Factor investing strategies: an assessment on performance in U.S. equity markets

Chris Peeters ANR: 282018 SNR: 1245965

Supervisor: Prof. dr. F.A. de Roon Second reader: Dr. A.H.F. Verboven Program: MSc Finance

Abstract A substantial amount of research has been dedicated to explain the factors that drive equity returns. This thesis reviews the existing theories that try to explain the persistence of factor premiums related to “size”, “value”, “”, “low ”, “quality” and “ ”, both from a systematic risk and behavioral perspective. The performance of different factor portfolios is empirically tested over a period of 54 years using U.S. data. I show that the most effective way to obtain higher risk-adjusted returns is by mixing different - portfolios using mean variance optimization. These multi factor portfolios have very clear diversification benefits as they help to overcome the cyclicality of individual factor premiums. Furthermore, I find that multi-factor portfolios based on a traditional long-short strategy outperform a more recently popularized long only strategy. However, implementation costs and personal preferences may still be reasons to go for the long-only approach. I conclude that both factor-based strategies prove to be a good alternative to traditional active and passive investing styles. Table of contents

1. Introduction ...... 3 1.1. Academic background ...... 3 1.2. Thesis objective and structure ...... 4

2. Literature review ...... 5 2.1. Capital asset pricing model (CAPM) ...... 5 2.2. and Multi factor models ...... 6 2.3. Size ...... 7 2.4. Value ...... 9 2.5. Momentum ...... 10 2.6. Low volatility ...... 11 2.7. Quality ...... 12 2.8. ...... 13

3. Data and methodology ...... 15 3.1. Thesis data ...... 15 3.2. Methodology ...... 15

4. Empirical results ...... 18 4.1. Single factor portfolios ...... 18 4.2. Multi factor portfolios ...... 22 4.2.1. Equally weighted portfolios ...... 22 4.2.2. Mean variance efficient portfolios ...... 24 4.3. Long-short vs. Long-only portfolios ...... 27

5. Conclusion ...... 30

Reference list ...... 32

Appendix A: cumulative returns individual factor portfolios ...... 36

2 1. Introduction 1.1. Academic background For decades the question of how to construct the optimal portfolio has been one of the most relevant and important ones for . It is therefore not surprising that a large amount of academic research has been dedicated to provide us insight and theories on how to build such a portfolio that maximizes an ’s utility. Already in the 1950’s Markowitz came up with a theory on how to select the optimal portfolio based on a tradeoff between risk and returns. Where expected returns are of course a desirable thing for investors, while the accompanying variance is the unfavorable consideration that has to be taken into account (Markowitz, 1952). It goes to show that combining multiple non-perfect correlated securities can reduce the total risk of a portfolio, and thus improve the risk/reward ratio. Later research by Tobin, Sharpe and Lintner (1958, 1964 and 1965) built on these concepts of diversification and mean variance optimization, and further developed the by coming up with the well-known Capital Asset Pricing Model (CAPM). They proposed that if investors have equal expectations about future markets, they should all choose the same optimal portfolio (Tobin, 1958). Sharpe (1964) reasoned that this optimal portfolio is equal to the market portfolio. Since the market portfolio is supposed to include all available assets in financial markets, it is by definition the most diversified portfolio. In theory, this diversification can eliminate all firm-specific (unsystematic) risks, leaving only the systematic risk (market risk) to be compensated for. The CAPM theory states that this exposure to the market is the only factor that is driving a ’s expected return. For this to be true in the real world however, one has to assume that markets are truly efficient. Which means that all available information should be reflected in the stock prices immediately. This is consistent with a strong form of market efficiency as defined in Fama’s Efficient Market Hypothesis (1965, 1970). It implies that there is no possibility to obtain excess returns by active management, and therefore justifies a passive asset management strategy that follows the market portfolio. Over the years however, a substantial amount of research has criticized the relation between the market factor and returns as presented in the CAPM theory. In 1976 Ross proposed an alternative model in which multiple factors are allowed to have an effect on stock returns. While this study did not specify which factors are playing a role, other studies did find persistent anomalies in the relation between risk and returns. Fama and French (1992) for instance came up with a renowned model that includes

3 the factors ‘Size’ and ‘Value’ in addition to the market factor. Carhart (1997) extended this three- factor model by adding the momentum factor. Over the last decades various other factors have been discovered, of which ‘Low-volatility’, ‘Quality’ and ‘Dividend yield’ have been the most prominent. Since these drivers of stock returns have proved to gain excess returns over the market, it can be interesting and rewarding for investors to incorporate them in their portfolio selection.

1.2. Thesis objective and structure The purpose of this thesis is to find out whether following a factor-based investing strategy can be a rewarding strategy in terms of risk adjusted returns. To do this, a focus will be made on six factors that literature has proved to be most relevant: ‘size’, ‘value’, ‘momentum’, ‘low- volatility’, ‘quality’ and ‘dividend yield’. Long-short portfolios for each of these factors are analyzed and assessed on performance over the last 54 years. Since diversification benefits can be achieved through combining multiple factors, I will also consider multi factor portfolios that keep in mind different investor’s goals. Once again the performance of these created portfolios will be evaluated over the period of 1964 - 2017. Finally the long-short strategy will be compared to an alternative strategy that only takes the long positions of the factor portfolios. This thesis will concentrate solely on the US equity market over the last 50 years. Which I believe is an interesting scope for a couple of reasons. Firstly because the US market is considered to be one of the most efficient markets. This means that the anomalies as found in the form of factor premia should be less likely to persist over time. The fact that they actually do provide excess returns over a long period is therefore even more surprising and requires an explanation. Besides this, the last 50 years can be characterized as a time where factor became increasingly popular. Both in the academic world as in real life practice, where investment funds try to incorporate factor-strategies in their asset allocation decisions.

This research is structured into five chapters, beginning with the introduction. Chapter 2 provides a synthesis on the different factors. Theories that try to explain the existence of these excess factor returns are discussed here. Chapter 3 describes the data and digs into the methodology that is used to form the factor-based portfolios. The empirical results that are found are presented in Chapter 4. Finally, this paper ends with a discussion of the results and concluding remarks in the last chapter.

4 2. Literature review 2.1. Capital Asset Pricing Model Since market exposure can be seen as the first factor that has been discovered to drive a stock’s return, this literature review starts with a brief discussion of the well-known Capital Asset Pricing Model (CAPM). After Markowitz (1952) introduced a first framework to link a portfolio’s risks and expected returns, academics reasoned that a stock’s risk could be decomposed into two categories. The one kind of risk being related to business specific events (unsystematic risk), while the other type of risk is the general economic uncertainty as visible in the market (systematic risk). Since all unsystematic risk can be reduced through diversification, only the market risk should be compensated for in the form of higher expected returns. It is for this reason that Treynor (1961), Sharpe (1964), Lintner (1965) and Mossin (1966) eventually developed the CAPM model that describes this relation between systematic risk and expected returns. They defined the following linear relationship in the form of the (SML):

�(�!) = �� + �!(�(�!) − ��)

In this equation, �(�!) is the expected return on an individual security. Which takes the value of �� for a risk free investment, and increases with the stock’s exposure to the market.

