The Performance of a Private Equity-Replicating Strategy with Leveraged Small QARP-Equities in the Nordic Public Markets

The performance of a Private Equity-replicating strategy with leveraged small QARP-equities in the Nordic public markets

Linus Lehto

Department of Finance

Hanken School of Economics

Helsinki

2021 i

HANKEN SCHOOL OF ECONOMICS

Department of: Type of work:

Department of Finance Master Thesis

Author: Linus Leopold Lehto Date: 28.3.2021 Title of thesis:

The performance of a Private Equity-replicating strategy with leveraged small QARP- equities in the Nordic public markets

Abstract:

This thesis adds to the growing literature on value and quality investing, and the cross- section Quality At a Reasonable Price (QARP), in the Nordic markets. The research question of this thesis centers around whether a Private Equity-replicating investing strategy, which focuses on leveraged small- and mid-cap QARP-equities in the Nordic public markets, yields higher risk-adjusted returns than the market. Secondary research questions focus on the individual performance of value, quality and QARP strategies. Furthermore, the study aims to answer whether leverage and consequently debt paydown increase risk-adjusted returns in QARP-equities, or if company size affect risk-adjusted returns for QARP-equities or leveraged QARP-equities.

The performances of the formed portfolios have been studied by using Capital Asset Pricing Model, Fama-French three-factor model and Fama-French five-factor model. The risk adjusted performance measures (Sharpe ratio, Treynor ratio, Sortino ratio and Information ratio) are also utilized. The study is conducted between 1.6.1991- 1.6.2020, utilizing data for 1692 public companies on OMX Stockholm, OMX Nordic Copenhagen, OMX Nordic Helsinki and Oslo Bors.

First, the results of the study show that value companies have outperformed the market, when measured by EV/EBITDA. Second, the results show that high quality companies outperform low quality, and that high quality companies exhibit excess returns in comparison to the market. Furthermore, companies at the cross-section of value and quality seem to have yielded higher returns than purely quality companies. Third, the results show that the returns can further be juiced with the addition of leverage and consequent debt paydown. This is most prominent in small- and mid-cap companies. Finally, the main findings indicate that the Private Equity-replicating portfolio exhibits excess returns, even with volatility considered, with risk adjusted performance being higher than for the benchmark index. Transaction cost, capital gain taxes and other costs are excluded, which can contribute to a possible bias. The results support the mispricing hypothesis but cannot reject the assumption of efficient markets.

Keywords: Value Investing, Quality Investing, QARP, Asset Pricing, Investing Strategy, Portfolio management, Private Equity replication

SVENSKA HANDELSHÖGSKOLAN

Institution: Arbetes art:

Avdelning för finansiell ekonomi Magister avhandling

Författare: Linus Leopold Lehto Date: 28.3.2021 Avhandlingens rubrik:

Prestationen av en Private Equity-replikerande strategi med belånade små QARP- aktier på de nordiska aktiemarknaderna Sammandrag:

Denna avhandling kontribuerar till den växande litteraturen om värde- och kvalitetsinvestering, och tvärsnittet Kvalitet till ett rimligt pris (QARP), på de nordiska aktiemarknaderna. Forskningsfrågan i denna avhandling handlar om huruvida en Private Equity-replikerande investeringsstrategi, som fokuserar på belånade små och medelstora QARP-aktier på de nordiska publika marknaderna, ger högre riskjusterad avkastning än marknaden. Övriga forskningsfrågor fokuserar på individuella prestationen av värde-, kvalitets- och QARP-strategier. Vidare syftar studien till att svara på om belåning och betalning av skuld ökar riskjusterad avkastning i QARP-aktier, eller om företagsstorlek påverkar riskjusterad avkastning för QARP-aktier eller belånade QARP-aktier.

Prestationen av portföljen har studerats med hjälp av Capital Asset Pricing Model, Fama-French trefaktormodell och Fama-French femfaktormodell. De riskjusterade resultatmåtten (Sharpe-kvot, Treynor-kvot, Sortino-kvot och Informations-kvot) används också. Studien genomförs mellan 1.6.1991-1.6.2020 och använder data för 1692 publika företag på OMX Stockholm, OMX Nordic Copenhagen, OMX Nordic Helsinki och Oslo Bors.

