past performance and analysts have been wrong in their forecasts before, uncertainty may increase. Our results show that uncertainty is related to the extrapolation of past information and to a low diffusion of information. We follow Doukas, Kim and Pantzalis (2003) by using the dispersion in analysts’ (consensus) earnings forecasts as a proxy for investor uncertainty. This is analogous to chapter 3 (e.g. Chapter 3, section 3.1), where we use analysts’ (consensus) earnings forecasts as a proxy for investors expectations of future earnings. Firstly, we find that firms with higher analyst forecast errors have higher dispersion in earnings forecasts. Furthermore, we find that dispersion in

4.1 Introduction 93 analysts’ earnings forecasts is increasing when analyst earnings forecast errors are large and negative two years in a row. This implies that analysts become more uncertain about future earnings when they have been too optimistic in the past. Second, we find that firms with low analyst coverage have higher dispersion in analysts’ earnings forecasts, suggesting that analysts become more uncertain when less firm-specific information is available. In addition, we find that when we divide stocks on past performance and size-adjusted analyst coverage, dispersion is higher for stocks with low analyst coverage and low past performance. This suggests that investors are more uncertain about stocks with low past performance and low analyst coverage. In addition, holding one year-ahead forecast errors fixed, loser stocks have higher dispersion than winner stocks. There is a strong asymmetry, since the effect of dispersion in analysts’ earnings forecasts is more pronounced for stocks for which analysts were too optimistic than for stocks for which analysts were too pessimistic. In other words, uncertainty increases more when analysts are too optimistic. This makes intuitively sense in the context where people prefer good news over bad news; analysts have to deal with their disappointment, because earnings are lower than expected. Overall, the results suggest that the less information revealed about a company, the more likely it is that too optimistic expectations and bad past performance lead to higher uncertainty. The second aim of this chapter is to test whether it is more likely for a stock to migrate from style when investors are more uncertain about future earnings. Again following the reasoning of Doukas, Kim and Pantzalis (2003) that analysts’ forecast dispersion reflects uncertainty, switching style stocks should be associated with higher dispersion in analysts’ earnings forecasts than fixed-style stocks. Switching of style classification implies that investors completely revise their expectations about future earnings, whereas the expectations for fixed style stocks

94 Chapter 4. The drivers behind uncertainty and style migration remain largely unchanged. The drastic change in expectations is the result of investors realizing that their expectations are too optimistic or too pessimistic. They are surprised by the results presented and change their expectations drastically in the opposite direction. In particular, surprises tend to occur for those stocks of which analysts are less informed. As is shown in chapter 3, switching-value and switching-growth stocks are the result of changes in investors’ expectations regarding the future profitability of stocks. Because of the uncertainty of investors about the prospects of the value of switching-style stocks, dispersion in analysts’ earnings forecasts for switching-style stocks will be higher. We apply a probit-analysis and find that dispersion in analysts’ earnings forecasts is positively related to style switches. This means that the chance of a style switch increases when analysts become more uncertain. The remainder of the chapter is organized as follows. Section 4.2 gives an overview of the data. Section 4.3 contains our main results on dispersion in analysts’ earnings forecasts. In section 4.4 some robustness tests and the results of the probit-model are presented. The final section presents some concluding comments.

4.2 Data

The sample covered in this study is from January 1976 to December 2003. The universe of stocks is the New York Stock Exchange (NYSE), American Stock Exchange (AMEX) and NASDAQ. Only common stocks are included in the sample, which means that REIT’s, ADR’s, closed end funds, foreign stocks and units of beneficial interest are excluded from the sample. We use COMPUSTAT to obtain annual data on the book value of equity, Tobin’s q and earnings. Tobin’s q is used to capture investment

4.2 Data 95 opportunities10. The book value of equity is computed as book value of equity plus deferred tax and investment tax credits minus the book value of preferred stock. Depending on the availability, we use for the book value of preferred equity the redemption value, liquidity value or par value in the order mentioned here. Earnings are defined as earnings before extraordinary items. Monthly data on returns, market capitalization and SIC codes are obtained from CRSP. Data on analysts’ earnings forecasts, expected earnings growth rates, prices and earnings are taken from the Institutional Brokers Estimates System (I/B/E/S). We select forecasts with a horizon of one year. Forecasts are defined as the median consensus forecasts reported by I/B/E/S. Forecast errors are calculated at year t-1, by matching the forecast Ft-1 with the relevant realized earnings number published in I/B/E/S. We follow Doukas, Kim and Pantzalis (2003)11 to compute the dispersion in analysts’ earnings forecasts as the standard deviation of the forecasts divided by the beginning of the fiscal year stock price (year t). We delete firm-year observations when the stock price at the beginning of the fiscal year is below the $3. By doing this we avoid extreme ratios due to price-effects. To compute analyst coverage we select the number of analyst forecasts issued eight months prior to fiscal year-end for all stocks covered by security analysts. Following Hong, Lim and Stein (2000), we control for the influence of size on analyst coverage by regressing coverage on firm size and using the residual analyst coverage. The dependent variable is log(1+Analyst coverage) and is the log of the number of analysts that give a forecast in April of year t. The independent variable is the log(Size) and is

10 Tobin’s q is measured as: [market value of common equity+preferred stock liquidating value+bookvalue of long-term debt+(short term debt-short term assets)]/net assets. 11 Doukas et al. (2003) examine alternative deflaters to construct the dispersion of analysts’ forecasts, e.g. sales, book value of total assets and absolute median forecasts. They show that the results are insensitive to the choice of the scaling.

96 Chapter 4. The drivers behind uncertainty and style migration the log of the firm’s market value in April of year t. Furthermore, we add a NASDAQ dummy (NASD) into the equation.12

Similar to our procedure in chapter 3, we divide stocks into three groups based on their book-to-market equity ratio at the end of June of each year. Growth and value stocks are determined by the breakpoints for the bottom and top 30% of the values of the book-to-market equity for NYSE stocks (we use the breakpoints available at the website of K. French13). The book- to-market equity ratio used to form portfolios in June of year t is the common book value of equity for the fiscal year ending in calendar year t-1, divided by its market capitalization of June t. Stocks with negative book values of equity are excluded. Within each portfolio, we equally weigh all the stocks and compute the average of each variable over each period. To ensure that the accounting variables are known before the returns, we match the accounting data for all fiscal year ends in calendar year t-1 with the style switch from July of year t to June of t+1. For each style-switching year we calculate the equally-weighted average of each variable prior to the year of the style switch. For example, the average annual return in 1979 is calculated from July 1978 to the following June in 1979. Table 4.1 provides descriptive statistics over the period 1976 to 2003. Stocks must have at least data on the standard deviation of analysts’ earnings forecasts in April of year t and data on book-to-market ratio, two years of monthly returns, earnings and Tobin’s q at the fiscal year-end t-1. A total of 29,148 firm-year observations meet these requirements. The first thing that emerges from table 4.1 is the skewness in analysts’ dispersion. The average dispersion is 1.2% and the median dispersion is 0.5%. Consistent with prior studies, mean and median 1-year forecast errors are negative. The average (median) forecast errors for the 26-year time period is

12 The regression is as follows: Number of log(Analysts+1) = log(Size)+NASD+residuals 13. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 97 style effects -1.80 (-0.30). The average (median) number of analysts that cover a firm is 10 (7) and the average (median) size-adjusted analyst coverage is -0.017 (0.100).

Table 4.1: summary statistics for the period 1976 to 2003 This table reports median values of dispersion in analysts’ earnings forecasts and annual returns. Portfolios are formed on the dispersion in analysts’ earnings forecasts. The dispersion of the analysts’ earnings forecasts (Dispt) is defined as the standard deviation of the one fiscal year ahead earnings as of eight months before the fiscal year end divided by the price at the beginning of fiscal year t. The 1- year forecast errors (FE1t-1) are defined as the difference in actual value and the 1-year forecast (8 months before the fiscal year end) divided by the price. Analyst coverage is the residual analyst coverage, where the residuals come from a regression of coverage on firm size. Earningst-1 is earnings before extraordinary items at fiscal year end. Tobin’s qt-1 is measured as: [market value of common equity+preferred stock liquidating value+bookvalue of long-term debt+(short term debt- short term assets)]/net assets. Annual returns are calculated over the period April of year t-1 to March of year t (R12,t-1 ) and over the period July of year t to June of year t+1 (R12,t). BMt-1 is the book-to- market ratio and Sizet-1 is the share price time shares outstanding at fiscal year end. Standard Mean Median Min Max deviation

Dispt 0.012 0.005 0.104 0.000 16.148 FE1t-1 -0.018 -0.003 0.217 -28.648 3.729 Analyst coveraget 9.869 7.000 7.999 3.000 48.000 a Analyst coveraget -0.017 0.100 0.776 -2.472 1.587

Earningst -1 (millions of $) 122.904 26.428 476.457 -7987 15990

Tobin’s qt-1 1.195 0.806 1.674 -0.455 77.910 Returnt-1 0.074 0.107 0.460 -5.381 3.121 Returnt 0.036 0.090 0.480 -4.744 2.855 BMt-1 0.754 0.645 1.034 0.002 105.321 Sizet (millions of $) 2382 469.6 9585 2.105 301240 aSize-adjusted

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and style effects

In section 4.3.1, we seek evidence for the information diffusion hypothesis and the error-in-expectation hypothesis. As a proxy of uncertainty to investors we use dispersion in analysts’ earnings forecasts.

98 Chapter 4. The drivers behind uncertainty and style migration

The dispersion in analysts’ earnings forecasts (Dispt) is measured as the standard deviation of the one year-ahead analysts’ earnings forecasts made eight months before the fiscal year end, standardized by the stock price at the beginning of the fiscal year. To test the information diffusion hypothesis, we analyze the effects of size-adjusted analyst coverage on uncertainty. Consistent with Hong, Lim and Stein (2000), it is expected that analysts’ coverage has a negative influence on a firm’s uncertainty, because if information diffuses more slowly and stock prices do not reflect their fundamental values, investors will be more uncertain. To test the error-in- expectation hypothesis we analyze the string of forecast errors and past performance on uncertainty. In line with Keastner (2005) who shows that investors react more heavily on a series of forecast errors, we expect that when analysts have been wrong in their earnings forecasts for a stock a couple of times, this, in itself, may lead to higher uncertainty among analysts. Furthermore, when stocks had a bad past performance and analysts have been wrong in their forecasts before, we expect uncertainty to increase. The analysis is going to proceed as follows. We divide stocks into quintiles based on past performance, size-adjusted analyst coverage and one-year forecast errors. Next, we measure dispersion in analysts’ earnings forecasts. In addition, we apply a comprehensive multivariate analysis to test whether uncertainty is increasing with low size-adjusted analyst coverage, too optimistic forecast errors and poor past performance. In section 4.3.2, we analyze whether uncertainty is increasing when analysts have been wrong in their forecasts for two consecutive years. In section 4.3.3, we analyze whether the chance of a style switch increases when analysts become more uncertain. We test whether excess size-adjusted analyst coverage, string of one-year forecast errors, and past performance have predictive power with respect to style migration. We test whether dispersion in analysts’ earnings forecasts is higher for switching-style

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 99 style effects stocks than fixed-style stocks. Then we apply a multivariate probit-analysis to test whether size-adjusted analyst coverage, the string of one-year forecast errors and past performance have significant predictive power to style migration.

4.3.1 Dispersion of analysts’ earnings forecasts, forecast errors, and value versus growth styles

In this section, we examine the impact of size-adjusted analyst coverage and the string of forecast errors on uncertainty. In line with the information- diffusion and error-in-expectation hypothesis, we expect that size-adjusted analyst coverage and the string of forecast errors in the past are negatively associated with the dispersion in analysts’ earnings forecasts. If analyst coverage is limited and firm-specific information moves more slowly across the investing public (Hong and Stein, 1999), firms with low analyst coverage should be more vulnerable to higher forecast errors and, therefore, to higher uncertainty. In addition, firms with low analyst coverage and a string of too optimistic forecasts should display higher uncertainty relative to the firms with a string of too pessimistic forecasts. As a proxy for uncertainty faced by investors we use dispersion in analysts’ earnings forecasts. The dispersion in analysts’ earnings forecasts

(Dispt) is measured as the standard deviation of the one year-ahead analysts’ earnings forecasts made eight months before the fiscal year end, standardized by the stock price at the beginning of the fiscal year. In table 4.2, we examine the impact of size-adjusted analyst coverage and 1-year forecast errors, FEt-1, on the dispersion in analysts’ earnings forecasts. We sort stocks on dispersion in analysts’ earnings forecasts into quintile portfolios: P1 through P5. Portfolio P1 contains the stocks with the twenty percent lowest dispersion and portfolio P5 contains the stocks with the

100 Chapter 4. The drivers behind uncertainty and style migration twenty percent highest dispersion. Consistent with the hypothesis that stocks with low analyst coverage are more uncertain than stocks with high analyst coverage, the evidence in table 4.2 shows that the 1-year ahead forecast errors are a negative function of analysts’ dispersion. Companies with high analysts’ dispersion also have larger negative 1-year forecast errors. The difference between the portfolio with the highest and lowest dispersion in analysts’ earnings forecasts is 2.28% (rounded to 2.3% in the table). The 1-year forecast errors for the lowest dispersion portfolio is 0.001 and the 1-year forecast errors for the highest dispersion portfolio is -0.032, a difference of 0.032. This implies that analyst uncertainty is increasing with the magnitude of the 1-year forecast errors in the last period. When the 1- year forecast error was high, investors will be more uncertain with respect to future earnings. These results are confirmed by Ackert (1997). In addition, the value of |P5–P3|/|P3–P1| ratio14 reported in the last row of table 4.2 is above one for the 1-year forecast errors and for analyst coverage, suggesting that the negative relation between dispersion and forecast errors versus analyst coverage is stronger when dispersion is high than when it is low. Another interesting pattern that emerges form table 4.2 is that firms with higher dispersion in analysts’ earnings forecasts more frequently have negative earnings and lower investment opportunities, as evidenced by the lower Tobin’s q. The median difference in Tobin’s q between firms with low and high analysts’ dispersion is 0.677 and statistically significant. The inclusion of Tobin’s q is dictated by other studies that have shown that analyst coverage and Tobin’s q are related (see, e.g. Doukas, Pantzalis and Kim, 2000, Doukas, Kim and Pantzalis, 2004).

14 This ratio shows that the bulk of the uncertainty effect seems to come from the uncertainty stocks, as opposed to low uncertainty stocks. Most of the differences come from the difference between P5-P3.

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 101 style effects The mean difference (P1-P5) in the percentage of firms with positive earnings is 34.5% and statistically significant at the one-percent level (t- statistic=8.608). Finally, we examine whether there is a direct relation between dispersion in analysts’ earnings forecasts and future returns. The two columns at the right-hand side of table 4.2 list the post formation and prior formation average annual returns. We find that the dispersion in analysts’ earnings forecasts is a decreasing function of post and prior formation returns. The post formation average annual return is 8.0% for the low dispersion portfolio and the average annual ex post return for high dispersion portfolio is -1.6%, for a difference of 9.6%. Our results confirm the results of Ackert (1997) and Diether et al. (2002), who find abnormal returns for portfolios with lower uncertainty. To examine whether the previous findings are driven by book-to- market effects, we perform additional tests. We divide stocks according to their book-to-market ratios into value or growth (using the methodology explained in section 4.2) and subdivide each of these two portfolios into quintile portfolios based on dispersion in analysts’ earnings forecasts. Table 4.3 presents the results. The differences in uncertainty between the low and high uncertainty portfolio do not seem to deviate from each other for value and growth stocks. Uncertainty appears to deviate by almost 2.20% for value stocks between stocks with low uncertainty and high uncertainty. For growth stocks the magnitude of the difference in dispersion is 2.48%. Although the distribution is equal, the number of stocks with high uncertainty is lower for growth stocks (1328) than for value stocks (2434). The opposite is shown for the low dispersion portfolio where the number of growth stocks is 4132 and the number of value stocks is 537. This implies that on average the future earnings of value stocks are more uncertain than for growth stocks. We find the same result when the stocks are divided on analyst dispersion scaled by its absolute 1-year forecast.

t short short ) are defined defined are ) t-1

a

12,t quintile portfolios, portfolios, quintile e standarddeviation 5.857 0.080 overage is the residual residual the is overage rrors (FE1 1.472 a R ** 12,t-1 0.324 -0.096 -0.096 0.324 ) and over the period July of year year of July period the over and ) 12,t-1 4.932 R ** ( t 0.611 -0.123 -0.016 -0.016 0.611 -0.123 0.888 0.054 0.158 0.789 0.066 0.105 0.699 0.033 0.032 Tobin's q Tobin's R is the fraction of stocks with positive earnings in year in year earnings positive with stocks of fraction is the

+ t d * isd 5% significance * level. 2108.881 a

+ t ** Earn -1 to March of year year of -1 March to t Earn liquidating value+bookvalue of long-term debt+(short term debt- term debt+(short long-term of value+bookvalue liquidating pril of year year of pril efore the fiscal year end) divided the by price. Analyst c Analyst Analyst s forecasts and annual returns. Portfolios P1 through P5 are P1 through Portfolios returns. annual and forecasts s coverage coverage fiscal year end divided theby price. The 1-year forecast e overage on firm size. 2.257 8.608 2.257 ). The dispersion in the earnings analysts’ forecasts is defined as th t **

t-1 Disp Chapter 4. The drivers behind uncertainty and style migration FE1 t Disp ) n -0.032 0.023 - -0.677 -0.345 -0.069 2275.961 7.308 7.415 0.357 2.375 3.915 ns ( ). The significance levels are presented with stars, is where 1% an ** observatio Number of of Number 12,t R +1 ( t is measured as: [market value of common equity+preferred stock equity+preferred common of value [market as: measured is P1] P3]/ P3]/ − P1 − − P1 (Low) 5650 0.001 0.001 0.001 0.959 1.288 0.201 (Low) 0.055 5650 Portfolios P1 P2 P3 (High) 5590 0.022 -0.032 P4 -0.014 0.614 5992 0.003 -0.000 P5 0.072 5985 0.005 -0.003 Difference 0.953 0.041 5931 0.009 -0.011 P5 0.918 0.003 Kruskal- 0.834 Wallis [P3 [P5 t-statistic over 26 years a Tobin’s q -1. to June of year year of to June formed on the dispersionin analysts’ earnings forecasts ( of the one fiscal year ahead earnings as of eight months before the 102 Table 4.2: Portfolios on formed dispersion analysts’ earnings in forecasts earning analysts’ in dispersion of values median reports table This as the difference in actual value and the 1-year forecast (8 months b t analyst coverage, where the residuals come from a regression of c term assets)]/net assets. Annual returns are calculated over the period A period the over calculated are returns Annual assets. assets)]/net term

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 103 style effects The average dispersion for value stocks is 0.0093 and the average dispersion for growth stocks is 0.0071. + Table 4.3 shows similar results with respect to Earnt and Tobin’s q. Firms with higher dispersion in analyst earnings forecasts more frequently have negative earnings and lower investment opportunities. Furthermore, there is a negative relation between dispersion in analysts’ earnings forecasts and future returns. The difference in future returns is -13.3% for value stocks and is -19.5% for growth stocks. To differentiate between the information diffusion hypothesis and the error-in-expectation hypothesis, we examine dispersion in analysts’ earnings forecasts (Dispt) and average annual returns of firms sorted on past twelve month returns and size-adjusted analyst coverage. We sort stocks based on past performance and size-adjusted analyst coverage into low (bottom 30%), medium (intermediate 40%) and high (top 30%) portfolios. The loser portfolio contains the 30% stocks that are the worst performing over the period April of year t-1 to March of year t. The winner portfolio contains the 30% stocks with the best performance over the past twelve months. The results in table 4.4 panel A show that for a constant level of analyst coverage, low (high) past performance is associated with high (low) analysts’ dispersion and lower (higher) future returns. The Dispt is 1.11% for the loser portfolio with low analyst coverage and Dispt is 0.75% for the loser portfolio with high analyst coverage. The Dispt is 0.35% for the winner portfolio with low analyst coverage and Dispt is 0.31% for the winner portfolio with high analyst coverage. Similar results are obtained when we divide stocks on 1-year forecast errors (FE1t-1) and ex ante twelve month returns (see panel B).

a

a

). The ). The 12,t 12,t 0.041 0.027 0.160 0.118 0.144 -0.038 -0.038 R ad earnings earnings ad ssets. Annual Annual ssets. +1 ( 2.414 2.793** t a a R 12,t-1 ts)]/net a ts)]/net dispersion in analysts’ 0.205 0.082 0.151 0.105 0.070 -0.279 -0.195 -0.195 -0.279 -0.181 -0.181 0.042 -0.005 -0.005 age, where the residuals is measured as: [market to June of year year of to June t Tobin’s q Tobin’s -1. t 1.485 -0.039 -0.115 1.617 0.380 0.074 0.174 1.541 1.500 1.995 0.240 0.080 0.668 0.399 0.484 -0.015 -0.256 -0.133 -0.133 -0.256 -0.015 Tobin's q Tobin's R 8.881** 3.473** 8.881** 194.664** 3.763** 194.664** a a

+ t ) are defined as the difference in 1-year forecast t-1 0.941 0.750 0.878 0.969 0.873 0.937 Earn FE1 38** 7.017** 38** 89** 7.566** 89** ) and over the period July of year year of July period the over and ) 0.081 0.000 0.029 0.086 0.016 0.072 Analyst Analyst coverage coverage 12,t-1 R ) is defined as the standard deviation of the one fiscal year ahe year fiscal one the of deviation standard the as defined is ) t ( t ub-portfolios based on dispersion in analysts’ earnings analysts’ on dispersion in ub-portfolios based

Disp t-1 0.000 -0.006 -0.006 -0.002 -0.002 -0.000 -0.000 -0.018 -0.018 -0.004 -0.004 * is 5% significance * level. ice. Theice. 1-year forecast errors ( nings forecasts and annual returns. Portfolios are formed on the formed are Portfolios returns. annual and forecasts nings orecasts ( FE1 lue+bookvalue of long-term debt+(short term debt-short term asse term debt-short term debt+(short long-term of lue+bookvalue t is the fraction of stocks with positive earnings in year in year earnings positive with stocks of fraction is the e divided theby price. Analyst coverage is the residual analyst cover + Chapter 4. The drivers behind uncertainty and style migration -1 to Marchyear of Disp t 0.002 0.002 0.008 0.004 0.009 0.004 Earn ) n 0.025 -0.043 0.050 -0.273 -0.273 0.050 -0.043 0.025 0.022 -0.024 -0.116 -0.420 0.510 -0.420 -0.116 -0.024 0.022 portfolios 537 0.001 -0.002 -0.068 0.912 1328 0.022 -0.023 -0.031 0.537 4132 0.000 0.001 0.085 0.956 2434 0.026 -0.045 -0.018 0.639 0.365 Number of of Number observations ( P1 P1 − − Value Growth portfolios portfolios Growth Portfolios P5 (high) P5 (high) Difference P5 Difference P4 1872 P3 1396 P2 887 P1 (low) P1 (low) 905** 226.3 235.905** Kruskal-Wallis P5 (high) P5 (high) P4 2899 Difference P5 Difference P3 2052 P1 (low) P1 (low) P2 2899 691** 507.8 474.691** Kruskal-Wallis t-statistic over 26 years years 26 over t-statistic 104 earnings forecasts. The dispersion the of analysts’ earnings f Table 4.3: Value and growth s into stocks classified forecasts ear in analysts’ dispersion of values median reports table This as of eight monthsbefore the fiscal year end divided theby pr (8 months before the fiscal year end) and the actual valu size. on firm coverage of regression a from come significance levels are presented with stars, where is 1% and** returns are calculated over the period April year of value of common equity+preferred stock liquidating va liquidating stock equity+preferred common of value a

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 105 style effects Holding the level of 1-year forecast errors constant, stocks with low (high) past performance have on average higher (lower) analysts’ dispersion and lower (higher) future returns. For example, the difference in Dispt between the loser portfolio with low FE1t-1 and the loser portfolio with medium

FE1t-1 is 1.13%. The winner portfolio shows a difference in Dispt between the low and medium FE1t-1 of 0.68%. For the portfolios with low FE1t-1, the difference between the loser and winner portfolio is 0.74%. Overall, the results in tables 4.3 and 4.4 demonstrate that future returns decline with increasing uncertainty. This is true even after controlling for analyst coverage and 1-year forecast errors, respectively, indicating that firms with higher uncertainty tend to be firms with low past performance. These results show invariably that dispersion in analysts’ earnings forecasts is increasing when analyst coverage is low, forecast errors are high and negative and past returns are low in the year before. The change in uncertainty is consistent with the information diffusion hypothesis and the error-in-expectation hypothesis.