The �! is the covariance between an individual stock and the market, divided by the market variance.

���(�!, �!) �! = ! �!

The (�(�!) − ��) represents the expected market premium. Meaning the extra reward an investor should receive for taking on systematic risk. For this theory to hold however, various assumptions had to be made about the real world. Black (1972) mentioned the following four main assumptions that describe the conditions in which the model holds. 1. Investors all share the same views about the probability distribution of future expected returns 2. The returns on all available assets follow a joint-normal distribution 3. Investors maximize utility and are risk averse 4. Unrestricted borrowing and lending at the risk free rate is possible

5 It is this fourth assumption that was particularly criticized in Black’s paper, since he regarded it as a bad approximation to the real world. By changing the assumption he found that the SML was flatter than in the original CAPM model by Sharpe (1964) and Lintner (1965), as low outperformed high beta stocks on a risk-adjusted basis. Over the years more criticism on the original CAPM model has been published. Roll (1977) reasoned that it is impossible to test the implications of the CAPM in the real world, considering there is no valid proxy for the market portfolio. Fama and French (2004) reviewed the empirical validity of the CAPM and summarized some of these critiques. They concluded that the market beta alone does not do a good job at explaining returns, and noted two prevailing views that try to justify why this is the case. One view says that irrational investor behavior is the root cause of the CAPM failure. The other view advocates that other unobserved variables exist that relate to systematic risk.

2.2. Arbitrage Pricing Theory and Multi Factor models

Since the CAPM can be seen as a rather simplistic asset-pricing model, researchers tried to come up with alternative models to associate expected returns to non-diversifiable risk. One of the most famous ones was the Arbitrage Pricing Model as defined by Ross (1976). He reasoned that it should not be possible to have any arbitrage opportunities between two well-diversified portfolios. For this to be the case, all systematic risks should be rewarded. The difference with the CAPM model however is that not only the sensitivity to the market is regarded as the source of systematic risk. Instead, multiple economic factors could play a role in driving a portfolio’s risk. Therefore, the APT formula can be expressed as follows:

�(�!) − �� = �!!�! + �!!�!+. . +�!"�! In this model, the �’s measure a stock’s sensitivity to a certain factor, while the accompanying risk premiums are noted by �! to �!. The number of factors that are included are neither fixed, nor specified in the paper. Since these economic factors are often not observable or measurable, the implementation of the model becomes problematic.

A different model that tried to take into account multiple factors is the ICAPM by Merton (1973)

6 Merton adjusted the static CAPM model by including state variables that consider consumption and investment opportunities over different time periods. With the addition of the state variables as factors to the CAPM model, the formula for expected returns can be stated as: ! �(�!) − �� = �!"[�(�!) − ��] + �!"[� �! − ��] !!!

Where �(�!) − �� denotes a stock’s excess return over the risk free rate, �!"[�(�!) − ��] is the market factor as in Sharpe and Lintner’s CAPM, �!" is the sensitivity of a stock to the state variable, while [� �! − ��] represents the excess return of this state variable. Fama (1996) notices that this is a multifactor efficient model, where a combination is made between a mean variance efficient portfolio and hedging portfolios for the variances in state variables. Just like the APT however, this model also did not yet specify the variables that actually play a role in driving systematic risk (besides the market factor of the CAPM). Thus to make these models empirically testable, relevant factors have to be identified from other academic research. Fama and French (1992) did this and came up with a model that incorporated risk premia for small firms and value stocks besides the market factor. Carhart (1997) extended this model with a momentum factor that looks at a stock’s short term past returns. With the addition of this factor, the model can be expressed as:

�(�!) − �� = �!! � �! − �� + �!! ��� + �!! ��� + �!! ���

In this equation, SMB (Small Minus Big) represents the excess return of a small market cap portfolio over a big market cap portfolio. HML (High Minus Low) stands for the excess returns of value stocks over growth stocks, and UMD (Up Minus Down) is the return premium of high momentum stocks over low momentum stocks. Over the years various other stock characteristics have been found to have an effect on returns. Such as low volatility (Haugen and Baker, 1991), quality (Piotroski, 2000) and dividend yield (Blume, 1980). The rest of this chapter will focus on each of these factors individually.

2.3. Size One of the first to discover the relation between a firm’s and returns was Banz (1981). He found that the average risk-adjusted returns for small firms have been higher than for their large counterparts. What should be noted, however, is that this relation between size

7 and returns is not linear. The effect for very small firms was much stronger than for medium and large sized firms. Furthermore, the cause of the ‘size effect’ remained unclear. It could be the case that the small cap premium is just acting as a proxy for other correlated factors. Fama and French (1992) incorporated and tested the size factor in their three-factor model, which also includes the market risk premium and value factor. They concluded that the size and value factors did a good job explaining the variance in average returns, while the market beta did not.

From an efficient market point of view, where the observed return premium compensates for systematic risk, numerous theories have tried to explain the small cap anomaly. Chan and Chen (1991) noted that small and big firms have different characteristics that define the risk-return correlation. Small firms on the NYSE tend to be stocks that underperformed in the past and thus show more signs of financial distress in the form of higher leverage or decreasing . As a result, investors require a return premium for this extra risk. Another explanation is that small stocks tend to be more illiquid than large stocks, implicating that the size premium is actually an illiquidity premium (Amihud, 2002). Zhang (2006) attributes the size factor to information uncertainty. He found that higher information uncertainty leads to overreaction of investors to good and bad news. This results in higher expected returns following good news and vice versa. Since there is a negative correlation between size and information uncertainty, the size factor could act as a proxy for this underlying variable. An alternative theory states that default risk is actually the deeper driver that explains both the size and the value premium. Vassalou and Xing (2004) discovered that the size effect was only significantly present in the highest default risk quintile. They also showed that higher default risks are related to higher expected returns, and concluded that these returns can be seen as compensation for systematic risk. Still, there is a fair amount of skepticism surrounding the size effect. Shumway (1997), for instance, found that missing delisting return data for CRSP stocks since 1962 caused a bias. As small stocks are more likely to get delisted and the returns associated with a delisting event are negative on average, the small size effect has been overstated in most of the early research. Furthermore, Keim (1983) uncovered that the observed excess returns on small caps happen almost exclusively in the first month of the year. In other research it became clear that the small cap anomaly disappeared after the early 1980’s. Schwert (2003) reasoned that this was the

8 consequence of the investor’s response to the increasing popularity of the size effect in academic literature. While it is up for debate whether the size anomaly is still ‘alive’, the latest consensus in academic world seems to be that more empirical research is required to test the robustness of the size premium (Van Dijk, 2011).

2.4. Value The value effect can be defined as the outperformance of stocks that seem undervalued relative to stocks that seem overvalued. Since claims for under and overvaluation can only be made once a reference point for price is available, its measurement always comprises a price variable relative to a firm’s fundamental variable. Ever since the 1930’s (see for instance Graham and Dodd, 1934) the concept of has been subject to academic research. In later years, a negative relation that was found between P/E ratios and risk-adjusted returns proved to be a challenge to the widely accepted CAPM model (Basu, 1977). A behavioral explanation for this phenomenon is that investors have irrational expectations for the performance of growth stocks as opposed to value stocks. This claim is supported by DeBondt & Thaler (1985, 1987), who found that low long-term returns in the past are followed by higher future returns and vice versa. The behavioral reason behind this is that investors overreact to good and bad news, and therefore underprice a stock that has done poorly in the past while overpricing a stock that has done well. As stock prices and expected returns have an inverse relation, the results that show this reversal of returns are justified. The value effect has also been included in Fama and French’s three-factor model as the High minus Low factor. They used the book to market ratio (B/M) instead of the E/P ratio as a measurement for value, considering it was the better of the two. Again a positive and persistent relation between the value factor and returns was found. From a systematic risk perspective, Lakonishok et al. (1994) and Fama and French (1995) found an explanation for the observed anomaly. They stated that the value premium is related to relative distress in the economy. Investors require an additional risk premium for stocks that share characteristics of distress. In times of economic crises this systematic risk increases, causing a higher premium for value stocks. However, various sources find this rationalization to be incomplete or simply not convincing. Novy-Marx (2013), for instance, discovered that value stocks performed better in combination with a quality strategy. This of course does not harmonize with the distress theory,

9 given the fact that quality firms are less likely to show signs of distress. Since neither the behavioral bias nor the risk premium theory seems to explain the full value effect, a conclusion can be drawn that both theories have some truth in them (Asness et al. 2015).

2.5. Momentum The momentum factor captures the excess return that results from short-term trends in stock prices. It was formalized first by Jagadeesh & Titman (1993), who found that a portfolio that buys winning stocks and shorts losing stocks outperforms a benchmark portfolio over holding periods of 3-12 months. For longer periods however, the effect loses strength and eventually even reverses over a 3-5 year period (Asness, 1995), consistent with earlier findings of DeBondt & Thaler (1985). This has implications for following a momentum strategy in practice, as it requires a high portfolio turnover and thus higher transaction costs. The return premium on has been confirmed in numerous other empirical research. Carhart (1997) added the momentum factor to the three-factor model of Fama and French (1992) and found it to be an improvement over the original Fama-French model. Geczy and Samonov (2016) tested the momentum strategy for a period of over 200 years and showed that it has provided excess returns very persistently over time by outperforming the benchmark market portfolio. When looking at possible explanations for the momentum factor, one can conclude that there is hardly any prevalent theory that is based on efficient markets. Instead, the momentum effect is better to be tackled from a behavioral finance point of view. The most common theories in this field suggest that stock prices either over or underreact to good and bad news, due to investor biases. Hong, Lim & Stein (1999) find justifications that both theories can jointly explain the momentum effect. Under reaction in the short-run (1-12 months) causes good (or bad) news to be incorporated slowly into stock prices. Over a longer period (3-5 years), however, a constant series of good (or bad) news increases the upward (or downward) price trend, causing future expected returns to diminish. Various investor biases can be seen as the root cause of the initial under reaction. Such as irrational conservatism (Barbaris et al., 1998), or the disposition effect (Frazzini, 2006). This disposition effect involves the irrational behavior of investors to sell ‘winning’ stocks to cash in gains, while holding on to ‘losing’ stocks to avoid losses. The delayed

10 over reaction can instead be attributed to an overconfidence bias (Daniel, Hirshleifer and Subrahmanyam, 1998). Another interesting theory suggests that ‘herding behavior’ can cause price trends, which lead to the momentum effect. Dasgupta, Prat and Verardo (2011), for instance, found that managers indeed follow the herd when it comes to portfolio selection, as a precaution for reputational losses. Even though the momentum effect has proved to provide a premium over time, there are market conditions in which it stops to deliver these excess returns. Daniel and Moskowitz (2016) show this, as they discover that momentum strategies fail after periods of enduring market declines when volatility is high. A possible solution to hedge this risk is to combine a momentum strategy with the value factor, since these factors seem to be negatively correlated (Asness, Moskowitz and Pedersen, 2013).

2.6. Low volatility The low volatility factor refers to the excess risk adjusted returns that low-volatility stocks earn over their higher-risk counterparts, where volatility can be referred to as the market beta, idiosyncratic risk, or simply total risk. Haugen and Baker (1991) were among the first to discover the anomaly when they examined market-cap weighted portfolio strategies. They saw that low- volatility stocks outperformed the market between 1972 and 1989. Numerous papers tested and confirmed this low volatility effect ever since. Frazzini and Pedersen (2014) proved that a low- volatility strategy gains significant returns over a longer time period (1926-2012). While Ang et al. (2006) showed that the volatility factor is still gaining excess returns after controlling for the Fama and French factors. These finding are of course in contrast with the CAPM theory, where riskier stocks should be compensated by higher returns through a higher beta. In empirical research, Black et al. (1972) already supported this deviation from the CAPM, with their discovery that the SML is actually flatter than it should be. Frazzini & Pedersen (2014) confirmed this result by testing a portfolio that takes a long in low-beta and a short position in high-beta stocks (Betting against beta). They found that this portfolio outperforms the benchmark and reasoned that leverage constraints for investors could explain this phenomenon. Especially institutional investors are often constrained from applying leverage in their investment decisions. This means that the only way to gain higher expected returns on a portfolio is by investing in high beta stocks, as opposed

11 to taking a leveraged position in a more optimal portfolio that includes low-beta stocks. This preference for high beta stocks eventually increases their price, causing the expected returns to drop. Another popular explanation that justifies the low volatility premium is the so called ‘lottery demand’. This behavioral theory states that some investors see the stock market as a lottery, where risky stocks are preferred for their ability to gain exceptionally high returns at a low probability. Bali et al. (2017) prove that this behavior drives the low-beta effect, as a greater demand for high-beta stocks impacts prices. This leads to an overvaluation of these stocks and causes expected returns to diminish. They also find that the anomaly can specifically be attributed to stocks where there is low concentration of institutional investor’s ownership and thus a high level of retail investors. Given the extensive documentation of the volatility premium, there is little doubt that the factor plays a role in explaining returns. However, there are conditions that can influence the performance of the volatility factor. During bull and bear markets, for instance, differences in investor behavior can cause the factor premium to change. Melas, Briand & Urwin (2011) note that in bear markets, the spread between the low and high beta portfolios is bigger than during bull markets. Therefore the potential losses are expected to be much lower during these periods. Hedegaard (2018) suggests that the ‘betting against beta’ strategy also performs better if past market returns have been high. Based on the leverage explanation, the conclusion is drawn that a shift in the investors aggregate demand function increases market prices, causing investors to become even more leverage-constrained. As a result they will overweight high beta stocks, which leads to an increase of the BAB factor.