4.3.2 Dispersion of analysts’ earnings forecasts and the multiple of forecast errors

The previous results show that dispersion in analysts’ earnings forecasts are negatively related to 1-year forecast errors and analyst coverage. The magnitude of the forecast errors may be the result of low analyst coverage (Doukas, Kim and Pantzalis, 2004). The lower the analyst coverage of a stock, the higher the forecast error will be. Another reason for high analysts’ dispersion is that analysts become uncertain about a stock, when they have been wrong more than once in succession with their earnings forecasts of that stock. Huberts and Fuller (1995), and Keastner (2005) find that earning surprises have predictive power with respect to stock returns.

). ). H and FE M FE , L FE ht months before the the before ht months 62.125** 62.125** 19.372** 19.372** 11.024** 11.024** s are formed on twelve- on formed are s Kruskal-Wallis -1 t toMarch and year of t one fiscal year earnings as

H P

− L s 1% and is 5% significance * level. 0.004 0.001 0.000 P (0.000) (0.000) (-0.031) (-0.031) (-0.011) (-0.011) Difference Difference ) ) and 1-year forecast errorsand1-year ( ) H H P P and M 0.008 0.004 0.003 P 0.0034 0.0034 (0.069) (0.069) (0.068) (0.068) (-0.026) (-0.026) (-0.094) (-0.094) , L P on 1-year forecast errors, analyst coverage and ) ( cov. High M turns are calculated over the period April of year year of April period the over calculated are turns P st coverage ( coverage st 0.007 s forecasts and annual returns (between brackets). Portfolio 0.0102 0.0102 0.0046 0.0046 0.0034 (0.069) (0.069) (0.063) the actual and forecast of the one-year fiscal earnings as eig (-0.045) (-0.045) (-0.117) (-0.117) arnings forecasts is defined as the standarddeviation of the past performance and size-adjusted analyst coverage coverage analyst size-adjusted and performance past Chapter 4. The drivers behind uncertainty and style migration ) Medium ( ) Medium L * 1316.544** 1316.544** * 622.519** P . The significance levels are presented with stars, where i ** t+1 0.008 0.011 0.005 0.004 (0.069) (0.069) (0.057) (-0.057) (-0.057) (-0.114**) (-0.114**) Low cov.Low ( to June of year year of to June Winner Winner Panel on A: Portfolios formed Portfolios Loser Medium Winner − Loser Difference 702.633* Kruskal-Wallis 106 formed Table 4.4: Analysts’ dispersion and portfolios This table reports median values of dispersion in analysts’ earning past performance performance past The 1-year forecast errors are defined as the difference between month lagged raw returns (into ‘loser’, ‘medium’ and ‘winner’), analy and ‘winner’), ‘medium’ ‘loser’, (into returns raw month lagged of eight months before the fiscal year end divided by the price. Annual re Annual price. the by divided end year fiscal the before months eight of fiscal end year scaled price. by The dispersionof the analysts’ e over the period of year t July

107

M,t-1 FE − 0.001 0.001 0.002 H,t-1 Difference Difference (39.460**) (39.460**) (190.254**) (190.254**) (143.496**) FE

− L,t-1

FE

M,t-1 0.011 0.008 0.007 FE

(1262.667**) (1262.667**) (2610.773**) (2610.773**) (1239.557**) Difference Difference

H,t-1 FE 0.007 0.004 0.004 0.003 (0.084) (0.084) (0.089) (-0.005) (-0.005) (-0.094) (-0.094) High

M,t-1 FE 0.005 0.003 0.003 0.003 (0.079) (0.079) (0.073) (-0.032) (-0.032) (-0.105) (-0.105)

600.472** 237.749** 237.749** 600.472** on past performance and 1-year forecast errors errors forecast and 1-year on performance past Medium Medium analysts’ forecast dispersion and L,t-1 FE 0.007 0.017 0.011 0.009 (0.053) (0.053) (0.053) (-0.065) (-0.065) (-0.118**) (-0.118**) Panel B: Portfolios formed Panel B: Portfolios Winner Winner − style effects Portfolios Low Loser Medium Winner Difference Loser 260.572** Kruskal-Wallis

4.3 Step-wise empirical analysis of [Table 4.4 continued] 108 Chapter 4. The drivers behind uncertainty and style migration

Keastner (2005) finds that stocks that have experienced a string of earnings surprises show a reversal in their stock prices when a subsequent opposite earnings surprise occurs, even when the subsequent earnings equals the analysts’ estimates. In table 4.5 we show that uncertainty and two consecutive forecasts errors with the same sign are related.

The methodology is as follows. Firstly, each stock is assigned according to the 1-year forecast errors into low (bottom 30%), medium (intermediate 40%) and high (top 30%) portfolios. The bottom 30% are stocks with negative forecast errors and is labeled as optimistic, P(opt). The top 30% are stocks with positive 1-year forecast errors and is labeled as pessimistic, P(pess). Subsequently, within each of the three portfolios we assigned each stock to one of the three portfolios according to the next year 1-year forecast-error. For example, P(opt,opt) is the portfolio with two subsequent years of too optimistic forecasts and P(pess,pess) is the portfolio with two subsequent years of too pessimistic forecasts. As can be seen from Panel A of table 4.5, dispersion is a decreasing function of the 1-year forecast errors. The median value of dispersion is 0.015 for the portfolio with two consecutive years of too optimistic forecast errors (portfolio P(opt,opt)) and the median value is 0.007 for the portfolio with a too optimistic in year 1 and a too pessimistic forecast error in year 2, P(opt,pess). The median value of dispersion is 0.012 for the portfolio with the first year too pessimistic and second year too optimistic forecast errors (portfolio P(pess,opt)) and the median value is 0.004 for portfolio P(pess,pess). This indicates that analysts are more uncertain when they have been wrong in their earnings forecasts two years in a row. Another result that comes up is that the more pessimistic analysts are about stocks, the higher the returns will be the year after. For example, the average annual return is 0.04% for P(opt,opt) (in the table rounded to 0.000) and the average annual return for portfolio P(pess,pess) is

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 109 style effects 10.1%, for a rounded difference of -10.1% which is significant at 5% level (see table 4.5).

Table 4.5: Two consecutive years of forecast errors and uncertainty Portfolios are formed on two subsequent years (t-2 and t-1) of 1-year forecast errors. First we divide stocks into three portfolios from negative to positive forecast errors: P(opt), P(med) and P(pess). Thereafter we form portfolios based on two subsequent years of 1-year forecast errors. For example, P(opt,opt) is the portfolio with two subsequent years of the lowest forecast errors. P(med,opt) is the portfolio with stocks that belongs in the first year in the portfolio with medium forecast errors and stocks belong in the second year to the portfolio with the lowest forecast errors. Dispt is the median of dispersion in analysts’ earnings forecasts in April of year t. R12,t is the average annual return for July of year t to June of year t+1. Kruskal-Wallis tests are performed to test whether the median differences in Dispt are significant; ** is 1% significance level, * is 5% significance level. T-tests are performed to test whether mean differences in Dispt are significant. Panel C: growth Panel A: all stocks Panel B: value stocks stocks Portfolios Dispt R12,t Dispt R12,t Dispt R12,t P(opt,opt) 0.015 0.000 0.020 0.004 0.013 -0.002 P(opt,med) 0.007 0.036 0.010 0.092 0.005 -0.049 P(opt,pess) 0.007 0.062 0.009 0.095 0.005 0.057 P(opt,opt)− 0.008** -0.062** 0.011** -0.091** 0.008** -0.059** P(opt,pess) P(med,opt) 0.010 0.043 0.012 0.022 0.008 0.002 P(med,med) 0.003 0.088 0.004 0.085 0.002 0.070 P(med,pess) 0.003 0.091 0.005 0.118 0.002 0.056 P(med,opt)− 0.006** -0.048** 0.007** -0.096** 0.005** -0.054** P(med,pess) P(pess,opt) 0.012 0.035 0.016 0.051 0.008 0.028 P(pess,med) 0.003 0.066 0.005 0.099 0.002 0.046 P(pess,pess) 0.004 0.101 0.007 0.161 0.003 0.069 P(pess,opt)− 0.008** -0.066** 0.009** -0.110** 0.005** -0.041** P(pess,pess) P(opt,opt)−P 0.012** -0.101** 0.012** -0.157** 0.011** -0.071** (pess,pess)

In addition, we have also controlled our analysis for the impact of the book- to-market ratio, see panels B and C of table 4.5. Here the subsamples of value stocks and growth stocks each contain 30% of the total stock sample, according to the methodology that has been explained in section 4.2. The dispersion in analysts’ earnings forecasts is more extreme for value stocks than for growth stocks. When analysts were too optimistic two years in a

110 Chapter 4. The drivers behind uncertainty and style migration row, the dispersion for value stocks is 0.020 and the dispersion in analysts’ earnings forecasts for growth stocks is 0.013, yielding a difference of 0.006.

Table 4.6 presents the change in dispersion (∆Disp) for each of the nine portfolios which are similar to the ones in table 4.5. To control for changes in price effects, the dispersion in analysts’ earnings forecasts is scaled by the price of year t-1. Independent of the forecast errors of last year (FE1t), analysts’ dispersion is higher for stocks with too optimistic earnings forecasts the year before (FE1t-1) compared to stocks with too pessimistic forecasts the year before. For example, dispersion in analysts’ earnings forecasts is 0.014 for P(opt,opt), 0.007 for P(med,opt) and 0.011 for P(pess,opt). In addition, uncertainty is increasing when past forecast errors are high the last year (FE1t) and decreasing when past forecast errors were low. For example, portfolio P(pess,opt) shows an increase in dispersion of 0.002. Also, when past forecast errors were too optimistic in the first year and too pessimistic in the second year, dispersion is decreasing by 0.003. These findings are consistent with Keastner (2005) in the sense that investors react more heavily to a series of surprises. The change in dispersion seems to be asymmetric. The portfolios with medium 1-year forecast errors in the first year, P(med,..), show an increase of 0.001 in analysts’ dispersion when analysts become too optimistic and a change of 0.001 in dispersion when analysts became too pessimistic in the year after. The results indicate that bad news leads to higher uncertainty compared to good news. To control for book-to-market effects, we also examine the change in analysts’ dispersion for value and growth stocks (see panels B and C of table 4.6). In the case of value stocks, the dispersion in analysts’ earnings forecasts increases with 0.003 when the forecast errors are extremely positive the first year and too negative the second year (P(pess,opt)). This implies that analysts become more nervous when forecasts are too

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 111 style effects optimistic. When the forecast error increases from negative to positive P(opt, pess), dispersion in analysts’ earnings forecasts decreases with 0.001. Growth stocks, on the other hand, show that the change from positive forecast errors to negative forecast errors (P(pess,opt)) leads to an increase in uncertainty of 0.001. The change from extreme negative forecast errors to positive forecast errors in the subsequent year (P(opt,pess)) leads to a decrease in uncertainty of 0.0002 (in table 4.6 rounded to 0.000). For value stocks, dispersion in analysts’ earnings forecasts seems to be more sensitive to negative changes in 1-year forecast errors than in the case of growth stocks.

The results of the previous section 4.3.1 have shown that uncertainty is negatively related to analyst coverage and 1-year forecast errors. The outcomes in tables 4.5 and 4.6 of the present section show that a string of forecast errors has impact on analysts’ forecast dispersion. In summary, the evidence suggests that information and past earnings surprises play an important role in explaining analysts’ uncertainty, measured in terms of dispersion in analysts’ earnings forecasts. Moreover, our results may imply that low analyst coverage and a string of too optimistic forecasts lead to higher uncertainty among analysts and to lower returns in the future.

are t is the the is

Disp Disp

∆ Disp -1.

t ∆ and and t

t n differences in n differences y and migration style y l of year l year of Disp Panel C: growth stocks t-1 Disp

Disp

∆ * 0.002** 0.004** 0.005** 0.005** 0.004** 0.002** * 0.001

t 004** 0.001** 0.002** 0.003** 0.003** 0.002** 0.001** 004** 0.001 0.005** 0.004** 0.005** 005** 0.001 nd the change in dispersion earnings analysts’ in Disp Panel B: value stocks Panel B: stocks value t-1 015 0.015 -0.001 015 0.015 -0.001 0.013 0.013 0.000 -0.001** 0.006 0.008 -0.002* 010 0.008 0.001* 0.006 0.005 0.001** 007 0.009 0.003** 0.007 009 0.012** 0.000** 0.008 0.002 0.002 0.001 0.001** -0.000** 004 0.004 0.003 0.003 -0.001** 006 0.008 0.014 0.011 -0.003 0.014 0.011 -0.003 0.010 0.008 -0.001 0.000** 0.004 0.004 0.000 0.002 0.002 0.001** 0.005 0.005 0.000 0.003 0.003 Disp vel. vel. . Kruskal-Wallis tests are performed to test whether the media the to test whether performed are tests . Kruskal-Wallis t Disp

∆ is the median dispersion in analysts’ earnings forecasts in Apri t -1 and year t Disp

t Panel A: all stocks Panel A: all stocks Disp t-1 0.000 0.003** 0.004** 0.002** 0.004* 0.002** 0.004** 0.000 0.003** 0.003** 0.003** 0.003** 0.003** 0.001** 0. 0.002** 0.006** 0.003** 0.003** 0. 0.003** Disp Variables Portfolios P(opt,opt) 0. 0.014 -0.000 0.015 P(opt,med) 0.008 0. 0.007 -0.002** 0.015 P(opt,pess) -0.003** 0.011 P(opt,opt)- P(opt,pess) 0.006 P(med,opt) 0. 0.008 0.001** 0.003 P(med,med) 0.003 0.000** 0.004 P(med,pess) 0.004 0.001** P(med,opt)- P(med,pess) 0.008 P(pess,opt) 0. 0.010 0.002** 0.003 0. 0.003 0.000** P(pess,med) 0.004 P(pess,pess) 0. 0.005 -0.001** P(pess,opt)- P(pess,pess) difference in analysts’ dispersion of year 112 Table 4.6: Two consecutive years of forecast errors a 5. to table similar formed are Portfolios drivers Chapter 4. The behind uncertaint forecasts significant; ** is 1% significance level, * is 5% significance le significance is 5% * level, significance is 1% ** significant; 4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 113 style effects

4.3.3 Dispersion of analysts’ earnings forecasts and style migration

In the previous sections we showed that analysts’ dispersion can predict future returns even after controlling for book-to-market ratio. In this section we test whether dispersion in analysts’ earnings forecasts can explain style migration. In doing so, we explicitly use the underlying assumption that the dispersion of analysts’ forecasts proxies investor uncertainty regarding stock’s future earnings (see section 4.1). While superior returns of value stocks have been shown by, a.o. Lakonishok, Shleifer and Vishny (1994) and Fama and French (1992), we have shown in the previous chapter 3 that the value premium is primarily driven by the migration of stocks from one style to another. This is the result of drastic changes in expectations of investors. It implies that at the time portfolios are formed, investors perceive relatively high uncertainty about future earnings for stocks that switch in the year after formation. We therefore also examine whether the ambiguity of investors about future performance of ‘style-switchers’ is greater in comparison to ‘fixed-style’ stocks. Before we analyze whether style migration is the result of uncertainty, we first examine whether the switching nature of stocks is driven by a small number of industries. To this end we check the two-digit Standard Industrial Classification code of each stock. The two-digit SIC grouping is based on Boudoukh and Richardson (1994) and Moskowitz and Grinblatt (1999). Table 4A.1 in the appendix presents an overview of the number of stocks that belong to each industry, distinguished among value and growth stocks and the subdivision of switching- versus fixed-style stocks.

114 Chapter 4. The drivers behind uncertainty and style migration

The average number of value, switching-value and fixed-value stocks per industry is 1404, 505 and 898, respectively. The average numbers for growth, switching-growth and fixed- growth stocks are 1635, 541 and 1094. The lowest number of stocks belonging to an industry for both stocks is the railroads industry. We perform an F-test to test the hypothesis that the mean percentages for switching- and fixed style stocks within each industry are equal. The F-test shows that the hypothesis of equal means cannot be rejected. This implies that the mean percentages of stocks in a particular industry are essentially equal for switching or fixed-style stocks for both value and growth stocks. This suggests that there is little cross-sectional variance in the mean percentages of stocks across industries, meaning that the switching behavior is not industry-dependent. As we mentioned above, in this section we test whether the ambiguity of investors about the future performance of style-switchers is larger in comparison with fixed-style stocks. The results are reported in table 4.7. They show that the dispersion of analysts’ earnings forecasts is larger for switching-style stocks than for fixed-style stocks, indicating that the future growth prospects of switching-style stocks are subject to greater uncertainty. The results also show that for value stocks the book-to-market ratio and the dispersion of analysts’ earnings forecasts are not positively related. The book-to-market ratio of switching-value stocks is lower in comparison to the book-to-market ratio of fixed-value stocks (difference of -0.119), whereas the scaled dispersion measures are higher (difference of 0.001). The difference in dispersion is for both measures statistically significant at a 1% level. On the other hand, fixed-growth stocks have a higher book-to-market ratio than switching-growth stocks.

115 | 1 /|F t 0.017 0.039 s /P Disp t N is the number observations. of ). ). ). BM 1 F Growth stocks stocks Growth

0.330 0.004 0.056 0.004 0.330 book-to-market ratio’s ( ratio’s book-to-market | N | N BM Disp 1 /|F t and absolute by 1-year forecasts ( P

gs forecastsgs and of /P Disp t

23.447** 16.406** 16.406** 23.447** 192.401** 284.388** Value stocks stocks Value ) are scaled by price t analysts’ forecast dispersion and 1.297 0.009 0.089 98200.261 0.002 98200.261 0.089 0.009 1.297 Disp

0.001 -0.119 0.011 0.069 0.002 N BM Disp N BM Switching 2361 1.178 0.010 0.099 4294 0.099 0.010 1.178 2361 Switching 3579 Fixed Difference Switching–Fixed Kruskal-Wallis

style effects 4.3 Step-wise empirical analysis of Table 4.7: Dispersion in analyst earnings forecasts for switching andfixed-style stock This table reports median values of dispersion in analysts’ earnin dispersionThe earnings forecasts in ( analysts’

116 Chapter 4. The drivers behind uncertainty and style migration

In order to refine our analysis further, we correct for size-effects (consistent with the findings by Lakonishok, Sleifer and Vishny, 1994, and Fama and French, 1992). We examine whether the median values of dispersion of analysts’ earnings forecasts change when we divide switching and fixed- style stocks into size-portfolios. Each stock is classified into one of the three portfolios (30-40-30%) depending on its size. The results reported in table 4.8 indicate that small stocks have a higher dispersion of analysts’ earnings forecasts than large caps (in all cases the dispersion difference ‘small-large’ is positive). This means that analysts are more uncertain about the future earnings of small caps as compared to future earnings of large caps. These results are consistent with Fama and French (1992) and Doukas, Kim and Pantzalis (2003), who show that the superior returns of size portfolios are based on risk. The results reported in panel A of table 4.8 show that the median dispersion in analysts’ earnings forecast is the highest (0.013) for small switching-value stocks, while the corresponding median values for large fixed-value stocks is the lowest (0.006). Growth stocks appear to show the same results (see panel B), although, small caps show slightly higher dispersion for the fixed-growth stocks than for the switching growth stocks. The difference in forecast dispersion among analysts for small caps is not significant in the case of growth stocks. Although we find size-effects as important inputs for uncertainty among investors, not all uncertainty is explained by size. In each size-portfolio the differences in median values of switching versus fixed style stocks (except small growth stocks) are significant at 5% level (see right-hand column). These results provide evidence that investors are more uncertain about the future earnings of switching-style stocks than of fixed-style stocks. In addition, investors are more uncertain about small-cap stocks than about large- and medium-cap stocks.

4.3 Step-wise empirical analysis of analysts’ forecast dispersion and 117 style effects

Table 4.8: Dispersion in analysts’ earnings forecasts of switching versus fixed-style stocks and of size sorted stock portfolios Size portfolios are formed on market capitalization of March in year t. Switching stocks are stocks that belong one year to the same style. Fixed-style stocks belong two or more consecutive years to the same style. N is the number of observations. The dispersion in analysts’ earnings forecasts (Dispt) are scaled by price. Kruskal-Wallis tests are performed to test whether the median differences in Dispt are significant; ** is 1% significance level, * is 5% significance level. Panel A: Value stocks Switching Fixed Difference Size switching- Kruskal- N Disp /P N Disp /P Portfolios t t fixed Wallis Small 1240 0.013 1766 0.011 0.002 18.204** Medium 710 0.008 1121 0.008 0.001 1.169** Large 410 0.007 692 0.006 0.001 4.587* Difference Small– 0.005 0.005 Large Kruskal- 72.029** 89.444** Wallis Panel B: Growth stocks Size switching- Kruskal- N Disp /P N Disp /P Portfolios t t fixed Wallis Small 1594 0.004 2452 0.005 -0.000 1.180 Medium 1767 0.003 3998 0.003 0.001 71.442** 180.855* Large 933 0.003 3370 0.002 0.002 * Difference Small– 0.001 0.003 Large Kruskal- 32.826** 498.138** Wallis

In summary, a first important finding is that information and past earnings surprises play an important role in explaining analysts’ uncertainty, measured in terms of dispersion in analysts’ earnings forecasts. Uncertainty increases more when analysts are too optimistic for two consecutive years. In addition, our findings show that uncertainty is negatively related to bad past performance in stock returns. These findings are consistent with the error-in-expectation hypothesis. Furthermore, the results suggest that if less

118 Chapter 4. The drivers behind uncertainty and style migration information is revealed about a company (low size-adjusted analyst coverage), uncertainty will be higher. This is in line with the information diffusion hypothesis of Hong and Stein (1999). The second important finding is that analysts are more uncertain about the prospects of earnings of switching-style stocks compared to fixed-style stocks.

4.4 Robustness tests

In the previous sections, we have identified a number of variables that are related to uncertainty. In this section we test which of these variables are significant in a multiple regression. In section 4.4.1, we apply a comprehensive multivariate analysis and in section 4.4.2, we apply a probit regression analysis to test whether these variables have significant power to predict the style switch of a stock the year after portfolio formation.

4.4.1 Comprehensive multivariate analysis of analysts’ forecast dispersion

In this section we apply a comprehensive multivariate analysis to test for the simultaneous impact of the relevant variables and test which of these variables are statistically significant. We examine whether dispersion in analysts’ earnings forecasts (Dispi,t) is related to the following variables: 1- year forecasts errors (FEi,t-1), the string of forecast errors (measured by dummy variables d1,i, d2,i and d3,i), size-adjusted analyst coverage (Covi,t-1),

Tobin’s q (Tobinqi,t-1), annual return (R12,i,t-1), a dummy for + positive/negative earnings ( Earni,t−1 ), book-to-market ratio (BMi,t) and the log of market capitalization (Sizei,t). The effect of the string of forecast

4.4 Robustness tests 119 errors on dispersion is measured by three dummies. The dummy represents the interaction between the 1-year forecast error in periods t-2 and t-1, where d1,i is (FE1 i,t-2=1)*(FE1 i,t-1=1), d2,i is (FE1i,t-2=1)*(FE1 i,t-1=2) and 15 d3,i is (FE1i,t-2=1)*(FE1 i,t-1=3) . The equation we estimate is as follows:

Disp = β + β FE + β d + β d + β d + β Cov + β Tobinq + i,t 0 1 i,t−1 2 1,i 3 2,i 4 3,i 5 i,t 6 i,t (4.1) + β7R12,i,t−1 + β8Earni,t−1 + β9BMi,t + β10Sizei,t + εi,t

The regression controls for the impact that growth opportunities, measured as Tobinqi,t, have on analysts’ forecast dispersion and the impact that negative earnings have on analysts’ forecast dispersion. The inclusion of

Tobinqi,t is dictated by other studies that have shown that analyst coverage and Tobinqi,t, are related (see, e.g. Doukas, Kim and Pantzalis, 2000, and Doukas, Pantzalis and Kim, 2004). A dummy for positive + earnings, Earni,t−1 , is included, because the study by Ali, Klein and Rosenfeld (1992) shows that the degree of overestimation is most evident for firms with negative earnings. Furthermore, the regression controls for book-to-market and size effects. Table 4.9 shows the time-series averages of the coefficients from year-to-year Fama and MacBeth regressions of the cross-section of analysts’ dispersion on the variables mentioned in equation 4.1. Following the procedure of Fama and MacBeth (1973), we run a regression separately for each year in which the dependent variable is the analysts’ forecast dispersion on stock i and the independent variables are the characteristics of stocks i (i.e. independent variables in (4.1)) observed at the beginning of the year. In our analysis, we have 26 portfolio formation periods (1976-2001) and therefore we run 26 separate cross-sectional regressions.

15 According to the 1-year forecast errors each stock is assigned into low (bottom 30%), medium (intermediate 40%) and high (top 30%) portfolios.

120 Chapter 4. The drivers behind uncertainty and style migration

Table 4.9: OLS regressions on analysts’ forecast dispersion The average slope is the time-series average of the annual regression slopes, and the t-statistic is the average slope divided by its time-series standard error. We use Newey-West correction to adjust the standard errors for autocorrelation and heteroskedasticity. The independent variables are 1-year forecasts errors (FE1i,t-1), string of 1-year forecast errors (, d1,i, d2,i and d3,i), size-adjusted analyst coverage (covi,t-1), Tobin’s q (Tobinqi,t-1), past 12-month return (R12,I,t-1), positive/negative earnings + ( Earn ), book-to-market (BMi,t) and the log of market capitalization (sizet). We use three i,t−1 dummies, d1,i, d2,i and d3,i for the string of 1-year forecast errors. The dummy represents the interaction between the 1-year forecast error in period t-2 and t-1, where d1,i is (FE1 i,t-2=1)*(FE1 i,t- 1=1), d 2,i is (FE1 i,t-2=1)*(FE1 i,t-1=2) and d 3,i is (FE1i,t-2=1)*(FE1 i,t-1=3). Each stock is assigned according to the 1-year forecast errors into low (bottom 30%), medium and high (top 30%) portfolios. Stars present significant levels: * 5% significance, ** 1% significance Variables: I II III IV 0.027** 0.068** 0.053** 0.051** Intercept (7.961) (4.155) (4.917) (10.519) -0.101** -0.095** FE1 , i t-1 (-3.406) (-3.103) 0.005** 0.004** d 1,i (3.639) (4.264) 0.000 0.001 d 2,i (0.415) (0.716) 0.009** 0.010** d 3,i (4.033) (4.249) -0.002** -0.001** Cov i,t (-2.423) (-5.768) -0.001** -0.003** -0.003** -0.006** Tobinq i,t (-2.115) (-2.205) (-2.040) (-3.571) -0.013** -0.001** R 12,i,t-1 (-3.043) (-1.999) -0.014** -0.034** -0.030** -0.012** Earn + i,t−1 (-3.414) (-4.065) (-3.947) (-3.126) -0.001 -0.003 -0.003 -0.001 BM i,t (-0.262) (-0.798) (-0.869) (-0.454) -0.001** -0.003** -0.001** -0.002** Size i,t (-4.809) (-3.105) (-6.296) (-10.114) Avg. Adj. R-squared 0.392 0.260 0.249 0.413 # of obs. 27494 27494 27494 27494 Average # of firms 1058 1058 1058 1058

The reported coefficients are the time-series averages of the coefficients obtained for each year. The t-statistics are computed using the standard error of the estimates for each year. We use Newey-West correction to adjust the standard errors for possible serial correlation and

4.4 Robustness tests 121 heteroskedasticity. Supporting to the results in tables 4.2 and 4.3, the regressions in table 4.9 show that FE1i,t-1, d1,i,, d2,i, d3,i, Covi,t, R12,i,t-1, + Earni,t−1 and sizet-1 explain the cross-section in analysts dispersion.

4.4.2 Probit analysis of style-switching behavior

The previous analyses have identified a variety of variables that are related to uncertainty. In section 4.3.3, we have shown that uncertainty is higher for switching-style stocks than for fixed-style stocks. In this section, we test which of these variables are significant in a probit analysis. We use a probit model where the dependent variable, yi, is a dummy variable representing the occurrence of an event. In this case the event is the style switch a stock may make the year after formation. The goal is to quantify the relationship between individual stock characteristics and the probability of a stock switching from style. The dependent variable, yi, takes only two values, zero and one.

 1 if stock i switches from style yi =   0 otherwise

Firstly, we test whether high dispersion in analysts’ earnings forecasts leads to a higher probability that the stock under consideration migrates from style. The following regression is considered:

y = β + β Disp + ε , (4.2) i,t 0 1 i,t i,t

where yi,t is a dummy with value one when stock i switches from style the year after formation and zero otherwise (the style-switch year is from July

122 Chapter 4. The drivers behind uncertainty and style migration of year t to June of year t+1). To test against the null-hypothesis that the slope coefficients are all equal to zero, we use the likelihood ratio test:

Lratio = 2[]L(a, β )− L(a,0) →a χ 2 (k −1), where L(a,β) is the maximized value of the log-likelihood of the model being estimated, L(a,0) is the value of the log-likelihood for a probit with only a constant term and k-1 is the number of slope coefficients. We improve the efficiency of the estimator by taking into account the serial correlation in the error term. Therefore, we estimate the standard errors using a generalized linear model (GLM) method (McCullagh and Nelder, 1989). Table 4.10 presents the outcomes of the probit for each stock with the characteristics of stocks that we have identified. We run the cross- sectional regressions, in which the dependent variable is one when a stock switches from style in the next period and zero otherwise. The independent variable is dispersion in analysts’ earnings forecasts in April of year t, Dispt. As we can see from the likelihood ratio (Lratio), the null hypothesis that the slope coefficients are equal to zero, is rejected. The coefficients of dispersion in analysts’ earnings forecasts, Dispt, are positive for value and growth stocks. This implies that the likelihood of switching increases with analysts’ uncertainty regarding future earnings. The Mac-Fadden R2, which is analogous to the R2 of linear regressions, is low with 0.003 and 0.005 respectively.

In table 4.9, we have shown that the dispersion in analysts’ earnings forecast is related to 1-year forecast errors, analyst coverage and past performance in stock returns.

4.4 Robustness tests 123

Table 4.10: Probit with dispersion in analysts’ earnings forecasts At the end of June between 1977 and 2002 we compute for every stock in the sample whether it behaves as a switcher or not in the next period. We then estimate equation 4.2. The dependent variable is a dummy with value one when the stock switches from style and zero otherwise. The independent variable is the dispersion in analysts’ earnings forecast, Dispt. Growth and value stocks are determined by the breakpoints for the bottom and top 30% of the values of the book-to-market equity for NYSE stocks (we use the breakpoints available at the website of K. French). GLM-method is used to estimate the standard errors. Stars present significant levels: * 5% significance, ** 1% significance. Value stocks Growth stocks -0.281** -0.539** Constant (-16.056) (-21.318) 1.100** 4.649** Disp i,t (3.802) (4.085) Mac-Fadden R2 0.003 0.005 Lratio 19.553** 80.484** Variance Factor estimate 1.001 1.522 # of obs. with dep.=zero 3008 8922 # of obs. with dep.=one 2023 3795

To test whether these variables have significant power to predict the style switch of a stock we apply the following regressions:

y = β + β Cov + β Tobinq + β Earn+ + β Size + ε (4.3) i,t 0 1 i,t−1 2 i, t − 1 3 i, t − 1 4 i,t−1 i,t

y = β + β FE + β d + β d + β d + β Tobinq + i,t 0 1 i,t−1 2 1, i 3 2,i 4 3,i 5 i, t − 1 (4.4) β Earn+ + β Size + ε 6 i, t − 1 7 i,t−1 i,t

+ y = β + β R + β Tobinq + β Earn + β Size + ε (4.5) i,t 0 1 12,i,t − 1 2 i, t − 1 3 i,t − 1 4 i,t−1 i,t

Table 4.11 presents the outcomes of the regression where the 1-year forecast error, FE1i,t-1, the string of forecast errors in the two years preceding the year of the style switch (d1,i, d2,i and d3,i), past annual return,

124 Chapter 4. The drivers behind uncertainty and style migration and the size-adjusted analyst coverage are the independent variables. The results of estimating (4.3) are in column I, the results of estimating (4.4) are in column II and the results of estimating (4.5) are in column III. The first result (column I) that comes up is that the coefficient of the size-adjusted analyst coverage has a positive sign for value stocks. Given the outcomes of table 4.2 and 4.3, we expect a negative relation between analyst coverage and uncertainty, because uncertainty increases when analyst coverage is low. On the other hand, the coefficient for growth stocks has the expected sign. However, the coefficients are not statistically significant and therefore not reliable. Another measure that reflects the rate of information diffusion is size. To detect size-effects in the style-switching behavior of stocks within a style, we add market capitalization in the regression (see: Sizei,t). Coefficients show negative signs, which means that the lower the market capitalization, the higher the chance will be that a stock switches from style. This may imply that the smaller the firm, the lower the rate of information diffusion and the higher uncertainty will be. The t-statistics show that size is statistically significant for value and growth stocks (except for the outcomes in column III). Hong, Lim and Stein (2004) use size as a proxy for the rate of information diffusion across the investing public and show that the profitability of momentum strategies declines with firm size. This implies that the slower firm-specific information diffusion, the more difficult it is to predict future earnings and, therefore, the higher uncertainty will be. The results in column II show that the coefficients for the 1-year forecast errors have opposite signs for value and growth stocks. This means that the 1-year forecast errors seem to be higher for fixed-value stocks than for switching-value stocks the year before the style switch. Growth stocks show the opposite, the lower the forecast error in the period for the style- switch the higher the chance that the stock switches from style. For value stocks, the coefficients for the 1-year forecast errors, FE1i,t-1, are not significant. In addition, it emerges from the table that the forecast errors

4.4 Robustness tests 125 made in April of year t-2 and t-1 for December of year t-2 and December t- 1 (style switch from first July of year t to end of June year t+1) have significant predictive power for switching dynamics of growth stocks (d1,i, d2,i and d3,i). If analysts are too optimistic two years in a row, the chance of a style switch is higher. Value stocks show negative (equation 4.4) but not significant coefficients for d1,i, d2,i and d3,i. This means that the more optimistic the analysts were in the two years before the style-switch, the lower the chance that a value stock switches from style next year. Column III presents the regression with past annual return as independent variable. The estimated coefficients are negative and significant for value stocks and growth stocks, which suggests that if value or growth stocks had negative returns in the year of formation, the chance of a style switch will be higher. The sign of the coefficients for the growth stocks are in line with Jegadeesh and Titman (1993), who find momentum in the short run. Value stocks on the other hand show contrarian effects. Looking at the log likelihood ratio, the results become better for the value portfolio after adding momentum in the probit analysis. In addition, we add other variables (Tobin’s q and a dummy for positive earnings and) in the regression, to test whether this has predictive power to style-switching. The first result emerging is that positive earnings and Tobin’s q have predictive power for the style switch the year after formation for both value and growth stocks. The coefficients for Tobin’s q show opposite signs, the coefficients of value stocks are positive and the coefficients of growth stocks are negative. This implies that if a value stock has many growth opportunities, the chance will be higher that a value stocks switches from style the next year. Overall then, table 4.10 provides further evidence that uncertainty is higher for stocks that switches from style. Table 4.11 provides evidence that past returns and the interaction between two consecutive years of forecast errors have significant power to predict style- switching the next year.

126 Chapter 4. The drivers behind uncertainty and style migration

Table 4.11: Probit-analysis with dispersion in analysts’ earnings forecasts At the end of June between 1977 and 2002 we compute for every company in the sample whether it as a switcher or not the next period. We then estimate equation 4.3 to 4.5. The dependent variable is a dummy with value one when the stock switches from style and zero otherwise. The independent variables are 1-year forecasts errors (FE1i,t-1), string of 1-year forecast errors (d1,i, d2,i and d3,i), size- adjusted analyst coverage (Covi,t-1), Tobin’s q (Tobinqi,t-1), past annual return (R12,t-1), + positive/negative earnings (EarnI,t-1 ), book-to-market (BMi,t) and the log of market capitalization (Sizei,t). We use three dummies, d1,i, d2,i and d3,i for the string of 1-year forecast errors. The dummy represents the interaction between the 1-year forecast error in period t-2 and t-1, where d1,i is (FE1i,t- 2=1)*(FE1i,t-1=1), d2,i is (FE1i,t-2=1)*(FE1i,t-1=2) and d3,i is (FE1i,t-2=1)*(FE1i,t-1=3). Each stock is assigned according to the 1-year forecast errors into low (bottom 30%), medium and high (top 30%) portfolios. GLM-method is used to estimate the standard errors. Stars present significant levels: * 5% significance, ** 1% significance. I II III Value Growth Value Growth Value Growth 0.383 0.239** 0.295 0.134* -0.071 0.248** Constant (1.385) (5.043) (1.141) (2.174) (-0.271) (3.862) -0.073 0.0020 FE i,t-1 (-0.878) (0.672) -0.045 0.129* d 1,i (-0.875) (2.215) -0.000 0.253** d 2,i (-0.000) (3.616) 0.059 0.241** d 3,i (0.767) (3.742) -0.281** -0.116** -0.289** -0.088* -0.209** -0.087* Earn + i,t−1 (-6.588) (-2.859) (-6.481) (-2.194) (-4.611) (-1.962) -0.176** -0.144** R 12,i,t-1 (-4.846) (-4.039) 0.332** -0.060** 0.332** -0.058** 0.268** -0.058** Tobinq i,t-1 (6.186) (-7.626) (6.115) (-7.774) (4.832) (-6.892) -0.028** -0.090** -0.023* -0.083** -0.010 -0.092** Size i,t (-2.097) (-9.441) (-1.961) (-9.107) (-0.794) (-8.932) 0.030 -0.007 Cov i,t (0.929) (-0.349)

4.5 Summary and conclusion 127

[Table 4.11 continued] Mc- 0.014 0.024 0.014 0.027 0.020 0.027 Fadden R2 Lratio 94.774** 378.721** 96.710** 422.324** 117.588** 410.877** Variance Factor 1.001 1.721 1.002 1.553 1.001 2.008 estimate # of obs. with 3008 8922 3008 8922 3008 8922 dep.=zero # of obs. with 2023 3795 2023 3795 2023 3795 dep.=one

4.5 Summary and conclusion

The first objective of this chapter is to seek evidence for the information diffusion hypothesis and the error-in-expectation hypothesis. As a proxy of uncertainty of investors we use dispersion in analysts’ earnings forecasts. The dispersion in analysts’ earnings forecasts reflects the analysts’ divergence of opinion in predicting future earnings. The more uncertain analysts are about future earnings of a company, the larger the divergence in opinion will be. The dispersion in analysts’ earnings forecasts (Dispt) is measured as the standard deviation of the one-year-ahead analysts’ earnings forecasts made eight months before the fiscal year end, standardized by the stock price at the beginning of the fiscal year. To test the information diffusion hypothesis, we examine uncertainty in relation with size-adjusted analyst coverage. Our findings support that if the analyst coverage is low, uncertainty will increase. This is in line with the information diffusion hypothesis of Hong and Stein (1999). To test the error-in-expectation hypothesis, we examine two consecutive years of forecast errors and past performance in stock returns. We draw several conclusions from the evidence reported in the tables. First, our

128 Chapter 4. The drivers behind uncertainty and style migration findings support that if analysts’ earnings forecasts have been wrong for two subsequent years, uncertainty will increase. This is in line with Keastner (2005) in the sense that investors react more heavily to a series of surprises. Second, after holding analyst coverage and 1-year forecast errors fixed, past performance in stock returns has a negative impact on analysts’ forecast dispersion. These findings are consistent with the results of Ackert (1997) and Diether et al. (2002), who show abnormal returns for portfolios with low uncertainty. Summarized, our findings demonstrate that firms with low analysts’ coverage, too optimistic earnings forecasts and low past performance have higher analysts’ dispersion. Hence, the evidence supports that uncertainty is consistent with the extrapolation and information diffusion hypotheses. Our empirical results also appear to hold after applying a comprehensive regression on the different variables with the dispersion in analysts’ earnings forecasts. The second objective of this chapter is to investigate whether it is more likely for a stock to migrate from style when investors are more uncertain about future earnings. The results indicate that there are differences in the dispersion in analysts’ earnings forecasts between switching and fixed-style stocks. Switching-style stocks show higher dispersion in analysts’ earnings forecasts. Hence the results support the contention that earnings uncertainty is higher for switching-style stocks than for fixed-style stocks. The results are confirmed by applying a multivariate probit-analysis. We conclude that dispersion in analysts’ earnings forecasts is positive related to style switching.