2.7. Quality The quality factor is a relatively new factor that appears in academic literature. In general it refers to the outperformance of firms that show strength in terms of profitability, stability, growth and efficiency. However, various definitions of the variable have been used in academic research. Sloan (1996) for instance found that accruals could be a driver of quality. He came to this conclusion after finding a negative relation between the level of accruals and earnings quality, implying that a low level of accruals indicates quality. This higher earnings quality in turn benefits stock returns. Piotroski (2000) expressed the quality factor as a mix of nine different

12 variables, including accruals, leverage, liquidity, return on assets and cash flows from operations. More straightforward definitions of quality have been used as well. For example by Fama and French (2016), who incorporated operating profitability as a measure of quality in their five- factor model. Asness, Frazzini & Pedersen (2013) took a different approach and proposed a ‘quality minus junk’ (QMJ) factor, which measures the excess return of a portfolio that invests in high quality stocks and shorts ‘junk’ stocks. Their definition of quality involved a mix of variables that indicate profitability, stable growth and safety. They also established that the quality strategy performs better during times of crisis. This so-called ‘flight to quality’ effect is caused by a change in the investor’s preference, which drives them towards ‘safer’ stocks with decent fundamentals. An often-successful strategy during these times involves the combination of value and quality stocks (see Novy-Marx, 2013). Asness et al. (2013) support this by showing excess returns on a ‘quality against reasonable price’ (QARP) factor that combines the two effects. Famous and successful active investors are often linked with this particular type of investing, with Warren Buffet as the most prominent example. This is illustrated by Frazzini et al. (2013), who show that the high alphas of Buffet’s mutual fund become insignificant after controlling for the ‘betting against beta’ (BAB) and the QMJ factors. Despite its success, literature hardly provides a common justification for why the quality factor works, troubled of course by the wide variety of measurements and definitions that exist in academic literature. Some researches argue that investors simply care more about cash flow fundamentals than they do about macroeconomic forces (Campbell et al., 2009). They conclude that systematic risks can be attributed to these fundamentals. Critics of the quality premium point to the subjectivity of the factor as mentioned before. Another often heard shortcoming is that the factor can only be implemented in practice using , which is a strategy particularly used by active managers. If the latter statement were true, the inference would be that the quality premium is no free lunch like some of the other factors.

2.8. Dividend yield Empirical research has shown that following a high dividend yield strategy has been able to deliver excess returns over the market for a long period of time (e.g. Clemens, 2012). Blume (1980) was among the first to report this relation between dividend yield and expected returns.

13 Later, Fama-French (1988) confirmed the effect, but reported that dividend yield only explains little variance in short-term stock returns and does a better job at explaining returns for a longer time period (2-4 years). An interesting strategy that involves dividend investing is the ‘Dogs of the Dow’, made popular in a book by O’Higgins in 1991. This strategy entails the selection of a top 10 stocks in the Dow-Jones with the highest dividend yield. He found that this small selection of stocks subsequently outperforms the Dow Jones Industrial Average. The theory gained some support, but has been criticized at the same time. Hirschey (2000), for instance, suggests that the strategy does not evidently outperform the DJIA after adjusting for rebalancing costs and taxes.

The existing theories that try to tackle the observed outperformance of dividend yield stocks tend to be more behavioral than risk based. One of the possible explanations is related to a principal- agent problem that occurs when substantial free cash flows are available to managers (see Jensen, 1986). Clemens (2012) builds on this and notes that paying out dividends can in fact mitigate this agency cost. In the same paper, another behavioral explanation is then considered, as he shows that high dividend paying stocks seem more expensive in their valuation multiples than stocks that pay less. This ‘illusion’ could lead to undervaluation of these dividend paying stocks and thus higher expected returns. Even though research has shown the dividend factor to be capable of gaining excess returns, it must be noted that there exists a considerable overlap with other successful factors, such as value and low-volatility. This comes from the fact that high dividend paying firms tend to be mature and stable firms, characteristics that are often shared with low-risk value firms. Over the years there has been growing skepticism towards the robustness and validity of the dividend yield premium. Ang and Bekaert (2006) claim that dividend yields do not have the predictive power to estimate future returns, which is inconsistent with earlier research (e.g. Fama and French, 1988). They additionally suggest that a firm’s management can manipulate dividends. Which is why it should not be seen as a reliable indicator of future returns. Besides this, Robertson and Wright (2006) also argue that an increase in share buybacks is visible amongst firms as an alternative to paying dividends. This of course weakens the explanatory power of the dividend yield on returns.

14 3. Data and methodology 3.1. Thesis data The monthly return data for the market cap weighted benchmark portfolio and factor-based portfolios for Size, Value, Momentum, Volatility and Dividend yield are retrieved from the Kenneth R. French database (2018). These portfolios are formed based on the CRSP data of all U.S. based stocks listed on the NYSE, NASDAQ and AMEX. The return data for the Quality factor portfolio comes from the monthly updated dataset as used in Asness, Frazzini & Pedersen (2014), available at the AQR Capital Management website (2018). Both the Fama & French (referred to as F&F hereafter) and the Asness et al. portfolios use the 1-month treasury bills as a proxy for the risk free rate. These risk free rates are necessary to obtain excess returns.

3.2. Methodology In academic research, long-short portfolios are often formed to capture a ‘pure’ factor premium that can help to explain excess returns. The reason why academics prefer this approach is that the market risk (assuming both the long and short portfolios are market neutral) can be hedged for. In this thesis I will assess the performance of these portfolios using various risk and return metrics.

It is important to note that the long-short factors are absolute return strategies, which makes it unreasonable to relate them to the market portfolio benchmark individually. Instead, I will mix these single factor premiums and include the market benchmark to form multi-factor portfolios using mean-variance optimization. All the portfolios that will be used consist of stocks that have been ranked after a sorting procedure based on factor specific measures. It takes a long position in the highest ranked stocks, while taking an equal negative weight in the lowest ranking stocks. These procedures are repeated monthly or yearly, dependent on the factor. The ways in which each specific factor is measured is discussed below.

Size To obtain Size portfolios, stocks are sorted annually on their market capitalization. F&F use NYSE breakpoints for their sorting and only include firms when market capitalization data is available for June. I will include the Small Minus Big (SMB) proposed by F&F as a long-short portfolio for my analysis, which is composed in the following way:

15 (� ����� + � ������� + � �����ℎ) (� ����� + � ������� + � �����ℎ) ��� = − 3 3 Where the first part is the average return of three small stock portfolios (with different B/M levels) minus the average of three big stock portfolios.