Appendix 4A 129

Appendix 4A

Table 4A.1: Description of industries for fixed versus switching-style stocks Stocks are divided into different industries based on the two-digit Standard Industrial Classification code. Between brackets are the percentages of stock in the specific industry relative to the total number of stocks in the style portfolio. In the bottom panel, an F-statistic is performed to test whether the average percentages of the different industries are equal to each other. Average Number of stocks Industry SIC Value Growth Codes All Switch Fixed All Switch Fixed 10-14 1452 542 910 1275 512 763 1. Mining (5.2%) (5.4%) (5.1%) (3.9%) (4.7%) (3.5%) 20 571 169 402 880 215 665 2. Food (2.0%) (1.7%) (2.2%) (2.7%) (2.0%) (3.0%) 22-23 679 202 477 293 124 169 3. Apparel (2.4%) (1.7%) (2.2%) (0.9%) (1.1%) (0.8% 26 316 93 223 224 68 156 4. Paper (1.1%) (0.9%) (1.2%) (0.7%) (0.6%) (0.7%) 28 854 398 456 3668 844 2824 5. Chemical (3.0%) (3.9%) (2.5%) (11.2%) (7.8%) (12.9%) 29 221 63 158 140 45 95 6. Petroleum (0.8%) (0.6%) (0.9%) (0.4%) (0.4%) (0.4%) 32 260 76 184 143 55 88 7. Construction (0.9%) (0.8%) (1.0%) (0.4%) (0.5%) (0.4%) 33 721 190 531 281 99 182 8. Prim. Metals (2.6%) (1.9%) (3.0%) (0.9%) (0.9%) (0.8%) 34 609 218 391 501 200 301 9. Fab. Metals (2.2%) (2.2%) (2.2%) (1.5%) (1.8%) (1.4%) 35 1776 740 1036 2447 858 1589 10. Machinery (6.3%) (7.3%) (5.8%) (7.5%) (7.9%) (7.3%) 11. Electrical 36 1909 860 1049 3279 1127 2152 Eq. (6.8%) (8.5%) (5.8%) (10.0%) (10.4%) (9.8%)

130 Chapter 4. The drivers behind uncertainty and style migration

[Table 4A.1 continued] 12. Transport 37 542 203 339 453 183 270 Eq. (1.9%) (2.0%) (1.9%) (1.4%) (1.7%) (1.2%) 13. Manu- 38-39 1648 696 952 3110 948 2162 facturing (5.9%) (6.9%) (5.3%) (9.5%) (8.8%) (9.9%) 14. Railroads 40 137 37 100 21 11 10 (0.5%) (0.4%) (0.6%) (0.1%) (0.1%) (0.0%) 15. Other 41-47 737 245 492 426 179 247 transport (2.6%) (2.4%) (2.7%) (1.3%) (1.7%) (1.1%) 16. Utilities 49 2768 592 2176 354 142 212 (9.9%) (5.9%) (12.1%) (1.1%) (1.3%) (1.0%) 17. Dept. Stores 53 279 94 185 220 58 162 (1.0%) (0.9%) (1.0%) (0.7%) (0.5%) (0.7%) 18. retail 50-52, 3469 1200 2269 3296 1169 2127 54-59 (12.4%) (11.9%) (12.6%) (10.1%) (10.8%) (9.7%) 19. Financial 60-69 2918 895 2023 1708 581 1127 (10.4%) (8.9%) (11.3%) (5.2%) (5.4%) (5.2%) 20. Others Other 6207 2596 3611 9975 3402 6573 (22.1%) (25.7%) (20.1%) (30.5%) (31.4%) (30.0%) Total number 28073 10109 17964 32694 10820 21874 Average 1404 505 898 1635 541 1094

numbers (4.1%) (3.9%) (4.2%) (3.7%) (3.6%) (3.7%) F-statistic (is 0.000 0.000 equal)

Chapter 5

Style popularity and the comovement of stocks∗

5.1 Introduction

In this chapter we link style investing to style popularity. Style investing has become an important issue for institutional as well as for private investors. Many institutional investors claim to follow a particular investment strategy, such as ‘value’ or ‘small-cap’. Investment strategies are often classified in terms of a specific style. A style can be defined as a classification of assets into a category based on common characteristics. Given frequent references to such categories in the media, it is likely that

∗ This chapter is a working paper of T. Wouters and A. Plantinga (2006)

131 132 Chapter 5. Style popularity and the comovement of stocks individual investors adopt and use this terminology for their own investing purposes. Meanwhile, the financial services industry has also responded to this terminology. For example, labels such as value and technology, are frequently used to reflect the objective of mutual funds. Barberis and Shleifer (2003) develop a model that explains the impact of style investing on financial markets and security valuation (see chapter 2, section 2.5.3). They combine style-based portfolio selection with a mechanism how investors choose among styles. In the model there are two kind of investors, fundamental traders and switchers 16 . The fundamental traders act as arbitrageurs that try to prevent the price of each asset to deviate too far from its fundamental value. The investment policy of switchers is determined by two distinctive characteristics. Firstly, switchers classify assets into categories where they give each category a label. In this way switchers try to simplify the information processing by making their decisions on a category level rather than an individual asset level. Secondly, the choice for a particular style is dependent on the relative past performance. Good fundamental news about the securities in a style is responsible for a style getting popular. A consequence of style investing is the emergence of life cycles of investment styles. When a style had a good past performance relative to other styles, switchers allocate to that style and withdraw resources from other styles. If the style matures, good past performance is important to add new resources to a style. The style loses its popularity when bad news arrives or when arbitrage levels out excess returns. These investment cycles show close resemblance with the fashion cycles as described by Shiller (2000).

16 In this chapter switchers have a different meaning than the switchers mentioned in chapter 3. In chapter 3 switchers are defined as stocks that migrate from one style to another style.

5.1 Introduction 133

Barberis and Shleifer (2003) hypothesize that as a consequence of investors applying style investing, comovement in prices (and returns) of styles is induced. Cornell (2004) illustrates this with an example. He shows that labeling increases the chance for investors to make errors when they allocate funds at the level of categories. Companies with different business activities might be linked to the same category. He illustrates this with two Internet companies, Yahoo and Amazon. At the start of the internet bubble the correlation between the price changes of two stocks was low (0.10). After that, the correlation between the returns started to grow to more than 0.80, and stayed above the level of 0.70 for three quarters. At the end it decreased to 0.30. Looking at the fundamentals of both companies it was not clear why these two firms should be highly correlated. Cornell suggests that the temporary popularity of the label ‘internet’ has caused investors to temporarily consider the two stocks as equivalent investment opportunities. Kumar (2002) studies the relation between style-based investing and stock returns. He divides stocks into opposite styles, value versus growth and large versus small. He uses data on the portfolio composition of the clients from a large discount brokerage house in the US and recommendations of investment newsletters from Hulbert Financial Digest. He finds evidence that individual investors formulate their demands at a style level and re- allocate funds between styles on the basis of past relative performance as well as ‘expert advice’ from investment newsletters. Pomorski (2004) examines the relation between mutual fund flows and style attractiveness. He finds that flows are positively related to past returns and negatively related to returns of competing styles. However, at the individual level the pattern disappears. If a fund does well when its style underperforms, the flow of that fund will be negatively related to the past performance of its style. The results support the hypothesis that investors evaluate fund managers both at a style-level and at a fund-level.

134 Chapter 5. Style popularity and the comovement of stocks

The main focus in this chapter is to test to what extent stock popularity can be attributed to style investing. In the context of style investing, the style investing hypothesis implies that popularity should vary at a style-level rather than at a stock-level. To test whether popularity is on a style-level rather than on a stock-level we examine the sector style dimension. We sort stocks from the US stock market into eleven different sectors. We use the cross standard deviation of the turnover ratio as a proxy for dispersion to test to what extent stock popularity can be attributed to style investing. If all stocks within a style become popular at the same time, the dispersion in turnover ratios will decrease. If only a fraction of the stocks within a style becomes popular, the dispersion of the turnover ratios will increase. The first step is to gather proxies for stock popularity that can be used as time series variables. We use a number of proxies for popularity suggested by recent work (see section 5.3), and construct a novel composite index based on principal component analysis. The resulting popularity proxies are highly correlated and the signs of the coefficients line up with expectations. We then apply a regression between the newly composed popularity index and the proxy for dispersion. We find that the popularity of stocks is stock-specific and not dependent on the investment style that the stocks belong to. In addition, we find a size-effect for stocks within styles that are not popular and no size- effect for the popular style stocks. When styles are less popular, the quintile with largest stocks has lower dispersion than the quintile with the smallest stocks. The evidence presented here challenges the view that investors base their asset allocation on a style level instead of an individual stock level. These results support the findings of Pomorski (2004) and contradict empirical work by Kumar (2002), Froot and Teo (2004), Cornell (2004) and Huang (2005). The style investing hypothesis implies that the inflow of resources should be positively related with style popularity. It is likely that style popularity is related to past returns. The representatviveness heuristic

5.2 Fashion 135

(Kahneman and Tversky, 1974) implies that investors extrapolate past performance and therefore investors believe that styles that performed well in the past will continue to do that in the future. Popularity should therefore be positively related to past returns. Our findings confirm that popularity is related to good past performance. These results fit closely with the findings of Pomorski (2004), Kumar (2002), Froot and Teo (2004) and Huang (2005). We also perform some robustness checks to show the life cycles of popularity (which can be compared to the life cycles described by Barberis and Shleifer, 2003). In addition, we perform a regression to test whether the movement in popularity of a particular style leads to comovement in returns between stocks in that style. Our findings show that an increase in popularity leads to a decrease in correlations in returns between stocks in the same style. The rest of the chapter is organized as follows: in the next section we discuss fashion in the context of investing. The reason is that popularity is closely related to fashion. First, popularity may be induced by fashion. Second, fashion and popularity both reflect the collective preferences of individuals and the changes of such preferences over time. In section 5.3 we describe several variables that measure popularity. In section 5.4 we present the methodology to form a popularity index and in section 5.5 we discuss the data and style description. In section 5.6, we interpret and discuss the results. This is followed with a robustness test in section 5.7. Finally, we provide concluding remarks in section 5.8.

5.2 Fashion

As mentioned in the previous section, the objective of this chapter is to investigate to what extent stock popularity can be attributed to style

136 Chapter 5. Style popularity and the comovement of stocks investing. Fashion may play an important role in the existence of stock popularity. Fashion can be defined as a collective preference that develops through social processes, where the need of identity and the social network are important determinants for market dynamics. In the absence of data on social interaction, fashion is closely related to popularity in the way that it both reflects the collective preferences of individuals and the changes of such preferences over time. In this section, we give a brief overview of fashion and show why it might be important for the decision-making process of investors. Investing is described in the literature as a process of individuals who choose based on their own opinions about risk characteristics and their prospects of returns rather than on other people’s opinion. Then it is less likely that investing should be vulnerable to fashions. However because fashions appear in many areas such as clothes, politics and health, it also is plausible that the fluctuations in fashion appear in the investment industry. The changes in attitude often occur widely in the population without any predictable reason. It is very plausible that fashions in investments also change spontaneously or as a social reaction to some event. Although we may be inclined to view movements in fashion in cyclical terms, it is also possible to view fashion in terms of permanent changes in collective behavior. As argued by Veblen (1899), changes in fashion are the result of a dynamic social process, where individuals are looking for ways to distinguish themselves from the large majority where the large majority is trying to copy the distinct group of innovative individuals. In Freeman’s (1994) view, fashion has a productive side, since it facilitates a cheap way of introducing innovative productive behavior. In terms of the investment industry, a new innovative way of investing can be used by a small group of elite investors, who use this investment as status enhancing. After a while, others try to copy this strategy. Eventually, this leads to the adoption of an asset class by a large group of investors. A

5.2 Fashion 137 recent example of such a transmission of a new way of investing is the emergence of hedge funds. Hedge funds, in their early stages, were offered to a small minority of investors. The official (most quoted) starting point of hedge funds was in 1949. A. Jones started an equity fund that was organized to provide flexibility in constructing a portfolio (he took long and short positions and used leverage to enhance his performance). Many hedge funds perished during the market downturns, 1969-1970, and 1973-1974. After 1974, hedge funds lost their popularity until the mid-1980s. In 1980, there were 30 hedge funds with an asset value of $193 million. During the 1990s, hedge funds became more accessible to large groups of investors and the industry became more heterogeneous. In 2005, the number of hedge funds grew to 6,900 with an asset value of $1.35 trillion17. The last couple of years, regular fund houses start to offer hedge funds to the general public.

Fashion is strongly related to the adoption cycles described in the marketing literature for product innovations. Everett M. Rogers (1983) makes a distinction between the stages of innovators, early adopters, early majority, and late majority laggards. Rogers associates these adopter groups as differing in their value orientations. Innovators are interested to try new ideas. Early adopters value the respect gained by others for their innovative consumer behavior. The early majority is deliberate in the sense that they considered the innovation carefully before actually adopting it. The late majority is skeptic, and only adopts an innovation after others do. Laggards are conservative or traditional. According to the adoption and diffusion model of Rogers, a fashion cycle starts with a small group of innovators. The demand for the product is low with 2.5% consumers adopting the product. Successively, other individuals start to emulate the fashion leaders and demand for the product is increasing to 16% of the consumers as the

17 ECB Financial Stability Review (June 2006)

138 Chapter 5. Style popularity and the comovement of stocks fashion cycle progresses. In the next phase the number of consumers that buy the product has grown to 48%. This phase is called the early majority phase. At a certain time, the number of individuals that follows the style reaches a peak. The next 32.5% of the consumers belongs to the late majority. Finally, the last group adopting the style is the laggards, which is 16% of the consumers. In appendix 5A, table 5A.1 shows the different stages of a fashion cycle for internet stocks. It is difficult to recognize when the introduction phase begins, because the small group of fashion leaders is difficult to identify. At this stage, the stocks in the particular style will be neglected by almost all equity analysts. The emulation phase is identified by a growing number of individuals that start to imitate the fashion leaders. In this phase, the face-to-face communication of the individual with friends, family and peers is very important. Some analysts will mention the stocks within a certain style and start to cover them. The investment media (papers, television, internet) may, if attention is given to the style, speed the rate of diffusion. This will lead to the early majority and late majority phase, where the general public starts to follow that particular group of stocks and where analysts become very optimistic about these stocks. The result is that optimism increases, which leads to an inflow in that particular ‘fashion’ style and an outflow in the rest of the styles. Furthermore, the increase in optimism can be noticed by an increase in volume, turnover and volatility and a decrease in the bid-ask spread. As a result the autocorrelation of the returns of that style and the correlation among stocks within the particular style increases. The number of mutual funds that start in the style and the number of IPO’s grow. Finally, the laggards’ phase shows a decrease in optimism, which lead to an outflow of resources and an increase in the bid-ask spread. Changes in fashion are related to the consumer adoption process. However, the emphasis with fashion is on the social approval of consumption behavior. This social approval is also associated with status.

5.2 Fashion 139

Buying fashion goods yields a status increase for the owner. However, the more people own the particular good, the smaller the status advantage of the particular good gets. Status wears out. Buying fashion goods is risky, since it may be difficult for an individual to make a correct assessment over its future status. An example of the riskiness of buying fashion stocks is the Internet hype. In the Internet bubble, investors tripped over themselves to buy stocks of the next hot internet company. It did not matter how much these companies lost or how awkward the operation activities were, if the name of the company included words like ‘internet’ or ‘.com’ stock price increases were guaranteed. Cooper, Dimitrov and Rau (2001) show that during the internet hype a corporate name change into dotcom related internet names lead to positive announcement returns on the order of 74% in the ten days surrounding the announcement. However, the E-commerce was still in its infancy and had not developed very much. In 1998, the internet industry was characterized by red marks, which would have made traditional companies desperate, but investors seemed not to care. For example, Amazon.com made a loss of $125 million, but the market price of the shares became worth almost 18 times as much in 1.5 years time. From this example we can conclude that risk is not only in terms of losing money but also in terms of losing status. Investors are not only concerned about the final result, but also about what other people might think when they do not invest in such companies. It seems that the need of identity and the social network are just as well important determinants leading investment decisions.

A large part of the investment literature is based on herding, bubbles and fads. For example, Wermers (1999) investigates the degree in which portfolio managers of mutual funds herd in their trades. This study suggests that herding can result from momentum-following (e.g. buying past winners) or repeating the predominant buy or sell pattern from previous

140 Chapter 5. Style popularity and the comovement of stocks period. While this study tests whether ‘too many’ portfolio managers appear to make the same choices, it does not directly test the social interaction between portfolio managers. Why do people herd? Fashion could be an additional explanation that clarifies phenomena such as overreaction and underreaction, herding, momentum, etc. The term fashion covers the three terms: bubbles, herding and fads. For example, bubbles and herding are part of the fashion cycle. Bubbles may start in the third stage of the fashion cycle when the mass starts to adopt the new style. Welch (2000) defines herding as behavior patterns that are correlated across individuals, which can lead to sub-optimal choices in the decision-making process. Many researchers examine the existence of herding in stock markets, but these studies neglect to explain the origin of herding. Reed (1992) compares fads with fashions. The difference between fashions and fads is that a fad has a rapid growth, which sinks into a rapid decline before it ever achieves maturity. In contrast, fashion has a slower growth phase and an observable period of maturity. A fad is a product, which satisfies the single utility of new experience. A fashion is more complex in the way that it satisfies a group with related desires. Fashions are not restricted to essential attributes of the product’s design, but are subject to modifications. The effect is that fashions are not independent and isolated, but are consecutive and overlapping. The individual lifecycles of different fashions may be aggregated to one life-cycle for the main product. For example, a mutual fund is the main product, which has several modifications based on different styles (internet fund, financial fund, etc.). The analysis of stock markets in terms of fashion is a valuable addition to the behavioral finance theory. Most of the behavioral finance has focused on the investor’s cognition and emotions. For example, Barberis, Shleifer and Vishny (1998) develop a model based on the representativeness and conservatism heuristics. It explains the over- and underreaction of investors to new information. Daniel, Hirshleifer and

5.3 Measures of style investing and style popularity 141

Subrahmanyam (1998) develop a model that is based on investor overconfidence and self-attribution. Their model intends to explain over – and underreaction of stock market prices. Barberis and Shleifer (2003) describe investment styles in terms of cycles, where the origin of the cycle is explained with the representativeness heuristic. In the literature of behavioral finance, social interactions have been (until recently) mostly ignored. To describe the investment process social interactions may be an important aspect to analyze, because social interactions may affect the investor’s emotions and biases, and in doing so also investment decisions. It is difficult to describe the stock market in terms of fashion (cycles), because it is complex to measure the interaction between investors in a social network directly. Without data on social interaction, it is not possible to investigate whether the preferences of individual investors change in the direction of the preferences of friends, families and relatives. Because the aim of this chapter is to investigate to what extent popularity can be attributed to style investing, the focus will be on collective preferences of investors rather than investigating social interaction directly. Since fashion is closely related to popularity in the way that it both reflects the collective preferences of individuals and the changes of such preferences over time, in the next sections, we will concentrate on variables that measure popularity.

5.3 Measures of style investing and style popularity

In the previous sections, we discussed style investing and its association with fashion cycles. In this section, we will develop a testable model of style investing and style popularity based on our previous discussion. The main focus is to measure to what extent the popularity can be attributed to style investing or to individual stocks in a particular style.

142 Chapter 5. Style popularity and the comovement of stocks

Following Barberis and Shleifer (2003), we define a style as a group of stocks that is classified based on a common characteristic. The process where investors allocate funds among groups of stocks rather than among individual securities is called style investing. This definition of style investing has a number of empirical predictions. When investors apply style investing they will not distinguish between stocks within a style. It may appear that fundamentally unrelated stocks are grouped in the same category, which leads to demand shocks across all stocks in the style. The demand shock across all stocks leads to a higher comovement in prices/returns than implied by their fundamentals. This has consequences for the correlation between stocks in the same style and the correlation between stocks in different styles. When a style becomes popular, the correlation between stocks in the same style will increase. Furthermore, fund inflow by one style drives resources out of competing styles, which leads to negative correlations in prices among styles. In addition, the presence of style switchers leads to positively autocorrelated returns in the short run and negatively autocorrelated returns in the long run. Good performance over the last period relative to other styles pushes the prices up again in the next period inducing positive autocorrelation. Eventually, the price is reversed in the long run inducing negative autocorrelation. The demand for stocks has also implications for the comovement in volumes and turnover ratios. Because stocks in the same style are regarded as the same kind of shares, the demand for these stocks will be equal. Consequently, when investors apply style investing, dispersion (defined as the cross-sectional standard deviation of the turnover ratio) will decrease. In summary, style investing should be reflected in the following measures (Barberis and Shleifer, 2003):

• autocorrelation of returns; • correlation between stock returns in the same style;

5.3 Measures of style investing and style popularity 143

• correlation between stock returns in different styles; • cross-sectional standard deviation of the stocks’ turnover ratios (dispersion); • relation between past performance and in- and outflows of mutual funds.

Style popularity is based on collective preferences and social pressure, which influence the demand for groups of stocks. This demand-driven approach is potentially very useful to describe cycles in the stock market. Both style popularity and style investing are based on the demand for groups of stocks. However, the definition of style investing is very rigid and makes no distinction between stocks in the same style. Style popularity on the other hand may be based on the popularity of some stocks within a style. For example, style popularity predicts an increase in correlation between some stocks in the same style but this does not necessarily concern the correlations between all stocks in the same style. It is even possible to find some negative correlations between stocks in the same style. In case the popularity of some stocks in the same style increases, the turnover ratio for each asset in the same style will be different. This leads to higher dispersion. Style investing also predicts a positive correlation between the popularity of a style and past returns, resulting in in- and outflow of mutual funds. However, the popularity of a style may also be the result of other factors than past performance. For example, popularity may occur spontaneously or in arbitrary reaction to some widely noted events (Shiller, 2000) In the next sections, we want to distinguish between the popularity of particular stocks and style investing. As described before, style popularity is based on collective preferences and social pressure, which influence the demand for groups of stocks. It is difficult to test style popularity explicitly, because the relation between the different variables

144 Chapter 5. Style popularity and the comovement of stocks can also be explained by increasing positive expectations about the prospects of a style’s fundamentals in the future. Nonetheless, we can examine the collective style popularity, because if a style is popular, many investors and analysts will own or follow the stocks within the style. In the previous paragraph, we listed the measures that reflect style investing. In order to test to what extent popularity can be attributed to style investing, we first have to identify variables that reflect collective preferences for groups of stocks. The following aspects are relevant to describe popularity:

1. The IPO market is often viewed as a measure of investor enthusiasm. The volume of IPOs displays large variations over time. Shiller’s (1990) hypothesis is that IPO markets are subject to fads that affect market prices. Ritter (1991) provides evidence concerning this hypothesis by showing a variation in underperformance year-to-year across industries, with companies that went public in high-volume years faring the worst. This is consistent with a scenario where firms go public when investors are (over)optimistic about the future potential of certain industries. We take the number of IPOs in a style as a measure for popularity.

2. The mutual fund industry has grown over the past two decades. Stocks under management have grown from 134.8 billion dollar at the end 1979 to 6.8 trillion dollars at the end of 1999 (http://www.sec.gov/news/studies/feestudy.htm). This is an increase of more than 4900%. The number of mutual funds increased from 276 in 1962 to 15644 in 1999, which is an increase of approximately 273% during this period. We take the number of mutual funds applying a specific style that start in a year as a measure of popularity for that particular style.

5.3 Measures of style investing and style popularity 145

3. Liquidity variables can measure the demand of large groups of investors for particular stocks or styles. Baker and Stein (2004) developed a model where an increase in the market liquidity such as lower bid-ask spreads and high turnover ratio’s, may be an indicator for the increase in sentiment in the market. This theory suggests that when the participation of irrational investor increases the market will become more liquid, which results in an increase in volatility and the turnover ratio and a decrease in the bid-ask spread. Ofek and Richardson (2003) illustrate this empirically for the internet industry in the period from January 1998 to February 2000. During this period the turnover ratio and volatility were extremely high and bid-ask spreads were low. For example, the turnover ratio was three times higher for internet companies compared to non-internet companies. Based on the model of Baker and Stein and the empirical study of Ofek and Richardson we assume that liquidity may be a proxy for the sentiment in the market. Because irrational investors also drive fashions in the investment industry, liquidity measures may be good indicators to describe the popularity of stocks. Examples of liquidity measures are volume, turnover ratio, bid-ask spreads, and volatility. In times of mass investment in a particular style or market the turnover ratio will be high because the irrational investors dominate the rational investors. For the same reason should the turnover ratio be low in times when the style is out of fashion.

4. As described above, popularity is a process of adopters and imitators. Both are influenced by two means of communication: mouth-to-mouth and mass media. The media may speed the rate of diffusion of opinions among investors. Analyst recommendations are one of the media channels in the investment industry. Style attractiveness could be measured in terms of the coverage of analysts and the number of analysts’ up- and downward revisions. The number of analysts’ up- and

146 Chapter 5. Style popularity and the comovement of stocks

downward revisions is a measure for analysts’ sentiment. In the context of style popularity, the ratio of up- and downward revisions should vary positively with the style attractiveness. When analysts become more optimistic (pessimistic) about a particular style the number of analysts and the ratio of upward divided by downward revisions will increase (decrease).

In summary, number of IPO’s and the number of mutual funds that start in a year, liquidity and communication channels can express style popularity. To distinguish between the popularity of particular stocks and style investing, the main focus in the next sections will be to test to what extent investors apply style investing. Firstly, we generate a popularity index by using the principal component analysis. Secondly, we test with a regression analysis whether popularity is based on a style level or on an individual stock level. We use the cross-sectional standard deviation of the turnover ratio as proxy for style. If a style becomes popular, the dispersion in the turnover ratio will become lower. In addition, we test whether the popularity of investment styles is related to past performance. Finally, we make some robustness checks where we first show the movement of popularity through time and then test whether the movement in popularity of investment styles leads to co-movement in prices/returns.

5.4 Methodology

In this section we describe the methodology used to test whether popularity of stocks takes place on a style or an individual level. The variables that measure style popularity is explained in section 5.4.1 and in section 5.4.2 the dispersion measure is described. In section 5.4.3 we explain the model

5.4 Methodology 147 we use to test whether dispersions are significantly lower than average during periods of style popularity.

5.4.1 Style popularity measures

In section 5.3 we described different variables that reflect the popularity of investment styles and stocks. According to our hypothesis the following variables measure popularity:

• number of IPOs (NipoX,t);

• number of mutual funds that start in a year (NmfX,t);

• turnover ratio (TurnX,t);

• bid-ask spread (SpreadX,t);

• analyst optimism (UpdnX,t);

• analyst coverage (AnalystX,t).

The number of IPOs is the number of IPOs in the specific style (X) in period t. The number of mutual funds is the number of funds applying the style under consideration that start in period t. The turnover ratio is the average daily turnover of all stocks within a style and is defined as the volume divided by the number of outstanding shares. The bid-ask spread is the average of daily spreads in a month for each stock in a style. The spread is the difference between the ask and bid price divided by the mid price. To measure style popularity among analysts, we use analyst coverage and analyst optimism. For analyst optimism, we use the number of upward revisions divided by the number of downward revisions for all stocks in style X at time t:

148 Chapter 5. Style popularity and the comovement of stocks

∑ i=1,t UPX ,t UpdnX ,t = , (5.1) ∑ i=1,t DOWN X ,t

where UPX,t is the number of upgrades and DOWNX,t is the number of downgrades for all stocks in style X during period t. For each period we express analysts’ coverage as the log of the number of different analysts that cover style X at time t. With the six variables described above we create the following popularity index:

PX,t = b0NipoX,t + b2NmfX,t + b3TurnX,t−1 + b4SpreadX,t−1 + , (5.2) b5UpdnX,t + b6AnalystX,t−1

where PX,t is the level of popularity for style X for a given period t. The coefficients of the popularity index are obtained using a principal component analysis. This analysis composites an index based on variables that capture a common factor (see section 5.6.1 for a further explanation). The unit of time is measured in terms of months. The number of mutual funds that start in a period is based on annual data. Therefore, for each month in a specific year the number of mutual funds is the same.

5.4.2 Dispersion measure: stock or style popularity

We follow the same methodology of Christie and Huang (1995) to test to what extent stock popularity can be attributed to style investing. We use the dispersion of the turnover ratio as proxy for style investing. If all stocks within a style become popular within the same period, the turnover ratio of stocks within a style will commove to each other. This will lead to a

5.4 Methodology 149 decrease in dispersion of the turnover ratio. The cross standard deviation of the turnover ratio is:

n 2 ∑()Turni − Turn σ = i=1 , (5.3) X ,t n −1

where Turni is the observed turnover ratio of stock i and Turn is the cross- sectional average of the n turnovers in a style. σX,t is an indicator of dispersion of stock popularity across the style category, i.e. a decrease of

σX,t means more “uniform” popularity.

5.4.3 Regression model

With the following regression we want to test to what extent investors apply style investing. During abnormal levels of popularity, style investing is likely to be more pronounced. In particular, the style investing hypothesis states that stocks (belonging to that style) do not differ in their sensitivity to popularity and therefore it predicts that periods of high popularity induce decreased levels of dispersion. In contrast the style popularity hypothesis predicts an increased level of dispersion. To differentiate between the two hypothesis, we isolate the level of dispersion, σX,t , in the extreme tail of the distribution of popularity and test whether it differs significantly from the average levels of dispersion that exclude the extreme level of popularity. To test the style investing hypothesis we perform the following regression:

σ X ,t = a + b1PX ,t + ε X ,t , (5.4)

150 Chapter 5. Style popularity and the comovement of stocks

where PX,t is the extreme level of popularity for style X. We use a dummy for the level of extreme popularity ( P + σ ). We adopt this criterion for X pX extreme levels of popularity because extreme levels of popularity are arbitrary. The dummy is one if the level of popularity in month t lies in the extreme tail of the popularity and zero otherwise. The a coefficient denotes the average dispersion of the sample excluding the region covered by a dummy variable for extreme levels of popularity. For each variable in this regression we determine whether they are stationary. If necessary, we take the first difference of the variables in this regression to obtain stationary series. If investors apply style investing, an increase in popularity of a style will lead to a lower level of dispersion. This implies that style investing predicts a significantly negative coefficient for b1. If investors differentiate between stocks within the style, an increase in stock popularity will lead to an increase in the level of dispersion. Therefore, positive estimates for b1 would be consistent with popularity on an individual stock level.

5.5 Data

To test whether a style becomes popular we try to find independent measures that can be used to label a style or sector. Examples of style dimensions are value/growth, small/large capitalization, industries and global regions. We have chosen to study eleven different industries. We have not chosen to study value and growth styles, because value and growth are defined using market variables. The stocks that are labeled as growth in one year will not necessarily be growth stocks in the next year. Styles based on industries or countries do not experience such difficulties, because for example a technology stock is labeled as technology and continues to be a technology stock in future, unless the nature of the firms operations changes due to acquisitions.

5.5 Data 151

We sort stocks into industries based on SIC codes using the 12 industry portfolio classification form French’s data library on the internet18. We use the list composed by Morgan Stanley19 with pure internet-related companies to form an internet portfolio. In our study, we include all NYSE, AMEX and NASDAQ stocks for the period 1982 to 2004. Real estate investment trusts (REITs), American Depository Receipts (ADRs), closed end mutual funds, foreign stocks, unit investment trusts and Americus trusts are excluded from our sample. We use the returns of the CRSP database and the accounting data of COMPUSTAT. We use CRSP to collect daily bid and ask prices and monthly data for SIC codes, market capitalization, returns, and volume trading. We use I/B/E/S to obtain the number of up- and downward revisions and the number of analysts that cover a particular style. We take the number of IPOs in a given month from Bloomberg. The mutual fund data is extracted from the CRSP Survivor-Bias Free US Mutual Fund Database. There are two different types of style- related objective codes in the CRSP database for the post-1991 period: the ICDI Fund Objective Codes and the Strategic Insight Objective Codes. We selected funds that only invest in US stocks. Each fund must have at least 70% of common stocks. For each industry we found mutual funds that invest in equity shares of companies engaged in that particular industry. For the health, financial, technology, energy and utility industry mutual funds exist that explicitly invest in stocks of that particular industry. For the manufacturing, retail, chemicals and consumer (non-)durable good industries we use the ICDI and SI objective codes. Because both the ICDI and SI objective codes do not distinguish between internet telecom and technology, we subdivide the mutual funds with the objective technology

18 http://www.mba.tuck.darthmouth.edu/pages/faculty/ken.french/ 19 http://www.morganstanley.com/institutional/research/research_reports.html?page=research

152 Chapter 5. Style popularity and the comovement of stocks into internet, telecom and technology. We subdivide funds into name-based categories, which is in line with the idea that investors base there asset allocation on categories to make the choice easier. We assume that investors infer from the name of a mutual fund the objective of the mutual fund. Mutual funds with the following words in the name are defined as internet funds: Internet, NetNet, Wireless and www. For telecom funds we use the word telecommunication. We use the internet to verify whether the objective of each fund is in line with the labels we chose.

5.6 Results

In section 5.3 and 5.4 we described a couple measures that reflect popularity. Table 5.1 shows some descriptive statistics over the period 1983 to 2004. The sample contains 276 months (N).

Table 5.1: Descriptive statistics (1983-2004)

N is the number of months that is included in our sample. Nipot is the number of IPO’s in a month. Nmft is the average number of mutual funds that start in a month. Turnt-1 is the log of the turnover ratio. Spreadt-1 is the average bid-ask spread. Updnt-1 is the number of upward revisions against the number of downward revisions and analystst is the log of number of analysts that cover the market in a month. N Mean Std. Deviation

Nipo t 276 13 12 Nmf t 276 66 81 Turn t-1 (log) 276 0.894 0.204 Spread t-1 276 5.955 1.343 Updn t-1 276 0.767 0.325 Analystst (log) 276 3.125 0.100

The number of IPOs is the number of IPOs in the respective sectors or styles in a month. The average number of IPOs in a month during this period was 13. The average number of mutual funds that started in a month was 66. The bid-ask spread is the average of daily spreads in a month for

5.6 Results 153 each stock in a style. The spread is the difference of the bid- and ask price divided by the mid price. The average bid-ask spread is 5.96%. The turnover ratio is the average monthly turnover and is defined as the volume divided by the number of outstanding shares. The average monthly turnover (log) was 0.89. The average number of analysts per stock on the US stock market during 1983 and 2003 was 3.125.

Table 5.2: Descriptive popularity statistics for each sector over the period 1983 to 2004

N is the number of months that is included in our sample. Nipot is the number of IPO’s in a month. Nmft is the average number of mutual funds that start in a month. Turnt-1 is the log of the turnover ratio. Spreadt-1 is the average bid-ask spread. Updnt-1 is the number of upward revisions against the number of downward revisions and analystst is the log of number of analysts that cover the market in a month. Pt is the average standardized popularity. The average popularity for the Internet sector is over the period 1993 to 2004.

Industries IPOt Nmft Turn t-1 Spread t-1 Updnt-1 Analystst Pt Manufacturing 0 0 1.871 5.233 74.612 5.944 0.358 Consumer 0 0 1.881 5.015 86.119 4.799 0.378 durables Consumer 1 1 1.863 5.026 76.713 5.312 0.437 non durables Financials 2 6 1.622 4.703 94.167 5.731 0.459 Health 3 55 2.352 7.049 84.871 5.392 0.436 Telecom 1 1 2.181 5.863 75.807 4.774 0.413 Utility 0 8 1.487 2.133 91.152 4.597 0.375 Business 3 18 2.513 7.398 82.043 6.241 0.410 Wholesale 0 0 1.854 4.867 81.479 5.882 0.443 Chemicals 2 1 2.134 6.016 84.666 4.752 0.299 Energy 1 6 1.799 8.671 108.942 4.898 0.461 Internet 3 5 3.429 6.975 315.714 1.368 0.682

Table 5.2 shows the monthly summary statistics for every industry over the period January 1983 to December 2004. The average turnover ratio is 1.157 for the business sector and 0.933 for the health sector. The average number of mutual funds that start in the business sector is 18 compared to 55 for the health sector. Also the number of analysts that cover both sectors is high. Utility and the chemical sector were not very popular during this period.

154 Chapter 5. Style popularity and the comovement of stocks

The turnover was the lowest with 0.731 and 0.162, respectively. Furthermore, the number of IPOs was on average zero and the number of analysts that covered the sectors was the lowest. In the next section we test whether popularity is focused on a style or individual stock level. Before we test the style investing hypothesis, we first present our findings for the average popularity of each investment style.

5.6.1 Popularity index

Following the procedure of section 5.4.1 the level of popularity is created by making an index of the different popularity measures described in section 5.3. The procedure is as follows. The model is estimated by using first principal component analysis. The first principal component of the six variables with their lags is estimated20. This gives a first-stage index with twelve loadings, one for each of the current and lagged variables. We then compute the popularity index with six variables, lead or lag, based on the Kaiser-Meyer-Olkin measure (the one which gives the highest value). This leads to the following the coefficients of our popularity index (cf. section 5.4.1):

P = 0.110Nipo + 0.234Nmf + 0.295Turn − 0.212Spread + X ,t X ,t X ,t X ,t−1 X ,t−1 (5.5) 0.211UpdnX ,t−1 + 0.286AnalystX ,t

where Nipot is the number of IPO’s in a month, Nmft is the number of mutual funds that start in a year, Turnt-1 is the log of the monthly turnover ratio, Spreadt-1 is the average monthly bid-ask spread, Updnt-1 is the number of upward revisions divided by the number of downward revisions in the

5.6 Results 155

given month for all stocks in style X and Analystt is the log of number of analysts that cover a sector in a particular month.

Figure 5.1: Scree plot A scree plot is a graphical method where the eigenvalues are plotted against the component number.

Scree Plot

3

2 Eigenvalue 1

0

123456 Component Number

Table 5.4 presents the Kaiser-Meyer-Olkin measure, which is 0.710, meaning that the principal component analysis gives useful results (if the value is above 0.60, the factors extracted will account for a fare amount of variance). Moreover, Bartlett’s test of sphericity is significant, indicating a good fit. This is confirmed by the correlation matrix in table 5.3, which shows that most of the correlations between the variables are statistically significant at a 1% level.

20 Other variables such as inflow and outflow of mutual funds and number of stopped analysts reduced the Kaiser-Meyer-Olkin measure.

whether the correlation correlation the whether

t

1 P t-1

Updn t is the number of degrees of freedom and Sig. is the the is Sig. and of freedom degrees of number the is df Analysts 15 t-1 .710 .000 684.090 684.090 nificant. nificant. Spread among variables is small. Bartlett’s test of sphericity tests sphericity of test Bartlett’s is small. variables among t-1

df Sig. Sig. and the popularity Chapter 5. Style comovement of stocks and Bartlett's Test of sphericity Turn Approx. Chi-Square Chi-Square Approx. t-1 e that the factor model is inappropriate. The The is inappropriate. model factor the that e Nmf t

1 1 .170 .613(**) .812(**) -.470(**) -.470(**) 1 .812(**) .170 .613(**) NIPO .0.07(*) .364(**) .414(**) -.386(**) .487(**) .487(**) -.386(**) .414(**) .364(**) .0.07(*) 1 .304(**) .609(**) .609(**) .304(**) 1 .208(**) 1 .208(**) .338(**) .721(**) .907(**) -.651(**) .880(**) .650(**) .650(**) .880(**) -.651(**) .907(**) .721(**) .338(**) -.229(**) -.154(**) -.550(**) -.550(**) -.154(**) -.229(**) 1

t-1 Kaiser-Meyer-Olkin Measure Sampling of Kaiser-Meyer-Olkin Adequacy. TestBartlett's of Sphericity

t

t-1

t t-1

t

t (log) (log) Turnover NIPO Nmf (log) Updn Spread Analysts P ** Correlation is significant at the 0.01 level (2-tailed). (2-tailed). level 0.01 the at is significant Correlation ** (2-tailed). level 0.05 the at is significant Correlation * probability value which measures whether the value is statistically sig is statistically value the whether measures which value probability 156 Table 5.3: Correlation scheme for variables Table 5.4: Kaiser-Meyer-Olkin measure correlations partial the whether tests measure Kaiser-Meyer-Olkin indicat would which matrix identity is an matrix 5.6 Results 157

Table 5.5 shows that the first principal component explains 51.3% of the standardized sample variance, and only the first eigenvalue is above 1.00. Figure 5.1 confirms that only one factor captures the common variance. The correlation between the twelve-term first stage index and the Popularity index is 0.99, suggesting that little information is lost in dropping six terms.

Table 5.5: Total Variance Explained This table presents the results form the principal component analysis. The variances extracted by the factors are called the eigenvalues. The first column (Total) contains the Eigenvalues. It shows the total variance that is extracted by each factor. The second column (% of Variance) contains the percent of total variance accounted for by each factor. The third column (Cumulative %) contains the cumulative variance extracted for the current and preceding factors. Component Initial Eigenvalues Extraction Sums of Squared Loadings Total % of Cumulative Total % of Cumulative Variance % Variance % 3.07 1 51.287 51.287 3.077 51.287 51.287 7 2 .989 16.477 67.764 3 .858 14.294 82.058 4 .635 10.579 92.637 5 .293 4.888 97.525 6 .148 2.475 100.000 Extraction Method: Principal Component Analysis.

The coefficients in equation 5.5 are intuitively appealing. Firstly, the variables have the expected sign. As expected, the variables (except for bid- ask spreads) show a positive relation with popularity. As one of these variables increases, the level of popularity tends to increase as well. If the level of popularity of a style or stock increases, the bid-ask spread will also decrease. Secondly, the proxies enter with the expected timing. Investor behavior such as liquidity leads to firm supply variables. More generally, proxies that involve firm supply responses (Nipot and Nmft) are likely to lag proxies that are based on investor demand (Spreadt-1 and Turnt-1). In addition, the timing of the variable Updnt-1 and Analystt suggests that a

158 Chapter 5. Style popularity and the comovement of stocks fraction of analysts have to become optimistic before more analysts start to cover a sector or stock. The coefficients obtained from this model are used to calculate a popularity index for each individual sector. For each sector the obtained popularity index will be regressed against the dispersion variable.

5.6.2 Popularity at a style or stock level

Using equation 5.5, we obtain a popularity index for each sector. Table 5.5 (column right-hand side) shows the average monthly popularity index for every industry over the period January 1983 to December 2004. The average popularity is the highest for the financial and internet sector with 0.459 and 0.682, respectively. The manufacturing and the chemical sector have the lowest average popularity with 0.358 and 0.299, respectively. These values conceal the cyclical nature of popularity (which can be compared to the fashion cycles mentioned in section 5.2). In section 5.7.1, we will further investigate the movement in popularity for each sector through time. When investors apply style investing there should be a negative relation between style popularity and the cross standard deviation of the turnover ratios. The turnover ratios of all stocks in the same style should comove, which lead to a decrease in the standard deviation of the stocks’ turnover ratios. Table 5.6 provides the average level of turnover dispersion for each sector. The average level of turnover dispersion is 17.9 percent a month across all stocks. Across the industries, the level of turnover dispersion ranges from a low of 4.0 percent for utilities to 19 percent for business sector in the period 1983 to 2004. Although, we show averages for popularity and dispersion, it seems that there is a positive relation between style popularity and dispersion.

5.6 Results 159

Table 5.6: Dispersion in turnover ratios over period 1983 to 2004 Dispersion is the cross standard deviation of the turnover ratio. The average dispersion for the Internet sector is over the period 1993 to 2004. Industries Dispersion All stocks 17.900 Manufacturing 11.412 Consumer durables 8.038 Consumer non durables 9.741 Financials 9.180 Health 15.039 Telecom 15.152 Utility 3.981 Business 19.340 Wholesale 14.082 Chemicals 8.084 Energy 8.859 Internet 35.075

Equation 5.4 was estimated using the coefficients obtained from the first principal component analysis (equation 5.5). Table 5.7 provides the regression estimates across industries over the period 1983 to 2004. Under the dispersion in turnover ratio as a dependent variable, the coefficient estimates are reliable and uniformly positive. Therefore, the popularity of stocks cannot be attributed to style investing. The sectors financials and energy, which have the highest popularity during this period, exhibit positive coefficients. The business sector has the highest average dispersion after excluding the region by the dummy variable (as indicated by the constant). The utility sector exhibits the lowest dispersion during this period and has a very low coefficient. The results show that the popular sectors have the highest dispersion and positive coefficients. This suggests that popularity is on an individual stock level instead of a style level.

160 Chapter 5. Style popularity and the comovement of stocks

Table 5.7: Regression analysis with as independent variable dispersion in turnover over period 1983 to 2004 The independent variable is a dummy for extreme movements in popularity. If necessary, we take the first difference of the variables to obtain stationary series. It is one when the value is above mean+standard deviation and otherwise zero. The dependent variable is the standard deviation of the turnover ratio. The detrended levels are obtained by taking the first difference. Newey-west is used to adjust the t-statistics for heteroskedasticity and autocorrelation. 2 Industries constant b1 t(constant) t(b1) adj. R Manufacturing 0.098 0.081 13.952 2.596 0.100 Consumer durables 0.077 0.027 21.319 3.838 0.056 Consumer non durables 0.090 0.063 16.525 3.873 0.116 Financials 0.083 0.049 9.093 2.330 0.024 Health 0.135 0.093 14.195 5.097 0.103 Telecom 0.112 0.223 13.001 3.611 0.165 Utility 0.039 0.014 19.138 3.417 0.062 Business 0.168 0.199 12.354 5.891 0.171 Wholesale 0.118 0.145 11.777 3.822 0.113 Chemicals 0.078 0.014 19.639 1.519 0.019 Energy 0.080 0.045 8.068 4.407 0.026 Detrended levels Financials 0.084 0.042 13.196 1.174 0.018 Health 0.148 0.028 12.806 2.243 0.006 Business 0.194 0.039 9.749 2.002 0.006 Energy 0.086 0.015 9.039 1.630 0.002

To show that the results are not dependent on the period we chose, we also perform regressions over the period 1992 to 2004. Table 5.8 presents the outcomes of the regression. The results are consistent with the results of table 5.7. The coefficient estimate for the internet sector is negative, which implies that the popularity can be attributed to style investing. However, the heteroskedasticity consistent t-statistics shows that this result is not reliable. When we use the full sample period, we find that the popularity index shows non stationary series for the financial, health, business and energy sector. When we either restrict the sample period to the 1992-2004 period or detrend the data, the relationship between the level of (detrended) popularity and the level of dispersion is still positive. Although the coefficients are still positive and the two out of four coefficients are statistically significant, detrending makes a considerable difference in the

5.6 Results 161 explanatory power. The adjusted R-squares of these regressions range from 0.002 to 0.018, which is lower than the adjusted R-squares of the regressions without detrending, which ranges from 0.024 to 0.171.