Value For the Value portfolios, stocks are ordered on their book to market ratio (B/M). F&F works with Compustat data to obtain yearly book equity and only include firms with available market cap data for June and December, and book equity data for December. To obtain a long-short factor, F&F take two portfolios (small and big stocks) for the top 30th percentile of value firms and subtract two portfolios belonging to the low 30th percentile of growth stocks. This High Minus Low Factor (HML) can therefore be defined as: (����� ����� + ��� �����) (����� �����ℎ + ��� �����ℎ) ��� = − 2 2

Momentum The F&F momentum portfolios have been sorted on prior 2-12 months of return data, similar to the approach of Carhart (1997). To separate the winning from losing stocks, the NYSE 30th and 70th percentiles are used as cutoffs. Since the momentum premium is based on short-run results, the portfolios have to be rebalanced each month in order to include new winners and losers. The long-short portfolio can be expressed as: (����� ���ℎ + ��� ���ℎ) (����� ��� + ��� ���) ��� = − 2 2 In this definition, UMD denotes the ‘Up Minus Down’ strategy, which consists of two portfolios of high return stocks minus two portfolios of low performing stocks.

Low volatility To capture the volatility effect, I use the F&F portfolios based on prior 60-day volatility. This means that every month the volatility of the two months of prior returns decides the ranking of stocks. To do this monthly rebalancing is required. As the lowest decile represents the low

16 volatility stocks and the top decile entails the most volatile stocks, a long-short portfolio can be obtained by subtracting the two in the following way: ��� = ��10 ��� − ��10 ���

Quality Asness et al. (2014) came up with a unique definition of the quality factor, which encompasses an equally weighted mix of profitability, growth, safety and payout. Each of these four dimensions is measured by multiple variables. Profitability, for example, is defined as the combination of the gross profits over assets, gross , ROE, ROA, cash flow over assets (CFOA), and cash over earnings as a measure for low accruals. For a more detailed explanation of their definition I would like to refer you to the original paper (Asness et al., 2014). Based on the total quality score, Asness et al. created multiple monthly-rebalanced portfolios. To obtain their factor portfolio they subtracted the low quality portfolios (Junk) from the high quality portfolios in the following manner: (����� ������� + ��� �������) (����� ���� + ��� ����) ��� = − 2 2 Where QMJ denotes ‘Quality minus Junk’, and the high- and low quality stocks are first divided in small and big portfolios, similar to F&F’s approach to the value and momentum factor.

Dividend yield F&F portfolios for dividend yield have been created by sorting stocks on their dividend/price ratio (D/P). This ratio is computed yearly in June, after which the portfolio is rebalanced. For my analysis I will select the portfolio based on the 9th decile ranking to represent high dividend yielding firs, since research has shown that the top decile of dividend paying firms do not earn the highest excess returns (Clemens, 2012). The low-dividend yield firms can be found in the lowest decile, which is why I define the long-short portfolio as: ��� = ���(9�ℎ ���. ) − ���(��10)

17 4. Empirical results 4.1. Single factor portfolios In this section the performance of the individual long-short factor portfolios is examined over a period of 54 years (Jan 1964 – Dec 2017). The cumulative return figures for each factor premium can be found in Appendix A.

Risk & return statistics - Factor premia 1964 - 2017

Market Size Value Momentum Low vol Quality Dividend

Total Return 5.12% 1.43% 3.45% 6.92% 0.70% 4.19% -0.08%

Volatility 15.25% 10.65% 9.77% 14.59% 27.13% 7.82% 13.42%

Sharpe ratio 0.34 0.13 0.35 0.47 0.03 0.54 -0.01 Maximum 62.28% 77.4% 31.3% 58.2% 94.5% 32.0% 100.0% drawdown Max drawdown 107 188 108 10 18 24 278 period (months) Table 1: Summary of annualized returns, volatilities, Sharpe ratios and maximum drawdowns for all factor portfolios (1964 – 2017).

Looking at both Table 1 and Figure 1, it becomes clear that not all the factor portfolios have performed equally well in terms of risk-adjusted returns. In terms of pure returns, one of the main discoveries is the outperformance of the Momentum factor with an annualized return of 6.92%, leading up to extreme cumulative returns over the full sample period. When the focus is put on risk-adjusted returns however, Quality has proved to be the best performing factor with a Sharpe ratio of 0.54. It has been a well-known fact that cyclicality plays an important role in the performance of factor strategies over time (e.g. Melas et al., 2011). Keeping this in mind, the annualized volatility and maximum drawdown could help us understand these cyclical patterns. A key thing to remember in this case is that the volatility presented here does not simply measure the risk of stocks with a certain factor characteristic (as in a long-only portfolio), but rather the uncertainty surrounding the outperformance of a long portfolio relative to a short portfolio. With the maximum drawdown the largest decrease in returns over the sample period is measured. The length of the period in

18 which this decline occurs, indicates how fast the cumulative return dropped from its peak to reach a trough.

Cumulative factor returns 1964-2017 7000.00%

6000.00%

5000.00% Size 4000.00% Value Momentum 3000.00% Low volatility 2000.00% Quality

1000.00% Dividend yield

0.00%

-1000.00% Jul-79 Jul-10 Jan-64 Jan-95 Jun-92 Oct-71 Oct-02 Sep-84 Sep-15 Feb-82 Feb-13 Dec-07 Apr-87 Dec-76 Aug-66 Aug-97 Nov-89 Mar-69 Mar-00 May-74 May-05 Figure 1: Cumulative returns on the long-short factor portfolios (1964 – 2017)

Market The annualized market return in excess of the risk free rate has been equal to 5.12% over the last 54 years. A premium that is consistent with the 5 or 5.5% equity risk premium that is often used as a rule of thumb for the long term. As expected, two sharp declines in the cumulative returns are visible around the periods 2000-2001 and 2007-2008, marking the two biggest financial crises of the last decades (dot com bubble and credit crisis).

Size What stands out when observing the returns of the size factor, is the cyclical pattern they seem to follow over time. It is apparent why early research in the 1980’s and 90’s found a clear factor premium, as the period up until the beginning of the 80’s evidently shows positive cumulative returns for the small minus big portfolio. After this, however, the opposite effect seems to happen as a long period of underperformance follows. Some argued that the discovery of the return premium itself caused the disappearance (e.g. Schwert, 2003). This statement would seem

19 reasonable, if not for the fact that the size premium has shown a ‘revival’ in the last two decades. It could be possible that underlying variables related to systematic risk play a role in this reappearance, but a clear consensus in the academic world still seems to be missing.

Value The outperformance of value stocks relative to growth stocks during bear markets (and underperformance during bull markets) proves that the value factor could be of an anti cyclical nature. A good example of this is the negative return series on the HML portfolio in the years leading up to the dot-com bubble (1997-2000) (illustrated in the below figure).

100.00%

80.00%

60.00%

40.00% Mkt

20.00% HML

0.00%

-20.00% Jul-97 Jul-99 Jul-00 Jul-01 Jul-02 Jul-03 Jul-98 Jan-97 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-98 -40.00% Figure 9: Cumulative returns HML vs. Market portfolio (1997-2003)

Eventually the burst of the bubble is followed by an outperformance of value stocks, while the market shows contemporary negative returns. Both the ‘relative distress’ theory and the behavioral explanation that investors have irrational expectations about growth stocks try to explain this phenomenon in their own way.