Table 5.8: Regression analysis with as independent variable dispersion in turnover over the period 1992 to 2004 The independent variable is a dummy for extreme movements in popularity. If necessary we take the first difference of the variables to obtain stationary series. It is one when the value is above mean+standard deviation and otherwise zero. The dependent variable is the standard deviation of the turnover ratio. Newey-west is used to adjust the t-statistics for heteroskedasticity and autocorrelation. 2 Industries: constant b1 t(constant) t(b1) adj. R Manufacturing 0.131 0.074 13.221 2.190 0.084 Consumer durables 0.088 0.018 18.951 2.393 0.035 Consumer non durables 0.116 0.038 14.927 2.218 0.051 Financials 0.088 0.044 23.902 2.296 0.121 Health 0.180 0.048 12.631 2.599 0.032 Telecom 0.166 0.169 15.679 2.730 0.092 Utility 0.041 0.010 12.983 2.425 0.038 Business 0.246 0.121 13.474 3.779 0.079 Wholesale 0.164 0.099 10.178 2.511 0.053 Chemicals 0.093 0.000 17.907 0.014 0.000 Energy 0.113 0.012 6.318 0.714 0.002 Internet 0.369 -0.080 14.115 1.389 0.015

To summarize, our findings show that the level of dispersion is high when the level of popularity is high, which indicates that popularity is stock specific and not style-specific. To detect size-effects in the dispersion of stocks within a style, we divide stocks into quintiles and run the regression again for each size-group within the sectors. Table 5.9 show the effect of size conditional on dispersion. We find a size-effect for most of the less popular industries. Sectors like consumer durables, chemicals, and utility show from small-size to the large-size a pattern of decreasing coefficients. When one of these sectors becomes more popular, the demand for large caps will increase. This results in a lower dispersion in turnover.

162 Chapter 5. Style popularity and the comovement of stocks

Table 5.9: regression analysis: industries divided into size quintiles over period 1983 to 2004 For each sector we form quintiles on market capitalization. Market capitalization is calculated at the end of each year and equals the number of shares outstanding times its market price. The independent variable is a dummy for extreme movements in popularity. It is one when the value is above mean+standard deviation and otherwise zero. The dependent variable is the standard deviation of the turnover ratio. In panel B, we take the first difference of the variables to obtain stationary series. For the internet sector, we perform the regression over the period 1998 to 2004. Number is the average number of stocks in each size portfolio. Newey-west is used to adjust the t-statistics for heteroskedasticity and autocorrelation. Panel A: Levels const Industries: number b t(constant) t(b ) adj. R2 ant 1 1 Manufacturing small 317 0.087 0.051 11.534 2.289 0.037 s2 91 0.090 0.045 17.748 3.732 0.119 s3 56 0.115 0.183 10.089 2.122 0.119 s4 48 0.078 0.042 12.094 3.452 0.080 large 32 0.076 0.025 10.776 2.445 0.025 Consumer small 40 0.074 0.023 20.428 2.499 0.037 durables s2 8 0.070 0.031 11.912 2.128 0.033 s3 5 0.058 0.020 9.002 1.576 0.007 s4 4 0.040 -0.011 9.361 -2.116 0.008 large 4 0.035 0.006 15.766 1.741 0.013 Consumer non small 167 0.086 0.087 13.426 3.715 0.135 durables s2 39 0.099 0.018 15.237 1.408 0.012 s3 31 0.073 0.028 20.612 3.730 0.077 s4 24 0.055 0.010 22.723 2.233 0.027 large 28 0.037 0.009 16.267 1.875 0.024 Financials small 526 0.082 0.045 6.530 1.894 0.011 s2 131 0.077 0.058 20.867 2.061 0.113 s3 81 0.070 0.050 19.430 3.502 0.147 s4 66 0.072 0.062 13.982 5.310 0.171 large 57 0.050 0.024 23.410 2.174 0.099 Health small 269 0.127 0.093 11.906 3.596 0.068 s2 57 0.138 0.067 13.965 3.962 0.080 s3 29 0.140 0.041 18.546 2.446 0.045 s4 20 0.118 0.088 13.001 4.157 0.145 large 24 0.070 0.031 12.580 2.162 0.055

5.6 Results 163

[Table 5.9 continued] Telecom small 35 0.127 0.093 11.906 3.596 0.068 s2 15 0.138 0.067 13.965 3.962 0.080 s3 14 0.140 0.041 18.546 2.446 0.045 s4 13 0.118 0.088 13.001 4.157 0.145 large 21 0.070 0.031 12.580 2.162 0.055 Utility small 35 0.030 0.010 16.895 1.520 0.026 s2 28 0.031 0.013 14.409 2.099 0.030 s3 35 0.035 0.018 15.198 2.204 0.048 s4 38 0.039 0.005 16.043 0.979 0.005 large 31 0.028 0.000 11.552 -0.050 0.000 Business small 493 0.135 0.205 11.214 5.143 0.175 s2 98 0.163 0.118 15.519 5.031 0.177 s3 58 0.187 0.098 17.501 5.151 0.137 s4 42 0.199 0.060 13.209 3.452 0.037 large 30 0.159 0.104 13.703 5.389 0.150 Wholesale small 310 0.112 0.169 9.505 3.328 0.092 s2 75 0.111 0.110 15.410 4.154 0.166 s3 47 0.112 0.096 14.283 3.569 0.102 s4 39 0.077 0.043 20.255 6.079 0.176 large 26 0.055 0.072 10.819 4.493 0.210 Chemicals small 47 0.070 0.021 20.871 2.377 0.039 s2 14 0.069 0.045 16.843 2.267 0.080 s3 17 0.078 -0.014 9.075 -1.373 0.005 s4 14 0.069 -0.011 6.880 -0.907 0.003 large 14 0.037 -0.004 22.703 -0.853 0.005 Energy small 117 0.082 0.056 5.494 3.757 0.017 s2 25 0.070 0.049 17.505 5.339 0.203 s3 16 0.059 0.044 15.234 6.185 0.169 s4 16 0.058 0.025 12.136 4.305 0.057 large 19 0.044 0.025 12.146 4.823 0.094 Internet small 84 0.290 -0.127 5.419 -1.900 0.035 s2 30 0.281 -0.075 9.768 -2.422 0.036 s3 20 0.333 -0.089 8.626 -2.253 0.026 s4 18 0.367 -0.029 7.490 -0.464 0.002 large 11 0.240 0.129 7.678 2.612 0.091

164 Chapter 5. Style popularity and the comovement of stocks

Panel B: Detrended levels Financials small 526 0.089 0.020 7.910 0.724 0.000 s2 131 0.087 -0.004 12.254 -0.363 0.000 s3 81 0.079 0.012 16.294 1.332 0.002 s4 66 0.083 0.012 12.545 0.833 0.001 large 57 0.054 -0.002 17.196 -0.327 0.000 Health small 269 0.141 0.087 11.817 1.809 0.012 s2 57 0.149 0.030 15.876 1.227 0.003 s3 29 0.146 0.046 21.116 1.712 0.012 s4 20 0.132 0.052 13.766 1.911 0.010 large 24 0.074 0.037 13.245 1.987 0.016 Business small 493 0.166 0.088 9.557 1.702 0.005 s2 98 0.180 0.104 16.040 4.620 0.019 s3 58 0.201 0.144 19.346 2.540 0.041 s4 42 0.208 0.077 15.532 3.820 0.009 large 30 0.175 0.074 15.176 4.633 0.011 Energy small 117 0.091 0.036 6.698 1.397 0.002 s2 25 0.078 0.011 17.108 0.922 0.002 s3 16 0.065 0.052 16.169 1.859 0.052 s4 16 0.063 0.009 14.209 1.308 0.002 large 19 0.049 0.014 13.658 1.668 0.006

For the popular sectors, financials and health, we cannot find size-effects. If one of these styles is popular, dispersion will be high independent of size. For the internet sector, we perform the regression over the period 1998 to 2004. The reason is that the internet sector has its origin in 1992 and, therefore, has a small number of stocks over the period 1992 to 1997. The results for the internet sector show from small-size to the large-size a pattern of increasing coefficients. This implies that when this sector becomes more popular, the demand for small caps increases, resulting in a lower level of dispersion. The low number of stocks in some of the quintiles may influence the results in the way that one stock may have a larger impact on the outcome. Therefore, we also divide stocks into three size portfolios (30%-40%-30%) and perform the same regression. We find similar results as is shown in table 5.9.

5.6 Results 165

As we mention before, the popularity index shows non stationary series for the financial, health, business and energy sector. For these sectors, we take the first difference to obtain stationary series. Panel B of table 5.9 shows similar results as panel A, with the exception that only for the business sector the coefficients are statistically significant. Baker and Wurgler (2004), show that size-effects exist in low- sentiment conditions only. They define sentiment as a force that drives the relative demand for speculative investments. Investors’ sentiment has strong effects on the cross-section of stock prices. If popularity is not related to the style’s fundamentals, popularity will be driven by investors’ sentiment. Although we do not know whether popularity is driven by investors’ sentiment or by fundamentals, our findings show close resemblance to the outcomes of Baker and Wurgler (2004). Barberis and Shleifer (2003) argue that an investment cycle starts after good information in terms of good past performance. Pomorski (2004) show this empirically. He finds that flows are positively related to past returns and negatively related to returns of competing styles. We want to test the relationship between the change in popularity (∆PX,t) and past returns. Firstly, we perform the Granger Causality test for each sector to test whether both variables, change in popularity and monthly returns, play a role in the determination of each other. The Granger probabilities show that there is causal relationship between the change in popularity and returns for the most popular sectors. Specifically, quarterly returns Granger cause popularity (see table 5.10).

166 Chapter 5. Style popularity and the comovement of stocks

Table 5.10: Granger causality test: quarterly returns and popularity over the period 1983 to 2004 For each quarter we calculated returns and the change in popularity. The change in popularity is reflected by ∆PX,t. The significance levels are presented with stars, where ** is 1% and * is 5% significance level. Granger causality tests21 Obs F-statistic probability Manufacturing

Return does not Granger Cause ∆PX,t 85 16.171** 0.000 ∆PX,t does not Granger Cause Return 0.082 0.921 Consumer durables

Return does not Granger Cause ∆PX,t 85 19.875** 0.000 ∆PX,t does not Granger Cause Return 1.234 0.297 Consumer non durables

Return does not Granger Cause ∆PX,t 85 15.030** 0.000

∆PX,t does not Granger Cause Return 0.282 0.755 Financials

Return does not Granger Cause ∆PX,t 85 4.145** 0.019 ∆PX,t does not Granger Cause Return 1.591 0.210 Health

Return does not Granger Cause ∆PX,t 85 24.884** 0.000 ∆PX,t does not Granger Cause Return 3.333 0.041 Telecom

Return does not Granger Cause ∆PX,t 85 17.773** 0.000 ∆PX,t does not Granger Cause Return 1.839 0.166 Utility

Return does not Granger Cause ∆PX,t 85 0.731 0.485 ∆PX,t does not Granger Cause Return 1.443 0.242 Business

Return does not Granger Cause ∆PX,t 85 11.701** 0.000 ∆PX,t does not Granger Cause Return 7.091** 0.001 Wholesale

Return does not Granger Cause ∆PX,t 85 8.753** 0.000 ∆PX,t does not Granger Cause Return 0.865 0.425

21 We include 8 lags for the Granger test. This lag length corresponds to a reasonable belief about the time in which past returns could predict popularity.

5.6 Results 167

[Table 5.10 continued] Chemicals

Return does not Granger Cause ∆PX,t 85 6.119** 0.003 ∆PX,t does not Granger Cause Return 0.016 0.985 Energy

Return does not Granger Cause ∆PX,t 85 3.859** 0.025 ∆PX,t does not Granger Cause Return 1.085 0.343 Internet

Return does not Granger Cause ∆PX,t 44 6.522** 0.004 ∆PX,t does not Granger Cause Return 3.583* 0.038

Because the Granger causality runs one-way from past returns to popularity and not the other way, we perform a regression to test the relation between the change in popularity and past performance:

∆PX ,t = ct + β1RX ,t−1 + β 2 ∆PX ,t−1 + ε t , (5.6)

where ∆PX,t-1 is the change in quarterly popularity and RX,t-1 is the quarterly return for style X at time t-1. With equation 5.6 we test whether the change in popularity of a style is the result of good past performance or popularity. If the change in popularity influences the change in popularity in the next period, b2 should be positive implying that there is persistence in popularity time series. If the popularity of a style depends on past performance, b1 should be positive. The outcomes of the regression are presented in table 5.11. As can be seen from the table, we find that lagged popularity (difference) and lagged returns influence current changes in popularity. Past returns seems to have a positive influence on popularity independent of the average popularity of a style. This implies that changes in popularity are induced by past performance in stock returns. That is, investors buy stocks from a style that have performed well in the past.

168 Chapter 5. Style popularity and the comovement of stocks

These results are consistent with Barberis and Shleifer (2003), who suggest that an investment cycle starts with good past performance. These results also fit closely with the literature on the positive-feedback trading of institutional investors. Grinblatt, Titman and Wermers (1995) and Carhart (1997) show that institutional investors tend to buy stocks that performed well in the past.

Table 5.11: Regression analysis with as dependent variable popularity over period 1983 to 2004 This table shows the results of equation 5.6. The dependent variable is the change in popularity and the independent variables are the past quarterly return and change in past popularity. Newey-west is used to adjust the t-statistics for heteroskedasticity and autocorrelation. 2 Industries: constant b1 b2 t(constant) t(b1) t(b2) adj. R Manufacturing -0.037 2.069-0.276 -1.107 6.348-2.828 0.321 Consumer durables -0.034 2.048 -0.370 -0.798 7.853 -3.854 0.313 Consumer non durables -0.021 2.175 -0.369 -0.572 7.083 -4.745 0.292 Financials -0.022 1.478-0.518 -0.560 3.145-6.832 0.248 Health -0.041 1.913-0.431 -1.282 6.112-5.552 0.367 Telecom -0.028 1.535-0.317 -0.671 5.254-3.847 0.297 Utility 0.009 0.640 -0.306 0.247 1.102 -2.922 0.086 Business -0.007 1.093-0.455 -0.182 5.163-2.945 0.304 Wholesale -0.001 1.532-0.472 -0.025 3.650-4.258 0.308 Chemicals -0.035 1.786-0.339 -0.827 4.707-3.826 0.234 Energy 0.018 0.861-0.406 0.499 3.321-5.335 0.194 Internet -0.016 0.2500.062 -0.286 1.3870.393 0.055

Overall, our results suggest that stock popularity cannot be attributed to style investing. We show a positive relation between dispersion and extreme levels of style popularity. This means that in periods of high style popularity, we cannot find comovement in trading activity within styles. This implies that only a fraction of stocks belonging to that style is popular. The fraction of popular stocks may be related to particular size groups. We have therefore tested for size-effects, to check whether popularity is centered on particular size groups. For most of the less popular sectors (from small size to the large size) we find a decreasing pattern of

5.7 Robustness analysis 169 coefficients. However, most of the coefficients are still positive, which points to the existence of popularity at a stock level instead of a style level. Finally, we test whether changes in popularity are related to past performance in returns and find a positive relation.

5.7 Robustness analysis

In section 5.6.2, we present an average popularity score for each sector over the period 1983 to 2004. This is a static value, which does not show the life cycles of popularity (which can be compared to the fashion cycles mentioned in section 5.2) and the movement in popularity through time. In section 5.7.1, we present the cyclical nature of popularity for each sector. The empirical analysis in section 5.6.2 shows evidence inconsistent with the predictions of style investing theory. A possible alternative explanation for our findings is that we investigate the comovement in turnover ratios rather than the comovement in prices/returns as is shown by a series of recent studies (Cornell (2004), and Barberis, Shleifer and Wurgler (2005)). Another explanation for our findings in section 5.6.2 is that we focus on the extreme level of popularity rather than the change in popularity. Hence, to explore whether movements in popularity lead to comovement in returns, we test the impact of the change in popularity on the comovement in returns for each sector in section 5.7.2.

5.7.1 Movement in popularity

Barberis and Shleifer (2003) describe style investing in terms of life-cycles. The birth of a style starts after good fundamental news about the securities in a style. If the style matures, good past performance in style returns is

170 Chapter 5. Style popularity and the comovement of stocks important to add new resources to a style. The style loses its popularity when bad news arrives or when arbitrage levels out excess returns. After a while, the cycle may start all over again. In this section, we show the movement in style popularity through time. Before we show the movement in popularity through time for the eleven different industries, we first present the movement in popularity for the internet sector. In appendix 5A we describe the internet sector in terms of a popularity cycle. The popularity cycle is divided into different stages based on the model of E. Rogers (1983). In appendix 5A we present a further outline of the procedure followed. Table 5A.3 shows the different stages of the popularity cycle for internet sector with the corresponding popularity. Popularity shows a low value in the leader stage and reaches a peak in the late majority stage. The right-hand column in table 5A.3 shows that dispersion reaches its peak in the early majority phase. This implies a positive relation between dispersion and popularity. In order to show the movement in popularity for the other eleven sectors, we calculate a 2.5-year rolling average popularity. Figure 5.2 shows that popularity of sectors is changing through time. For example, the popularity of the business sector was relatively low during the eighties and started to increase in the nineties. On the other hand, the popularity of the utility sector was relatively high over the period 1988 to 1993 and declined after 1994. We also calculate the 2.5-year rolling average dispersion. Figure 5.2 shows that dispersion moves in a similar way as popularity. For the business sector dispersion shows an increasing pattern, while dispersion for the utility sector shows a decreasing pattern in the mid-nineties.

5.7 Robustness analysis 171

Figure 5.2: The 2.5-year rolling average popularity and the 2.5-year rolling average dispersion over the period 1983 to 2004

Manufacturing Consumer Durables Consumer Non Durables

2 4 2 3 2 3

3 2 1 2 1 1 Dispersion Dispersion Dispersion 2 1 0 1 0 1 0 0 -1 0 popularity

0 Popularity -1 Popularity -1 -1 -2 -1 -1 -2

-2 -2 -3 -3 -2 -2 1987 1991 1995 1999 1987 1991 1995 1999 1987 1991 1995 1999

Health Telecom Utility

1.5 2 2.0 4 3 3

1.0 1.5 3 2 2 1

Dispersion 1.0 Dispersion 0.5 2 1 1 Dispersion 0.5 0.0 0 1 0 0.0 0

Popularity -0.5 0 Popularity -1 -0.5 -1 Popularity -1 -1.0 -1.0 -1 -2

-1.5 -2 -1.5 -2 -3 -2 1987 1991 1995 1999 1987 1991 1995 1999 1987 1991 1995 1999

Wholesale Chemicals Energy

2 3 1.5 3 2 3

1.0 1 2 2 2

1 Dispersion Dispersion Dispersion 0.5 0 1 1 1 0.0 0 -1 0 0 0 -0.5 Popularity Popularity

-1 -2 -1 Popularity -1 -1 -1.0

-3 -2 -1.5 -2 -2 -2 1987 1991 1995 1999 1987 1991 1995 1999 1987 1991 1995 1999 Financials Business

2 3 2 2

2 1 1 1 Dispsersion

1 Dispersion Popularity Dispersion 0 0 0 0 Popularity Popularity -1 -1 -1 -1

-2 -2 -2 -2 1987 1991 1995 1999 1987 1991 1995 1999

Table 5.12 presents the average popularity for four different periods. The numbers confirm our analysis of figure 5.2. The utility sector is popular during the eighties and becomes less popular in the nineties. Other sectors, like business and energy, are not popular during the eighties but increase in popularity during the nineties. Overall, figure 5.2 and table 5.12 show that

172 Chapter 5. Style popularity and the comovement of stocks the movement in popularity shows close resemblance with the fashion cycles as described in section 5.2.

Table 5.12: Average popularity over different horizons Average popularity Industries: 1983-1986 1987-1990 1991-1994 1995-1999 2000-2004 Manufacturing 0.149 -0.493 -0.070 0.733 0.702 Consumer durables -0.129 0.077 0.207 0.728 0.373 Consumer non durables -0.530 -0.455 0.122 1.047 0.771 Financials -0.578 -0.583 -0.204 1.041 1.057 Health -0.616 -0.834 0.284 0.978 1.058 Telecom -0.461 -0.597 0.045 0.939 0.949 Utility -0.150 -0.025 0.706 0.397 0.482 Business -0.482 -0.797 -0.040 0.846 1.216 Wholesale -0.591 -0.602 0.292 0.908 0.942 Chemicals 0.194 -0.199 0.313 0.481 0.495 Energy -0.807 -0.790 0.129 1.139 1.099

5.7.2 Popularity and the comovement in prices/returns

In section 5.7.1, we show the movement in popularity through time. In this section, we explore whether the movement in popularity leads to comovement in returns. If investors apply style investing, they will not distinguish between stocks within a style. Stocks that may be fundamentally unrelated are grouped to the same category, which lead to demand shocks across all stocks in the style, resulting in comovement in returns. The correlation between returns is a good indicator to distinguish between style popularity and stock popularity. If investors apply style investing the returns across all stocks in the style will be highly correlated. Before we test for the eleven sectors whether the movement in popularity leads to comovement in returns, we first analyze the comovement in returns of internet stocks. In appendix 5A, table 5A.4 shows the average correlations in returns between internet stocks for different

5.7 Robustness analysis 173 stages in the cycle. As subperiods we use the different stages of the fashion cycle which are defined in appendix 5A. The internet sector does not show the same high correlations in returns as the results of Cornell (2004). The correlation increases slightly in the emulation and mass phase, but is even lower than Cornell’s correlation of 30% at the end of the boom. Table 5A.5 in appendix 5A presents the distribution of the 60-day rolling correlation through time over the period 1994 to 2003. We calculate for each sub period and correlation group the average and median fraction of 60-day rolling correlation between all pairs of stocks. This table shows that there is a very low fraction of stocks that was highly correlated with each other. For 4.5 % of the cases the 60-day correlation increases to above 40% in the introduction period, 0.5% in the emulation period and 0.4% in the mass phase. We also calculate the 60-day rolling correlations between Yahoo and Amazon and calculated the average and median (between the brackets) correlation for each sub period. The average correlations were in the emulation period 56% (56%) and for the mass phase 66% (70%). Another note that can be made on the correlations is that fifty percent of the stocks are negatively or not (0%) related with each other (in all five phases). Comparing these results with the results of Cornell (2004) we believe that the results of Cornell are a result of chance instead of evidence for the style investing hypothesis. He chose just those two internet stocks that show high comovement in returns. An explanation for the results found by Cornell may be stock popularity. Both stocks, Yahoo and Amazon, could have been popular during this period. In order to test for comovement in returns for the other eleven industries, we perform the following regression:

∆corrX ,t = at + β1∆PX ,t + ε t , (5.7)

174 Chapter 5. Style popularity and the comovement of stocks

where ∆corrX,t is the change in percentages of correlations between daily returns in a quarter that fall between –0.20 and 0.20 and ∆PX,t is the change in popularity. Table 5.13 provides the estimates of the coefficient across industries. The third row contains the estimates of β1 and shows that the coefficients are uniformly positive. This implies that correlation between returns is decreasing when a style shows an increase in popularity, although, the heteroskedasticity consistent t-statistics show that the results are not reliable.