Momentum As figure 1 already shows, following the momentum strategy has proved to be the most rewarding one over the last decades. However, this does not mean that the strategy provides stable returns in all market conditions. The proof that investing in the momentum factor can be a risky business comes in 2008-2009 when it experiences large negative returns. The maximum drawdown indicates that 58.2% of the cumulative returns the strategy had earned in the decades before were wiped out in just 10 months after the financial crisis of 2007. These ‘momentum

20 crashes’ have been reported to occur in extreme market conditions after volatility has been high (Daniel & Moskowitz, 2016).

Low volatility Of all the factor portfolios examined in this thesis, it is the low volatility premium that surprisingly exhibits the largest volatility. This volatility is visible in the cumulative returns graph (see appendix), where high peaks and troughs in returns succeed each other in a relative short period of time. It proves that the spread between low and high volatility stocks is very sensitive to changing market conditions. This conclusion is shared in other papers, where the return difference between low and high beta portfolios is larger during bear markets than during bull markets (e.g. Bender et al., 2013). The more severe fluctuations in returns could also be due to the way in which the factor is defined in this thesis. Since the long and short portfolios comprise the top and bottom deciles, the performance spread is more prone to extreme values.

Quality The quality factor, as defined by the QMJ portfolio, exhibited the lowest risk and highest Sharpe ratio over time. It is for this reason that investing in quality can be a stable and persistent source of returns, which is less prone to cyclicality than other factors. Still some interesting patterns in returns can be observed. The best example of this is the increase of the return premium in periods following financial crises, proving that many investors go for a ‘flight to quality’ as a response to economic turmoil and uncertainty (see for instance Novy-Marx, 2013). The subsequent underperformance of the factor portfolio after these flights to quality indicates that quality stocks have been overvalued during these phases.

Dividend yield The performance of the dividend yield factor can be characterized by different periods of outperformance and underperformance. Overall the average return is slightly negative, which could be a confirmation of the skeptic view that the dividend yield premium lacks robustness (e.g. Ang & Bekaert, 2006).

21 4.2. Multi factor portfolios 4.2.1. Equally weighted portfolios In order to mix different factors into an optimal portfolio, it is important to know how they can complement each other. This will give us a clearer insight on how we can eventually gain maximal diversification benefits. Correlation matrix factor portfolios Market Size Value Mom Vol Qual Div Market 1 Size 0.29 1 Value -0.26 -0.19 1 Mom -0.13 0.00 -0.18 1 Vol -0.61 -0.66 0.35 0.18 1 Qual -0.52 -0.48 -0.05 0.28 0.70 1 Div -0.43 -0.28 0.57 -0.13 0.53 0.17 1 Table 2: Factor portfolio correlations

Some factor premiums seem to follow similar cyclical paths over time, while other factors tend to move in opposite directions. Based on the correlations presented in table 2, some strong examples of factor pairs that move together are quality with volatility and value with dividend. Both of these correlations make sense, since high quality firms tend to exhibit low volatility and value firms are often mature ‘traditional’ firms who pay out higher dividends.

Risk & return statistics – Multi factor portfolios 1964 - 2017 Size-Val-Mom Qual-Val Val-Mom All factors

Total Return 4.67% 4.07% 5.74% 4.08% Volatility 6.05% 6.09% 8.00% 7.39% Sharpe ratio 0.77 0.67 0.72 0.55 Maximum drawdown 23.15% 34.90% 35.33% 28.86% Max drawdown period 13 18 39 7 (months) Table 3: Summary of annualized returns, volatilities, Sharpe ratios and maximum drawdowns for equally weighted multi-factor portfolios (1964 – 2017).

22

Especially the low and negative correlations between factors are interesting to examine, as it indicates that diversification benefits are achievable. These low and negative correlations are particularly observable between the ‘traditional’ factors ‘Size’, ‘Value’ and ‘Momentum’, which is why an equally weighted multifactor portfolio (1/3 Size + 1/3 Value + 1/3 Momentum) is tested. Other combinations that have demonstrated to improve performance include Quality mixed with Value (as discussed in section 2), and a 50-50 portfolio of Momentum and Value (e.g. Asness et al. (2013) proves the strength of this combination).

3000.00%

2500.00%

2000.00%

1500.00%

1000.00%

500.00%

0.00%

-500.00% Jan-64 Jan-66 Jan-68 Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 Jan-08 Jan-10 Jan-12 Jan-14 Jan-16

Size+Val+Mom Qual+Val Val+Mom All factors

Figure 10: Cumulative returns on the long-short multi factor portfolios (1964 – 2017)

For all four multi factor portfolios the diversification benefits are evident from table 3 and figure 10. The Size, Value and Momentum combination shows the highest risk-adjusted returns as measured by the Sharpe ratio, while the Momentum-Value portfolio displays the highest average returns. Even though the returns did not improve tremendously (one can only achieve this by leveraging up), the risks associated with the single factor’s cyclicality have dropped significantly. This becomes visible through the lower levels of volatility and decrease in maximum drawdowns, as well as in the smoother paths of the portfolio’s cumulative returns. In the value-momentum

23 portfolio for instance, the value factor now acts as a cushion for the negative impact of the ‘momentum crash’. This of course is due to the increase in the value factor over the same period.

4.2.2. Mean-variance efficient portfolios The results up until now have focused solely on the six single factor portfolios and showed that equally weighted combinations of these factors increase risk-adjusted returns. In this section of my thesis I mix the factor premiums with the market portfolio. While doing this, different objectives and constraints are introduced, after which I use mean-variance optimization to obtain the multi factor portfolio weights.

Risk & return statistics – Multi factor portfolios 1964 - 2017 Max ret Min vol at Max SR Min vol Max SR 2.25% vol Mkt ret 50% Mkt Total Return 4.21% 4.54% 6.61% 6.21% 5.77% Volatility 2.84% 2.93% 7.79% 6.19% 6.07% Sharpe ratio 1.49 1.55 0.85 1.00 0.95 Maximum drawdown 6.10% 7.84% 34.02% 26.60% 19.54% Max drawdown period 5 5 15 15 9 (months) Table 4: Summary of annualized returns, volatilities, Sharpe ratios and maximum drawdowns for optimized multi-factor portfolios (1964 – 2017).

The multi factor portfolio that earns the highest risk-adjusted returns is the one that follows the objective of maximizing the Sharpe ratio. As presented in table 4, the average risk and return of this portfolio is quite similar to the one that minimizes volatility. Figure 3 reveals that both portfolios therefore share comparable weights. The weights show that this low volatility is obtained by using large proportions of the Quality, Value and Size premiums. This makes sense, considering that these three single factors already exhibit relatively low risk (see Table 1). The slightly negative correlations between the portfolios only help to diminish this risk even more through diversification.

For another factor portfolio the average return is maximized, but with the constraint that the average monthly volatility should not exceed the limit of 2.25%. By doing so, a higher return of

24 6.61% can be achieved. Since the momentum factor and the market proved to gain the largest returns, it is not surprising that they make up 83% of the total weight of this portfolio. The volatility factor makes up the rest of the weight, providing diversification benefits.

Min volatility Max Sharpe ratio Max return 2.25%vol.