Table 5.13: Regression coefficients: correlation between returns and the change in popularity over period 1983 to 2004 This table shows the results of equation 5.7, where the dependent variable is the number of stocks that have a correlation in returns between –0.20 and 0.20. Correlations are calculated for each quarter over daily returns over the period 1983 to 2004. The independent variable is the change in popularity. Newey-west is used to adjust the t-statistics for heteroskedasticity and autocorrelation. 2 Industries: constant b1 t(constant) t(b1) adj. R Manufacturing 0.031 0.015 0.128 0.008 0.000 Consumer durables -0.229 2.825 -3.555 0.800 0.007 Consumer non durables -0.115 3.046 -0.306 1.327 0.020 Financials -0.066 2.022 -0.260 1.555 0.017 Health -0.113 2.088 -0.411 0.842 0.019 Telecom -0.389 10.868 -0.590 3.491 0.093 Utility -0.088 5.795 -0.172 1.380 0.025 Business 0.012 2.627 0.023 1.391 0.039 Wholesale 0.005 2.019 0.029 0.644 0.006 Chemicals -0.175 4.186 -0.371 1.557 0.037 Energy 0.103 0.740 0.295 0.247 0.001

In summary, using the comovement in returns rather than the comovement of turnover ratios, we find similar results as in section 5.6.2. Notably, the comovement in returns decreases with an increase in popularity. However, the adjusted R-squares of these regressions range from 0.000 to 0.093, lower than the adjusted R-squares of the regressions with comovement in turnover ratios, which, as reported in table 5.7, ranges from 0.024 to 0.171.

5.8 Conclusion 175

Nevertheless, the coefficients are uniformly positive, which points to the existence of popularity at an individual stock level instead of a style level. Taken together the results of 5.6 and 5.7, our findings are consistent with the predictions of stock popularity hypothesis instead of the predictions of the style investing hypothesis.

5.8 Conclusion

This chapter provides evidence that popularity is at an individual stock level instead of a style level. Because popularity is closely related to fashion, we discuss fashion in the context of investing in section 5.2. Fashion and popularity are related in the way that they both reflect the collective preferences of individuals and the changes of such preferences over time. The chapter uses different sources of data, such as data on stocks, mutual funds, IPOs and analysts to reflect the collective preferences of investors. With the different sources of data we compose a popularity index. The popularity index is obtained with principal component analysis. This analysis constructs an index based on variables that capture a common factor. We find strong evidence that style popularity cannot be attributed to style investing. That is, popularity is stock-specific rather than style- specific. Styles that are less popular show size-effects. Investors choose for large caps when a style is less popular. Barberis and Shleifer argue that an investment cycle starts after good information in terms of good past performance. Our findings show that popularity is positively related to past returns. These findings are closely related to the literature on positive feedback trading (momentum traders). Grinblatt, Titman and Wermers (1995 and 1997) and Carhart (1997) show that institutional investors tend to buy stocks that performed well in the past.

176 Chapter 5. Style popularity and the comovement of stocks

Finally, we perform some robustness checks to show the life cycles of popularity which can be compared to fashion cycles as is described in section 5.2. In addition, we perform a regression to test whether the change in popularity of a particular style leads to comovement in returns between stocks in that style. Our findings show that an increase in popularity leads to a decrease in correlations in returns between stocks in the same style. Taken together, our findings are consistent with the predictions of stock popularity hypothesis instead of the predictions of the style investing hypothesis.

Appendix 5A 177

Appendix 5A: Fashion cycle for the internet sector

Everett Rogers developed the diffusion of innovation model to help understand the social process through which a change or innovation is accepted. Rogers states that "diffusion is the process by which an innovation is communicated through certain channels over time among the members of a social system." This process has proven effective in a variety of situations from deciding on a plan of action in a small social gathering to introducing a new product in the market place. Rogers suggests that trying to quickly and massively convince a group to adopt a new idea usually results in failure. He, therefore, determined that any group could be divided into five categories, based on the idea that certain individuals are more accepting of new ideas (i.e. are more innovative) and others are less accepting and may never adopt or embrace new ideas. The five adopter categories are: innovators, early adopters, early majority, late majority and laggards.

Classification of analysts into categories following five segments of individual innovativeness by Rogers (1983):

Innovators: up to 2.5% participants Early adaptors: up to 13.5% participants Early majority: up to 34% participants Late majority: more than 34% participants Laggards: less than 16% participants

178 Chapter 5. Style popularity and the comovement of stocks

Table 5A.1: Classification of analysts into categories following five segments of individual innovativeness by Rogers (1983) for internet stocks Total Fashion cycle Total number Brokers internet sector number of based on the of brokers in in % of total number of brokers in model of internet sector brokers in I/B/E/S I/B/E/S Rogers 1992 3 221 1.4% Innovators 1993 10 221 4.5% 1994 14 237 5.9% Early adopters 1995 24 253 9.5% 1996 40 280 14.3% 1997 66 336 19.6% 1998 96 365 26.3% 1999 136 356 38.2% Early majority 2000 154 341 45.2% 2001 157 326 48.2% 2002 154 293 52.6% Late majority 2003 161 380 42.4%

Because the internet sector had its origin in the nineties it was completely new, we can express this sector in terms of fashion cycles. We use the adoption and diffusion model of Rogers (1983) to divide the internet cycle in different stages. Table 5A.2 presents the level of popularity among investors reported by popularity measures described in section 5.4.1. Table 5A.2 shows the different stages of the fashion cycle with the corresponding values of the different variables for the internet sector. The fashion cycle of internet stocks started in 1992 where the first internet firm, America Online, went public. The first mutual fund that specializes in internet stocks started trading in 1996. The number of IPO’s grew to 261 in the early majority phase, which was between 1997 and 1999 and fell to 123 in the period 2000 to 2003. At the same time the average percentage of inflow for each mutual fund in a year reached its peak with 153.75%. Liquidity increased in the same period, the average turnover ratio increased to 4.0. The number of analysts that cover internet stocks in the

Appendix 5A 179 early majority phase is 12% and reaches its peak in the late majority phase with 18.7% of all analysts covering the internet sector. The measures that reflect optimism reach their peak in the early majority phase.

Table 5A.2: Descriptive statistics for the internet sector over the period 1993 to 2003 The adoption and diffusion model by Rogers (1983) is used to divide the internet period in different stages. Turnover ratio is style volume divided by the style’s number of outstanding shares. Nmft is the number of mutual funds that is organized during the period. Avg. Inflow is the average in –and outflow per mutual fund on an annual basis. Analyst coverage is the total number of analysts with respect to the total number of analysts in period t that follows internet stocks. Nup/Ndn is ratio with the number of upgrades with respect to the number of downgrades.

Mutual funds Analyst Avg. Number Turn- bid-ask Avg. Nup/Ndn of IPO's over Cove- spread Nmf Inflow t rage (%) 1993 Leaders 1 2.378 4.667 0 0 0.00% 0 1994- Early 33 1.624 5.288 2 0.506 4.90% 1.083 1996 adopters 153.7 1997- Early 261 4.044 7.493 36 12.10% 0.901 1999 majority 51 2000- Late 123 2.533 8.474 26 0.003 18.70% 2.501 2003 majority

Table 5A.3 presents the average level of return and turnover dispersion for the internet sector. The average level of return dispersion grows from 16.5 percent in the leaders phase to 26 % in the late majority phase. The standard deviation of the turnover ratio across the assets is 17.4% in the leader phase and grows to 52.2% in the late majority phase. This is a positive relation between dispersion and popularity, which implies that investors do not choose stocks on a group basis but on an individual level within the group. Table 5A.4 presents the style investing measures, the average correlations in returns between stocks and the autocorrelation, for different stages in the cycle. The internet sector does not show the same high correlations in returns as the results of Cornell shows.

180 Chapter 5. Style popularity and the comovement of stocks

Table 5A.3: Popularity and dispersion for the internet sector for the different stages of the fashion cycle For each phase we calculated the average standardized popularity and the cross standard deviation of the turnover ratio (see equation 5.3 and 5.5 in section 5.4.2 and 5.6.1).

Average Average popularity turnover dispersion 1993 Leaders 0 0.174 Early 1994-1996 -0.057 0.298 adopters Early 1997-1999 0.521 0.522 majority Late 2000-2003 1.299 0.284 majority

Table 5A.4: Style investing measures The autocorrelation with one lag is calculated for the time series of returns of the internet sector. For each pair of internet stocks we calculated the correlation and then we calculated the average correlation of all pairs. Style investing Correlation Auto- among correlation stocks 1993 Leaders - -0.047 Early 1994-1996 0.008 0.258 adopters Early 1997-1999 0.013 -0.820 majority Late 2000-2003 0.011 -0.787 majority

Other sectors already existed for a long time and are difficult to express in terms of the five stages used by Rogers. We calculate the different stages of the fashion cycle for the other ten sectors. Our findings suggest that all ten sectors were in their early and late majority in the nineties.

181

-100% -100% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% ion for each pair and and pair each ion for (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.1%) (0.1%) 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.8% 0.8% (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.0%) (0.7%) (0.7%) 0.1% 0.1% 0.0% 0.0% 0.4% 0.4% 0.4% 0.4% 3.7% 3.7% of 60-day rolling correlations for correlations for 60-day rolling of (0.1%) (0.1%) (0.0%) (0.0%) (0.3%) (0.3%) (0.3%) (0.3%) (3.4%) (3.4%) 2.1% 2.1% 0.6% 0.6% 4.7% 4.7% 7.3% 7.3% 12.7% 12.7% (2.1%) (2.1%) (0.4%) (0.4%) (5.7%) (5.7%) (7.2%) (7.2%) (13.5%) (13.5%) 44.4% 44.4% 45.7% 45.7% 42.4% 42.4% 40.2% 40.2% 30.5% 30.5% (43.8%) (43.8%) (45.8%) (45.8%) (41.4%) (41.4%) (40.4%) (40.4%) (29.9%) (29.9%)

ferent correlation groups. groups. correlation ferent lation. For each calculated phase we the rolling average correlat 49.2% 49.2% 51.2% 51.2% 45.5% 45.5% 42.0% 42.0% 31.2% 31.2% (49.2%) (49.2%) (51.2%) (51.2%) (44.2%) (44.2%) (42.4%) (42.4%) (30.9%) (30.9%)

(between the brackets) fraction 2.5% 2.5% 0.9% 0.9% 5.0% 5.0% 7.9% 7.9% 13.8% 13.8% (2.7%) (2.7%) (0.9%) (0.9%) (6.1%) (6.1%) (7.6%) (7.6%) (13.9%) (13.9%) -40% - -21% -20%-0% 1-20% 21-40% 41-60% 61-80% 81% 61-80% 41-60% -20%-0% -21% 21-40% 1-20% - -40% The fraction of correlations that belong to each correlation interval interval correlation to each that belong correlations of The fraction -40% -40% 0.1% 0.1% 0.0% 0.0% 0.3% 0.3% 0.5% 0.5% 5.5% 5.5% < (0.1%) (0.1%) (0.0%) (0.0%) (0.2%) (0.2%) (0.3%) (0.3%) (5.8%) (5.8%) 2001.7-2003 2001.7-2003 2000.7-2001.6 2000.7-2001.6 1998.7-2000.6 1998.7-2000.6 1997.7-1998.6 1997.7-1998.6 1994.1-1997.6 Subperiod Subperiod each correlation group and phase in the fashion cycle. Appendix 5A average and median Table 5A.5: The For calculated each stocks pair of rollingwe the corre 60-day then calculated the fraction of correlations that belongs to the dif the to belongs that correlations of fraction the calculated then 182 Chapter 5. Style popularity and the comovement of stocks

Chapter 6

Conclusions

6.1 Overview

For the last two decades, empirical evidence has shown that patterns in stock return data exist that cannot be explained with classical finance models like the CAPM. Several behavioral and rational models have been developed to explain the patterns in stock returns. As has been mentioned in chapter 1, the main purpose of this thesis is to identify, analyze and further develop the behavioral reasoning underlying empirical observations of return patterns. In this thesis we have presented four chapters in which different aspects of behavioral models and the impact of the underlying assumptions on stock returns are analyzed. In chapter 2 an overview of the relevant literature has been presented. We can categorize the other three chapters according to two issues:

183 184 Chapter 6. Conclusions

1. Value premium With respect to the value premium we investigate the expectational error hypothesis and the drivers behind investors’ uncertainty. So far, both issues have been explored in different kinds of ways to explain the value premium. All of these empirical studies use the same method for the classification of value and growth stocks. We develop an alternative method to show better insights in the dynamical process of the life of value and growth stocks. 2. Style investing With respect to the style investing hypothesis of Barberis and Shleifer (2003), we investigate to what extent stock popularity can be attributed to style investing. The model by Barberis and Shleifer has been tested by several researches using in- and outflows of mutual funds and portfolios of individual investors. So far, social effects such as collective preferences of investors have been neglected in these studies. We use different variables that reflect the collective preferences of investors and investors’ sentiment over time to test the popularity issue.

The part that is dedicated to the value premium consists of chapter 3 and 4. Chapter 5 is dedicated to style investing and stock popularity. The purpose of the present chapter is to summarize our main findings, point to unanswered questions and offer some suggestions for further research.

6.2 Main findings

In this thesis we analyze empirically several underlying assumptions of behavioral finance models. The general hypothesis is that behavioral finance has explanatory power with respect to the patterns found in stock

6.2 Main findings 185 returns. In this section, we summarize our main results and highlight the most important conclusions that we derive from these results. In chapter 2 we give a review of models, rational versus behavioral, that explain stock returns. We show that some anomalies have not been fully explained and that there is room for further analyses. With respect to the value premium two possibilities seem worth to investigate: first, the error- in-expectation hypothesis, second, the drivers behind investors’ uncertainty. So far, both issues have been explored in different kinds of ways to explain the value premium. Another issue that deserves a closer look is the style investing hypothesis of Barberis and Shleifer (2003). Based on our review of the literature we have decided to investigate to what extent the stock popularity can be attributed to style investing. In chapter 3 and 4 we analyze an alternative classification method to show better insights in the dynamical process underlying value stocks and the value premium. We make a distinction between switching versus fixed- style stocks. Within each style (i.e. value versus growth stock investing) we distinguish between stocks that stay for one period within a particular style and stocks that stay for two or more periods within a particular style. We analyze how stocks behave when they switch from style and what variables or factors are important to explain the style-switching behavior. We find that only a small fraction of the ‘value group’ is responsible for the value premium, notably the switching-style stocks. In chapter 3, using our newly obtained classification method, we investigate the role of investors’ optimism/pessimism in explaining the value premium. In order to attain this goal, we use forecasts of financial analysts and focus on the bias in earnings in the next two years after portfolio formation. We assume that investors’ expectations can be proxied by analysts’ earnings forecasts. 186 Chapter 6. Conclusions

To test the optimism hypothesis, we compare analysts forecast with the final earnings realization, i.e. investors are optimistic when analysts’ earnings forecasts are higher than actual earnings realization and pessimistic when analysts’ earnings forecasts are lower than actual earnings realization. It turns out that the value premium is not determined by pessimism of investors who extrapolate the poor performance of value stocks too far into the future. Instead, our results show that analysts’ earnings forecasts of value stocks loosing their initial classification (i.e. style-switching value stocks) are associated with increasing optimism. This result contradicts the main conclusion of La Porta (1996) and La Porta et al. (1997). We believe that our results are more robust, since we focus only at a small group of value stocks that generate the value premium. By analyzing only that fraction of stocks that is responsible for the value premium, we show better insights in which variables or factors are important in the dynamical process underlying value stocks and the value premium. In chapter 4, we focus on uncertainty of expected earnings. As a proxy of investors’ uncertainty we use dispersion in analysts’ earnings forecasts. We investigate whether uncertainty is related to past information and to the speed of information diffusion. Firstly, we look for evidence that uncertainty is increasing when less information about a stock is revealed. Secondly, we examine whether uncertainty is increasing because investors extrapolate past information into the future. This information can be in the form of stock returns but also in the form of forecast errors. If investors’ earnings forecasts have been wrong a couple of times, investors may feel deceived and investors’ uncertainty about future earnings will increase. We conclude that the less information is revealed about a company, the more likely it is that too optimistic expectations and bad past performance lead to higher uncertainty. In addition, we have investigated whether switching style stocks should be associated with high uncertainty in earnings prospects than fixed-style stocks. Our findings show evidence that

6.2 Main findings 187 analysts are more uncertain about the earnings prospects of switching style stocks than they are about the earnings prospects of fixed-style stocks. Combined with the evidence from chapter 3, we conclude that the value premium is the result of uncertainty accompanied by changing expectations of future earnings in the year after formation. This means that investors are initially uncertain about the prospects of switching-style stocks. During the post formation year in which the style-switch takes place, investors are surprised and change their expectations drastically in the opposite direction. This results in an increase (decrease) in optimism for switching-value (-growth) stocks.

Whereas chapters 3 and 4 focus on explanations for the value premium, chapter 5 investigates to what extent the popularity of a stock can be attributed to style investing. We gather proxies for stock popularity that can be used as time series variables to construct a novel composite popularity index based on principal component analysis. We then apply a regression analysis between this popularity index and the proxy for dispersion (dispersion being our measure of heterogeneity of stock behavior within a style category). We use the cross standard deviation of the turnover ratio as a proxy for dispersion to test whether stock popularity can be attributed to style investing. The evidence that we present challenges the view that popularity is on a style level rather than on an individual stock level. From our findings we can conclude that the popularity of a stock cannot be attributed to style investing. This suggests that the popularity of stocks is stock specific and not dependent on the investment style that it belongs to. Next, we investigate whether our results are influenced by size-effects. We find size-effects for styles that are not popular and no size-effects for the popular styles. Moreover, when styles are less popular, the quintile with largest stocks has lower dispersion than the quintile with the smallest stocks. This suggests that if the on average less popular styles become

188 Chapter 6. Conclusions popular, investors will prefer large-cap stocks over small-cap stocks. In addition, we investigate the impact of past performance in returns on style popularity. It turns out that style popularity is determined by past performance in returns. This result confirms the findings by Pomorski (2004), Kumar (2002), Froot and Teo (2004). We have identified and analyzed the behavioral reasoning underlying empirical observations of return patterns. The analyses in chapters 3 and 4 with a newly obtained classification method show better insights in the dynamic behavior of value and growth stocks. The analysis of uncertainty in chapter 4 shows that uncertainty is increasing if firms have low analysts’ coverage, have too optimistic earnings forecasts and have low past performance. With respect to style investing, the evidence in chapter 5 suggests that stock popularity cannot be attributed to style investing. This is more pronounced for small stocks than large stocks. Summarized, our findings suggest that the behavioral reasoning in the literature underlying empirical observations of return patterns has to be reconsidered.

6.3 Discussion

The question whether anomalies can be explained with rational or behavioral explanations remains a vividly debated one. Based on our findings we have to conclude that investors are subject to biases. In other words, we advocate behavioral explanations. Compared to the existing literature on the value premium, we use an alternative method of classification. We find that our approach of classification leads to different outcomes, and may therefore be an important step in improving our understanding of the existence of the value premium. For example, contrarian to the literature, we find that the value premium is caused by

6.3 Discussion 189 investors’ optimism instead of investor’s pessimism. In a dominant strand of the literature the value premium has been explained by the expectational error hypothesis. The superior return of value stocks is due to expectational errors made by investors, who tend to extrapolate past earnings growth rates too far into the future. Our results tell a different story. Apart from the fact that analysts are more optimistic about the future earnings of value stocks than growth stocks, we also find that the value premium is caused by an increase in analysts’ optimism for a small fraction of the value stocks that is responsible for the value premium. This result puts the discussion about the explanation of the value premium in a different perspective. A second explanation for the value premium is from Doukas, Kim and Pantzalis (2003), who suggest that the value premium is the result of investors’ uncertainty. They use analysts’ uncertainty as a proxy for risk22 and show that the superior returns of value stocks are due to higher uncertainty about future earnings. Our alternative classification leads to different outcomes. Apart from the fact that uncertainty is not positively related to stock returns, we also find a nonlinear relation between the book- to-market ratio and uncertainty. The switching-style stocks show higher uncertainty than the fixed-style stocks for both value and growth portfolios. In line with this, we find that the chance for a stock to migrate from one style category to another in the next year is higher when uncertainty is higher. This result also puts the discussion about the explanation of the value premium in a different perspective.

This thesis is based on empirical studies, which depend on the availability of data. Therefore, a number of interesting topics has not been analyzed, but

22 Doukas, Kim and Pantzalis (2003) use dispersion in analysts’ earnings forecasts as an uncertainty-metric, which is positively related to uncertainty of future growth in earnings and, therefore, to the riskiness of equity investment.

190 Chapter 6. Conclusions should be mentioned here. First, we use analysts’ earnings forecasts and dispersion in analysts’ earnings forecasts from the I/B/E/S database as a proxy for investors’ expectations and uncertainty about future earnings. The analysts’ earnings forecasts reflect the analysts’ expectations of future earnings, and the dispersion in analysts’ forecasts manifests the analysts’ divergence of opinion in predicting future earnings. As a consequence, we have only dealt with the expectations and uncertainty of future earnings of financial analysts instead of the expectations and uncertainty of investors. In addition, the measurement of financial analysts’ expectations as a measurement of investors’ expectations may have a pitfall as well. The expectations of investors might be less optimistic in nature than the expectations of financial analysts23. Financial analysts may have a self- interest in recommending stocks to generate commissions and other investment banking activities, such as equity issues and IPO’s. The role and measurement of investors’ expectations and uncertainty remains unclear and must be further analyzed. Second, we use a number of proxies that reflect the degree of collective preferences of investors in order to measure popularity. Popularity will often be related to fashion and, therefore, to fashion cycles. With data on social interaction, an analysis of stock markets in terms of fashion might have been performed. Investigating the effect of social interaction in the decision making process of investors seems worthwhile to investigate further. For example, it would be interesting to investigate to what extent the preferences of an individual investor are influenced by the preferences of friends, families and relatives. To describe the investment process in terms of fashion and fashion cycles, social interactions may be an important aspect to be analyzed further.