MKT-RF MKT-RF MKT-RF SMB SMB SMB HML HML HML UMD UMD UMD VOL VOL VOL QMJ QMJ QMJ DIV DIV DIV

Max SR with 50% Mkt Min vol. for Mkt return

MKT-RF MKT-RF SMB SMB HML HML UMD UMD VOL VOL QMJ QMJ DIV DIV Figure 11: optimal portfolio weights for 5 different strategies

A different approach is to create a portfolio that matches the observed average return of the market, but at a lowest possible volatility. Figure 11 indicates that again a mix of the market and momentum drives the return for this portfolio. While smaller weights of negatively correlated factors (in this case Value, Quality and Volatility) reduce the volatility. The last portfolio maximizes the Sharpe ratio, but as a constraint invests a minimum of 50% in the market portfolio. A reason for setting this constraint could be a practical one, since it reduces the amount of leverage that is used to invest in the long-short factor portfolios. It also creates possibilities to use different weighting schemes in order to avoid turnover and the costs of going short. Consider for example a stock that you want to short to keep a factor portfolio. As the stock is already part of the market portfolio as well, you could simply give it less weight and save the use of leverage.

25 Portfolio risk vs returns 8.00% Min vol 7.00% Max SR 6.00%

5.00% Min vol Mkt ret.

4.00% Max SR 50% mkt 3.00% Market

2.00% Max ret 2.25% vol. 1.00%

0.00% 0.00% 5.00% 10.00% 15.00% 20.00%

Figure 12: Risk-Returns for Multifactor portfolios and the Market While the use of long-short portfolios at first glance seems to be an active strategy which aims at gaining high excess returns (a strategy typically used by hedge funds), the optimized factor portfolios demonstrate that it can as well be a method to decrease risk. Figure 12 displays the average risk and return over the past 54 years for the five created portfolios and the market portfolio.

Cumulative returns Multifactor portfolios vs Market

3500.00%

3000.00%

2500.00%

2000.00%

1500.00%

1000.00%

500.00%

0.00%

-500.00% Jul-68 Jul-77 Jul-86 Jul-95 Jul-04 Jul-13 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 Oct-70 Oct-79 Oct-97 Oct-15 Oct-88 Oct-06 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11 Apr-66

Min vol Max SR Max ret 2.25% vol. Min vol Mkt ret. Max SR 50% mkt Market

Figure 13: Cumulative returns on the optimized multi factor portfolios (1964 – 2017)

26 Even though all the multi factor portfolios outperform the market on a risk-adjusted basis (as measured by the Sharpe ratio), the market can only be beaten in absolute returns when a high portion of the momentum factor is included or when extra leverage would be used. Still, the cumulative returns tell a different story as the impact of a higher volatility is displayed in figure 13. This can be explained by the effect that market drawdowns can have on accumulated returns. When a portfolio experiences big negative shocks in its returns it can take a long time to recover, even when the average returns have been high.

4.3. Long-short vs. Long-only portfolios The results in the previous sections prove that there exist clear risk and return benefits to the long-short factor strategy. However, these portfolios are still purely theoretical. An investor who wants to invest in these portfolios faces various implementation issues that arise with taking short positions. One might have to consider a required margin to get into a short trade. In times of negative returns this could pose an extra risk. Besides this, the strong cyclicality of some factors could also harm the returns in the long run. It could even be possible that a factor premium will disappear in the future. A different approach to factor investing is to take the long position of the factor portfolios only. This strategy is easier to implement, since it does not involve short selling. It is therefore that these factor portfolios have gained a lot of popularity over the last decades. Examples of this popularity are the rise of indexation (for instance by the likes of MSCI and Russell), and the increase in so called smart-beta funds. In contrast to the long-short approach, the long-only strategy does not hedge the market risk, but merely tilts the portfolio weights away from the market cap portfolio towards stocks that share a certain factor characteristic.

This section tests whether the long-only strategy can outperform the more theoretical long-short factor portfolios. The long portfolios in this case comprise the stocks that belong to the top or bottom decile (and 9th decile for Dividend yield) after the same ranking procedures explained in chapter 3. To compare the two strategies a relevant benchmark is used to assess the portfolios performance. A problem that arises here is that the long-short portfolios have much lower betas than the long-only portfolios, and as a result lesser risk and returns. The previous section already

27 demonstrated that the possibilities of gaining excess returns on long short portfolios are limited, as one cannot obtain a return higher than the greatest factor premium. One way to overcome this is to get rid of the market neutral nature of the long-short strategy by taking an additional position in the market portfolio. I take a similar method as Huij et al. (2014) and create portfolios that are 200/100 percent long/short invested, with a 100% long position in the market. Two multifactor portfolios for both the long-short and long-only strategy are created and benchmarked against the market cap portfolio.

Long-short strategy Long-only strategy

200/100 Equal 200/100 Equal Maximum SR weighted Maximum SR weighted Absolute risk-return characteristics Total return 10.53% 11.62% 8.10% 9.50%

Volatility 12.07% 12.14% 14.98% 15.57%

Sharpe ratio 0.87 0.96 0.54 0.61

Max drawdown 32.54% 34% 55.06% 52.77%

Max drawdown period 19 19 21 16

(months) Relative performance characteristics (benchmarked against the market portfolio) Beta 0.70 0.58 0.94 0.96

Active return 5.41% 6.50% 2.98% 4.38%

Tracking error 7.39% 10.43% 4.22% 5.50%

Information 0.73 0.62 0.71 0.80 ratio Table 5: Absolute and relative risk-return characteristics for Long-short vs. Long-only portfolios over full sample period 1964 - 2017

In the equal weighted portfolios, each of the six factors takes up a proportion of 1/6th of the total multifactor portfolio. The other two portfolios are created with the goal of maximizing the Sharpe ratio, using mean variance optimization. The weights of these portfolios are shown in figure 14.

It is clear that both the long-short portfolios gain superior risk adjusted returns compared to the long only counterparts. The long only strategies show a higher risk as measured by the volatility and maximum drawdown over the sample period. This can be due to the fact that long-short factors have greater diversification benefits caused by their negative betas. Table 2 already

28 indicates this, as it tells us the correlation between the ‘pure’ factors and the market is mostly negative. The betas presented in table 5 prove the magnitude of this negative relation. Even with the additional position in the market portfolio these betas are still way below 1. The betas for the long-only strategies are considerably higher, indicating that the long-only strategy tends to follow the market portfolio more closely. The accompanying lower tracking errors (which measure the volatility of active returns) also confirm this. As a result, the information ratios are slightly higher for the long-only portfolios, even though the long-short strategy outperforms in terms of active returns. This could be relevant for managers whose performance is benchmarked to a market cap weighted portfolio.

A mean variance approach to maximize the Sharpe ratio aids to improve the performance of both factor strategies. These portfolios are obtained by changing the equal weights to the weights as presented in figure 14.