23 Although, La Porta (1996) and Elton, Gruber and Gultekin (1981) show that analysts’ forecasts represent a relatively good proxy for market’s earnings expectations of future earnings.

6.3 Discussion 191

Finally, the last area that deserves more attention is the impact of risk on stock returns. The ‘rational school’ believes that the value premium should be explained in terms of non-diversifiable risk. We have not investigated whether the switch that stocks make from one style to other styles is the result of non-diversifiable risk. Although we have shown that uncertainty is higher for switching-style stocks compared to fixed-style stocks, we have also shown that there is a negative relation between uncertainty and future returns. The negative relation between uncertainty and future returns is difficult to reconcile within a risk-based framework. Barron et al. (1998) and Doukas et al. (2006) argue that uncertainty captured by the dispersion in analysts’ earnings forecasts is likely to be a poor proxy for risk, since it is contaminated by the idiosyncratic elements of uncertainty in analyst information. They believe that the differences of opinion as a proxy for uncertainty should stem from the volatility of a firm’s underlying fundamentals rather than poor or limited information. This issue still remains open and further research is needed.

192 Chapter 6. Conclusions

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Samenvatting (Summary in Dutch)

In de afgelopen twintig jaar zijn patronen in rendementen van aandelen gevonden die niet vanuit de neo-klassieke economische theorie kunnen worden verklaard. Modellen als CAPM zijn niet in staat om de gevonden anomalieën te verklaren. Verscheidene modellen, rationele en ‘behavioral’, zijn vervolgens ontwikkeld. Dit proefschrift bestaat uit drie empirische studies met onderzoek naar aandelenmarkten in de Verenigde Staten. In deze studies worden vanuit verschillende invalshoeken verklaringen voor deze anomalieën geanalyseerd en gezocht. In dit proefschrift concentreren we ons voornamelijk op de waarde- en groeiaandelen (‘value’ en ‘growth’ stocks). Een van de anomalieën die over de afgelopen twintig jaar gevonden is, is de z.g. ‘value premium’. De ‘value premium’ is het verschil in rendement tussen waarde- en groeiaandelen. Aangezien waardeaandelen gemiddeld een hoger rendement genereren dan groeiaandelen, wordt dit de ‘value premium’ genoemd. Deze ‘value premium’ is niet te verklaren met risicomaatstaven zoals die gebruikt worden in Modern Portfolio Theorie (MPT) gebaseerde modellen, zoals (markt) bèta en standaarddeviatie.

Dit proefschrift bestaat uit twee delen met elk een eigen doelstelling:

207 208 Samenvatting (Summary in Dutch)

1. Het eerste doel is om verklaringen te zoeken voor de ‘value premium’. We onderzoeken de ‘error-in-expectation’ hypothese en indicatoren die van invloed zijn op onzekerheid in winstverwachtingen van beleggers. Zowel de ‘error-in- expectation’ hypothese als onzekerheid van beleggers zijn eerder onderzocht. Echter, deze studies hanteren dezelfde classificatiemethode voor waarde- en groeiaandelen. In dit proefschrift ontwikkelen we een alternatieve classificatiemethode, waarbij we alleen die aandelen analyseren die verantwoordelijk zijn voor de ‘value premium’. 2. Het tweede doel is om verklaringen te vinden door de invloed van sociale effecten te introduceren in aandelenmarkten. We introduceren populariteit op beleggingsstijl- en individueel aandelenniveau als een belangrijke factor in het beleggingsproces. We onderzoeken in welke mate de populariteit van individuele aandelen kan worden toegeschreven aan de populariteit van beleggingsstijlen.

Het inleidende hoofdstuk bevat een definitie van het begrip beleggingsstijl, en een overzicht van beleggingstijlen die de afgelopen eeuw door beleggers zijn gevolgd. Een stijl kan gedefinieerd worden als een classificatie van aandelen in dezelfde groep gebaseerd op bepaalde gemeenschappelijke karakteristieken. Het beleggingsbeleid waarbij beleggers hun keuze baseren op stijlniveau in plaats van op individueel aandelenniveau wordt ‘style investing’ genoemd. Een grote verscheidenheid aan beleggingsstijlen is ontwikkeld in de vorige eeuw. Voorbeelden zijn strategieën gebaseerd op landen, sectoren, markt kapitalisatie, op rendementen uit voorgaande perioden, en waarderingsratio’s zoals de ‘book-to-market’ ratio en de ‘earnings-to-price’ ratio. Tot 1980 was het doel van beleggers om vooral diversificatie te verkrijgen. Na 1980 verschoof de doelstelling van

Samenvatting (Summary in Dutch) 209 diversificatie naar het creëren van extra rendementen boven een bepaalde evenwichtswaarde.

In hoofdstuk 2 wordt een overzicht van empirische studies gegeven die patronen in aandelenrendementen laten zien die inconsistent zijn met modellen die uitgaan van de efficiënte markten. Een markt wordt volkomen efficiënt genoemd wanneer alle nieuwe informatie zonder vertraging en zonder vertekening in de prijsverhoudingen van de financiële instrumenten tot uitdrukking komt. Deze definitie geeft aan dat beleggers niet in staat zijn om systematisch de markt te verslaan. Voorbeelden van patronen die in aandelenrendementen gevonden zijn en die moeilijk te verklaren zijn vanuit het gedachtegoed van efficiënte markten zijn momentum en contrarian effect, ‘value premium’, ‘size-effect’ en onder- en overreactie van aandelenkoersen op nieuws. Als antwoord op de gevonden anomalieën, de verschijnselen die niet lijken te passen binnen de rationele verwachtingentheorie, zijn de laatste jaren verscheidene verklaringen vanuit zowel de rationele als de ‘behavioral’ stroming gevonden. De rationele stroming probeert vanuit risico-rendement raamwerken anomalieën te verklaren. Hierbij staat centraal dat markten efficiënt zijn en beleggers rationeel. Rationalisten gaan er van uit dat anomalieën voortkomen uit fouten in de bestaande modellen. Een voorbeeld van een binnen deze stroming vallende aanpassing is het drie-factorenmodel. Dit model is door Fama en French (1992) ontwikkeld om het spanningsveld tussen aan de ene kant het CAPM en aan de andere kant de nieuwe empirische gevonden aandelenpatronen te overbruggen. De ‘behavioral finance’ probeert anomalieën te verklaren vanuit de cognitieve psychologie. Onderzoekers uit de ‘behavioral finance’ analyseren het gedrag van beleggers en focussen zich vooral op het gedrag dat afwijkt van rationeel gedrag. Deze benadering concentreert zich op de wijze waarop individuen uitkomsten waarderen en informatie verwerken en gebruiken. Volgens het principe van

210 Samenvatting (Summary in Dutch) marktefficiëntie hoeven niet alle beleggers rationeel te zijn. Alleen een klein aantal wordt geacht rationeel te zijn, zodat zij de prijsinefficiënties wegwerken (Black and Litterman (. Volgens de ‘behavioral finance’ is dit niet noodzakelijkerwijs het geval. Volgens hen zijn arbitrageurs niet altijd in staat om te corrigeren voor prijsinefficiënties, aangezien het plegen van arbitrage risicovol en kostbaar is (De Long et al., 1990, Shleifer and Vishny, 1997). In dit hoofdstuk worden een drietal rationele en een drietal ‘behavioral’ modellen beschreven. We laten zien dat deze modellen nog niet in staat zijn om anomalieën te verklaren en dat er nog ruimte is voor nader onderzoek. Vooral de veronderstellingen van de ‘behavioral’ modellen vragen om nader onderzoek. Daarom hebben we ons in dit proefschrift vooral geconcentreerd op verklaringen uit de ‘behavioral finance’.

In hoofdstuk 3 en 4 analyseren we een alternatieve classificatiemethode om een beter inzicht te krijgen in de ‘value premium’. We maken een onderscheid tussen ‘switching-’ en ‘fixed’-stijl aandelen. Binnen elke stijl, zowel de ‘value’ stijl als ‘growth’ stijl, onderscheiden we aandelen die voor één periode binnen de stijl blijven en aandelen die twee of meer perioden binnen een stijl blijven. Vervolgens analyseren we welke aandelen migreren van stijl en welke kenmerken belangrijk zijn voor het migreren van de ene naar een andere stijl. Een klein aantal aandelen is verantwoordelijk voor de ‘value premium’, namelijk die aandelen die migreren van een stijl naar de andere stijl na één periode. Met de verkregen classificatie onderzoeken we in hoofdstuk 3 de rol van verwachtingen van beleggers voor toekomstige winsten. Om dit doel te bewerkstelligen wordt een proxy gebruikt voor de verwachtingen van beleggers. Als proxy hanteren we winstvoorspellingen van analisten. Vervolgens kijken we naar de afwijking tussen de voorspelde winstwaarde en de werkelijke winstwaarde. Analisten zijn optimistisch indien de voorspelde waarde hoger is dan de werkelijke waarde en

Samenvatting (Summary in Dutch) 211 pessimistisch indien de voorspelde waarde lager is dan de werkelijke waarde. We toetsen in hoeverre de ‘value premium’ verklaard kan worden met de ‘error-in-expectation’ hypothese. Deze hypothese houdt in dat beleggers, wanneer ze hun verwachting vormen omtrent toekomstige winsten en verliezen, gegevens uit het verleden te ver naar de toekomst extrapoleren. Aangezien waardeaandelen een gemiddeld lagere groei laten zien dan groeiaandelen, zijn beleggers minder optimistisch voor de toekomstige prestaties van waardeaandelen ten opzichte van de prestaties van groeiaandelen. Op de datum van aankondiging van cijfers worden beleggers vervolgens verrast. Het blijkt dan dat ze te pessimistisch waren voor waardeaandelen en te optimistisch voor groeiaandelen. Hierdoor moeten ze hun verwachtingen bijstellen, hetgeen voor waardeaandelen een bijstelling naar boven en voor groeiaandelen een bijstelling naar beneden betekent. Dit leidt tot een toename in rendementen voor waardeaandelen en een afname in rendementen voor groeiaandelen. Met andere woorden, de ‘error-in-expectation’ hypothese voorspelt dat analisten te optimistisch zullen zijn voor groeiaandelen en te pessimistisch zullen zijn voor waardeaandelen. Onze analyse laat zien dat de ‘error-in-expectation’ hypothese wordt verworpen en dat ‘value premium’ niet verklaard kan worden met pessimisme voor waardeaandelen en optimisme voor groeiaandelen. In plaats van dat beleggers te pessimistisch zijn over toekomstige winsten van waardeaandelen (omdat ze de slechte performance uit het verleden te ver in de toekomst extrapoleren) vinden we dat beleggers juist optimistischer zijn voor waardeaandelen dan voor groeiaandelen. Omdat analisten optimistischer zijn voor waardeaandelen dan voor groeiaandelen, analyseren we vervolgens de verandering in verwachtingen voor het jaar na portefeuilleformatie. Als gevolg van de stijlmigratie valt te verwachten dat analisten voor ‘switching’-stijl aandelen een verandering in hun verwachtingen zullen laten zien. We vergelijken daarom de

212 Samenvatting (Summary in Dutch) winstvoorspellingen van analisten voor de stijlmigratie met de winstvoorspellingen na stijlmigratie. Onze resultaten laten zien dat voor het kleine aantal aandelen dat verantwoordelijk is voor de ‘value premium’, namelijk ‘switching-value’ aandelen, beleggers juist een toename in optimisme laten zien in het jaar na portefeuilleformatie. Deze resultaten contrasteren met de resultaten van La Porta (1996) en La Porta et al. (1997), die bewijs vinden voor de ‘error-in-expectation’ hypothese. Onze resultaten zijn meer robuust, aangezien we ons alleen concentreren op die aandelen die daadwerkelijk verantwoordelijk zijn voor de ‘value premium’. Door ons alleen op deze aandelen te concentreren kunnen we beter onderzoeken welke variabelen belangrijk zijn voor het dynamische proces onderliggend aan waardeaandelen en de ‘value premium’. Onzekerheid over toekomstige winsten staat centraal in hoofdstuk 4. In dit hoofdstuk analyseren we welke variabelen van invloed zijn op de onzekerheid van beleggers omtrent toekomstige winsten. Als een proxy voor onzekerheid van beleggers gebruiken we de spreiding in analistenvoorspellingen voor toekomstige winsten. Als toekomstige winsten onzeker zijn, zullen analisten het moeilijker vinden om toekomstige winsten te bepalen. Dit zal leiden tot een divergentie van winstvoorspellingen. Op basis van de extrapolatie theorie en de ‘information diffusion’ theorie bepalen we in welke mate analisten onzekerder worden over toekomstige winsten, en onderzoeken vervolgens wat de relatie tussen de verschillende variabelen en onzekerheid is. De ‘information diffusion’ hypothese voorspelt dat naarmate de snelheid waarmee informatie verstrekt wordt laag is, onzekerheid over toekomstige winsten toeneemt. De snelheid waarmee informatie bekend wordt, kan belangrijk zijn voor de mate waarin beleggers onzeker zijn over toekomstige winsten. Indien minder informatie bekend is, is het moeilijker voor beleggers om toekomstige winsten te voorspellen. De marktprijs zal daardoor niet meer in overeenstemming zijn met zijn fundamentele waarde. Dit leidt tot meer onzekerheid over toekomstige

Samenvatting (Summary in Dutch) 213 winsten en verliezen. In dit hoofdstuk analyseren we of onzekerheid toeneemt indien de snelheid waarmee informatie over een aandeel beschikbaar wordt lager is. De snelheid waarmee informatie beschikbaar wordt, wordt benaderd met de variabele analistendekking (aangepast voor marktkapitalisatie). Naarmate meer analisten een onderneming volgen, zal meer informatie over de onderneming bekend zijn. Volgens de extrapolatie theorie kan informatie uit het nabije verleden van invloed zijn op de onzekerheid van beleggers, zoals vroegere winsten en verliezen, aandelenrendementen, en voorspellingsfouten. Indien beleggers gegevens uit het verleden extrapoleren naar de toekomst kan dit leiden tot meer onzekerheid over aandelen die de afgelopen periode een slecht resultaat laten zien. Daarnaast kunnen beleggers onzekerder worden als de winsten in het verleden lager waren dan verwacht. Indien ze een aantal keer verkeerd zaten met hun voorspellingen betreffende toekomstige winsten kan dit leiden tot een toename in onzekerheid. In dit hoofdstuk analyseren we of onzekerheid toeneemt naarmate beleggers informatie uit het verleden extrapoleren naar de toekomst. Onze resultaten tonen aan dat onzekerheid toeneemt naarmate er minder informatie beschikbaar is over een onderneming, wat overeenkomstig is met de ‘information diffusion’ theorie. Hoe lager het aantal analisten dat een onderneming volgt en hoe kleiner de marktkapitalisatie van de onderneming, des te minder informatie beschikbaar is en des te onzekerder analisten worden over toekomstige winsten. Verder vinden we een negatieve relatie tussen informatie uit het verleden en onzekerheid, hetgeen in samenspraak is met de extrapolatie theorie. Als aandelen een relatief slechte prestatie laten zien in de periode er voor, valt te verwachten dat onzekerheid van analisten zal toenemen. Daarnaast zal de onzekerheid toenemen indien analisten een aantal keer fout zaten met hun winstprognoses. Het uitvoeren van een meervoudige regressie, waarbij we het gezamenlijke effect toetsen van de extrapolatie

214 Samenvatting (Summary in Dutch) theorie en de ‘information diffusion’ theorie, laat zien dat de variabelen statistisch significant zijn. ‘Switching’- en ‘fixed’-stijl aandelen worden ook verder onderzocht in hoofdstuk 4. Stijlmigratie kan het resultaat zijn van beleggers die hun verwachtingen over toekomstige groei bijstellen. Deze verandering in verwachtingen is het resultaat van beleggers die zich realiseren dat ze verkeerd zaten met hun verwachtingen. Vervolgens zullen ze hun verwachtingen drastisch wijzigen in de tegenovergestelde richting. Hoofdstuk 3 laat zien dat stijl-‘switching’ het resultaat is van verandering in de verwachtingen van beleggers voor toekomstige winsten. Als de winstverwachtingen moeilijker te voorspellen zijn, zullen beleggers meer onzeker zijn over toekomstige winsten en verliezen. Dit betekent dat de kans op een stijl-‘switch’ groter zal zijn indien beleggers meer onzeker zijn over bepaalde aandelen. De onzekerheidshypothese voorspelt dat onzekerheid groter zal zijn voor ‘switching’-stijl aandelen en lager zal zijn voor ‘fixed’-stijl aandelen. Onze resultaten laten een positieve relatie zien tussen onzekerheid en de stijl-‘switch’ die aandelen maken het jaar na formatie. Uit hoofdstuk 3 en 4 kunnen we concluderen dat de ‘value premium’ het resultaat is van onzekerheid over toekomstige winsten die gepaard gaan met een verandering in verwachtingen voor toekomstige winsten in het jaar na formatie. Dit betekent dat beleggers aanvankelijk onzeker zijn over de toekomstige vooruitzichten van ‘switching-style’ aandelen. Gedurende het jaar na formatie, worden beleggers verrast met de werkelijke cijfers en veranderen ze vervolgens hun verwachtingen in tegenovergestelde richting. Dit leidt tot een toename (afname) in optimisme voor switching-waarde (groei) aandelen. We zijn voorzichtig met het interpreteren van onze resultaten. Ten eerste gebruiken wij analistenvoorspellingen en de spreiding in analistenvoorspellingen als een proxy voor winstverwachtingen en

Samenvatting (Summary in Dutch) 215 onzekerheid van beleggers. De analistenvoorspellingen geven de toekomstige winstverwachtingen van beleggers weer en de spreiding in analistenvoorspellingen geeft de mate van consensus over toekomstige winsten weer. Daarom hebben we de verwachtingen en onzekerheid van analisten geanalyseerd en niet zozeer die van beleggers zelf. Daarnaast kan de maatstaf - analistenvoorspellingen - zelf problemen geven. De verwachtingen van beleggers kunnen minder optimistisch zijn dan de verwachtingen van financiële analisten. Financiële analisten kunnen een eigen belang hebben bij het aanbevelen van aandelen, zoals het generen van opdrachten en andere bankactiviteiten zoals aandelenemissies en initial public offerings (IPO’s). Empirische studies van La Porta (1996) en Elton et al. (1981) laten echter zien dat analistenvoorspellingen een relatief goede proxy zijn voor winstverwachtingen in de markt.

Hoewel we in hoofdstuk 3 en 4 ons concentreren op de ‘value premium’ is de focus in hoofdstuk 5 op de ‘style investing’ hypothese. Deze hypothese suggereert dat beleggers vermogen alloceren op stijlniveau in plaats van op individueel aandelenniveau. Deze definitie van ‘style investing’ heeft een aantal empirische implicaties, aangezien beleggers geen onderscheid maken tussen aandelen binnen een stijl, waardoor aandelen die op fundamentele basis verschillen ten onrechte als hetzelfde worden behandeld. Dit kan leiden tot vraagschokken voor alle aandelen binnen die stijl. Als een gevolg van ‘style investing’ kunnen aandelen die op fundamentele basis niet gerelateerd zijn wel wat betreft prijs/rendement naar elkaar toe bewegen. In hoofdstuk 5 onderzoeken we in welke mate de populariteit van individuele aandelen kan worden toegeschreven aan ‘style investing’. De ‘style investing’ hypothese voorspelt dat populariteit op stijlniveau varieert en niet op individueel aandelenniveau. Immers als de populariteit van een stijl toeneemt, zullen beleggers hun vermogen op stijlniveau in plaats van op individueel aandelenniveau alloceren. Om te onderzoeken of populariteit

216 Samenvatting (Summary in Dutch) op een stijl- of individueel aandelenniveau wordt bepaald, vormen we een populariteitsindex op stijlniveau. Als eerste worden variabelen verzameld die populariteit reflecteren. Vervolgens wordt met ‘principal component analysis’ de verschillende variabelen tot een populariteitsvariabele gereduceerd. De ‘style investing’ variabele is de spreidingsmaatstaf die in dit geval de standaarddeviatie in ‘turnover’ ratio’s is. Immers als beleggers hun keuze op stijlniveau maken in plaats van op individueel aandelenniveau zal de ‘turnover’ ratio van alle aandelen binnen een stijl toenemen. Dit zal leiden tot een daling in de standaarddeviatie van de ‘turnover’ ratio’s binnen een stijl. Om te toetsen of populariteit op stijl of individueel aandelenniveau is, voeren we een regressie uit waarbij we perioden van extreme populariteit regresseren tegen de verstrooiingsmaatstaf. Onze analyse laat een positieve relatie zien tussen populariteit en de verstrooiingsmaatstaf, wat betekent dat populariteit wordt bepaald op een individueel aandelenniveau in plaats van, zoals de ‘style investing’ hypothese voorspelt, op een stijlniveau. Wanneer we de industrieportefeuilles indelen op basis van marktkapitalisatie – in quintielen – vinden we voor sectoren die gemiddeld minder populair zijn ‘size-effects’. De portefeuille met de ‘large-cap’ aandelen laten een lagere verstrooiing in turnover ratio’s zien dan de portefeuille met ‘small-cap’ aandelen. Dit betekent dat indien één van deze sectoren populairder wordt, beleggers zullen kiezen voor de ‘large-cap’ aandelen in plaats van de ‘small-cap’ aandelen. Ook een andere methode om te toetsen op de ‘style investing’ hypothese laat zien dat de populariteit op individueel aandelenniveau in plaats van op stijlniveau plaatsvindt. De theorie over ‘style investing’ impliceert dat beleggers de keuze van een stijl laten beïnvloeden door de het rendement uit het nabije verleden. Als een stijl hoge rendementen laat zien ten opzichte van concurrerende stijlen, zullen beleggers hun keuze laten vallen op de beter presterende stijl. De ‘style investing’ theorie zal daarom een positieve relatie voorspellen tussen populariteit en de aandelenrendementen uit het verleden. Op basis van de

Samenvatting (Summary in Dutch) 217 verkregen populariteitsindices per sector onderzoeken we in welke mate populariteit beïnvloed wordt door rendementen uit het nabije verleden. We vinden een positieve relatie tussen populariteit en rendementen uit het nabije verleden, hetgeen conform de ‘style investing’ theorie is. Als het gemiddelde rendement van een sector relatief hoog was in de afgelopen periode heeft dat een positief effect op de populariteit van die sector.