Optimal weights Long-short Optimal weights Long-only

Size Value Momentum Low Vol SMB HML UMD VOL QMJ DIV Quality Dividend yield

Figure 14: optimal portfolio weights that maximize the Sharpe ratio for the Long-short and Long-only strategy

It displays that the two strategies involve a different composition of factors. The portfolio weights seem to be more balanced in the long-short strategy, with reasonable allocations to quality, momentum, volatility and value. On the contrary, the long portfolio requires large allocations to momentum and dividend. In this case the momentum factor is driving the high returns, while the

29 dividend yield factor mainly acts as a diversifier. It is remarkable that the long-short dividend factor does not add similar benefits. Instead, the volatility, value and quality factors are the main drivers of diversification in the long-short strategy, caused by their negative correlations with the market portfolio.

5. Conclusion Based on the empirical results of this thesis, the conclusion can be drawn that factor strategies have paid off significantly over the last 50 years in risk-adjusted terms. The existence of the observed return premiums proves to be a challenge to the efficient markets view where the market cap weighted portfolio is considered to be mean-variance optimal. This means that investors can achieve a more optimal portfolio when weights are allocated to factor portfolios.

All the six factor premiums that have been examined in this thesis can be confirmed in the sample period after analyzing the single factor portfolios, although some have shown a stronger persistence over time than others. The observed patterns in the returns are consistent with earlier research and prove that factors are of a cyclical nature (e.g. Bender et al. 2013). Some of the premiums tend to be heavily dependent on certain market conditions. This is especially visible for low-volatility (where there is a high outperformance of low volatility stocks in times of bear markets) and momentum (where momentum crashes are observed after high market volatility). The size factor on the other hand displays longer cycles of under and outperformance lasting up to 10-20 years in the sample period. The evidence for the dividend yield factor is the weakest of the six factors and even shows negative cumulative returns in some periods (figure 8). However, an interesting observation is that the dividend premium seems to be on a rise again in the last two decades. The cyclicality of all the individual factors could be disadvantageous for investors with a shorter time horizon. Investors could have made considerable losses if they would have stepped in at a wrong time. Over very long investment horizons however (the full sample period), all of the long-short factors demonstrated to gain positive cumulative returns. To benefit from the different patterns of factor returns over time, a strategy of long-short multifactor portfolios can be employed to increase diversification. The results in chapter 4.2 proved that this strategy could

30 decrease overall volatility tremendously. The most optimal way to implement this strategy is by using mean variance optimization, since it takes into account the covariance of the different factors. Still one has to keep in mind that various burdens can affect the investability of these theoretical portfolios. Especially the costs associated with taking large short positions can be problematical in real life, which is why taking long-only portfolios could be a reasonable alternative. Since these kinds of costs and risks are not easy to quantify and may differ among different types of investors, they are not accounted for in the comparison between the two strategies. What this thesis does find is that without these considerations the theoretical long-short portfolios outperform their long-only counterparts in terms of risk and returns (see chapter 4.3). The question of which of the strategies would perform better in practice is therefore decided by a trade off between the excess returns that a long-short strategy obtains versus the extra implementation costs a manager has to make in order to take the short positions. Another thing to keep in mind in this matter is that the long only strategy has become much more accessible to investors in the form of indexed funds, making it easier to invest in these portfolios as if it were a purely passive strategy. One could argue that investing in long-short factors, on the other hand, still requires a more active approach.

Even though this thesis shows that factor premiums have existed for decades, there are no guarantees that they will still persist in the future. To predict the performance in future periods a deep understanding of the drivers of factor returns is required. Since the current economical explanations that advocate their existence can be conflicting (e.g. behavioral versus risk based theories), I think that more research in the broad field of factor investing will still be very useful.

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35 Appendix A: Cumulative returns individual factor portfolios

Market

1600.00% 1400.00% 1200.00% 1000.00% 800.00% 600.00% 400.00% 200.00% 0.00% -200.00% Jul-77 Jul-95 Jul-04 Jul-13 Jul-68 Jul-86 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 Oct-70 Oct-79 Oct-97 Oct-15 Oct-88 Oct-06 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11 Apr-66

Market

Figure 2: Cumulative excess returns for the market portfolio (1964 – 2017)

Size

300.00%

250.00%

200.00%

150.00%

100.00%

50.00%

0.00%

-50.00% Jul-77 Jul-95 Jul-04 Jul-13 Jul-68 Jul-86 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 Oct-70 Oct-79 Oct-97 Oct-15 Oct-88 Oct-06 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11 Apr-66

Size

Figure 3: Cumulative excess returns for the Size portfolio (1964 – 2017)

36 Value

900.00% 800.00% 700.00% 600.00% 500.00% 400.00% 300.00% 200.00% 100.00% 0.00% Jul-70 Jul-83 Jul-09 Jul-96 Jan-64 Jan-77 Jan-90 Jan-03 Jan-16 Sep-72 Sep-85 Sep-11 Sep-98 Nov-74 Nov-87 Nov-00 Nov-13 Mar-79 Mar-92 Mar-05 Mar-66 May-81 May-94 May-07 May-68

Value

Figure 4: Cumulative excess returns for the Value portfolio (1964 – 2017)

Momentum

7000.00%

6000.00%

5000.00%

4000.00%

3000.00%

2000.00%

1000.00%

0.00% Jul-77 Jul-95 Jul-04 Jul-13 Jul-68 Jul-86 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 Oct-70 Oct-79 Oct-97 Oct-15 Oct-88 Oct-06 Apr-66 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11

Momentum

Figure 5: Cumulative excess returns for the Momentum portfolio (1964 – 2017)

37 Low volatility

1000.00%

800.00%

600.00%

400.00%

200.00%

0.00% Jul-77 Jul-95 Jul-04 Jul-13 Jul-68 Jul-86 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 -200.00% Oct-70 Oct-79 Oct-88 Oct-97 Oct-06 Oct-15 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11 Apr-66

Low volatility

Figure 6: Cumulative excess returns for the Low volatility portfolio (1964 – 2017)

Quality

1000.00%

800.00%

600.00%

400.00%

200.00%

0.00% Jul-77 Jul-95 Jul-04 Jul-13 Jul-68 Jul-86 Jan-64 Jan-73 Jan-82 Jan-91 Jan-00 Jan-09 Oct-70 Oct-79 Oct-97 Oct-15 Oct-88 Oct-06

-200.00% Apr-66 Apr-75 Apr-84 Apr-93 Apr-02 Apr-11

Quality

Figure 7: Cumulative excess returns for the Quality portfolio (1964 – 2017)

38 Dividend yield

200.00%

150.00%

100.00%

50.00%

0.00% Jul-07 Jul-78 Jan-64 Jan-93 Jun-95 Oct-85 Oct-14 Jun-66 Sep-73 Sep-02 Feb-05 Feb-76 Dec-80 Dec-09 Apr-71 Apr-00 Aug-90 Nov-97 -50.00% Mar-17 Nov-68 Mar-88 May-83 May-12

-100.00%

Dividend yield

Figure 8: Cumulative excess returns for the Dividend yield portfolio (1964 – 2017)

39