Resultaten av studien visar att värdeföretag, mätt med EV/EBITDA, har presterat bättre än marknaden. Resultaten visar också att företag av hög kvalitet presterar bättre än av låg kvalitet och att företag av hög kvalitet uppvisar överavkastning jämfört med marknaden. Dessutom verkar företag i tvärsnittet mellan värde och kvalitet ha haft högre avkastning än rent kvalitetsföretag. Resultaten visar även att avkastningen kan förbättras ytterligare med tillägg av hävstång och nedbetalning av skuld. Detta är mest framträdande i små och medelstora företag. Slutligen indikerar resultaten att Private Equity-replikerande portföljen uppvisar överavkastning, även då volatilitet beaktas. Portföljen har en riskjusterad prestation som är högre än för jämförelseindexet. Transaktionskostnader, kapitalvinstskatter och andra kostnader är exkluderade, vilket kan bidra till en möjlig partiskhet i resultaten. Resultaten stöder hypotesen om felprissättning, men kan inte avvisa antagandet om effektiva marknader.

Nyckelord: värde investering, kvalitetsinvestering, QARP, prissättning av tillgångar, portföljförvaltning, replikering av Private Equity

CONTENTS

1 Introduction ...... 5 1.1 Background and motivation...... 5 1.2 Purpose of the study ...... 6 1.3 Research questions ...... 6 1.4 Contribution ...... 6 1.5 Limitations and main concerns of the study ...... 7 1.6 Key terminology and definitions ...... 7 2 Literature overview ...... 8 2.1 Value investing ...... 8 2.1.1 Definition of value and value metrics ...... 9 2.2 Quality investing ...... 11 2.2.1 Quality definition and investing strategies ...... 11 2.3 Quality at A Reasonable Price ...... 12 2.4 Size-effect ...... 13 2.5 Leverage and capital structure ...... 13 2.6 Private Equity ...... 14 2.6.1 Private Equity asset selection ...... 14 2.6.2 Private Equity and LBOs ...... 15 2.6.3 Private Equity returns and performance ...... 16 3 Theoretical framework ...... 17 3.1 Efficient Market Hypothesis and Modern Portfolio theory ...... 17 3.2 Criticism of the Efficient Market Hypothesis ...... 18 3.3 Capital Asset Pricing Model ...... 19 3.4 Multifactor models ...... 19 3.4.1 Arbitrage Pricing Theory ...... 20 3.4.2 Fama and French three-factor model ...... 20 3.4.3 Carhart four-factor model ...... 21 3.4.4 Fama and French five-factor model ...... 21 4 Previous research ...... 22 4.1 Size Matters, If You Control Your Junk (2018) ...... 22 4.1.1 Data, method and results ...... 22 2

4.2 Global Return Premiums on Earnings Quality, Value, and Size (2013) ...... 24 4.2.1 Data, method and results ...... 24 4.3 A Bottom-Up Approach to the Risk-Adjusted Performance of the Buyout Fund Market (2016) ...... 25 4.3.1 Data, method and result ...... 25 4.4 Leveraged Small Value Equities (2015) ...... 26 4.4.1 Data, method and result ...... 26 4.5 Replicating Private Equity with Value Investing, Homemade Leverage, and Hold-to-Maturity Accounting (2017) ...... 28 4.5.1 Data, method and results ...... 28 4.6 Other relevant papers ...... 29 5 Data...... 30 5.1 Overview of data sample, description and restrictions ...... 30 5.1.1 Exclusions...... 30 5.1.2 Summary of data and exclusions ...... 31 5.2 Variables ...... 31 5.2.1 Value variables...... 31 5.2.2 Quality variables ...... 31 5.2.3 Size ...... 31 5.2.4 Leverage variables ...... 32 5.2.5 Variable summary ...... 33 5.3 Portfolio formation and ranking ...... 33 5.3.1 Ranking of variables ...... 33 5.3.2 Formation and rebalancing of portfolios ...... 34 5.4 Return data for companies ...... 35 5.5 Market benchmark index, risk-free rate and market factors data ...... 36 5.6 Descriptive statistics ...... 36 5.6.1 Portfolios, market, risk free rate, factor returns ...... 38 6 Methodology ...... 40 6.1 Main Hypothesis formulation ...... 40 6.2 Perfomance measurement of risk-adjusted returns ...... 40 6.2.1 Sharpe ratio, Treynor-ratio, Sortino ratio and Information ratio ...... 40 6.2.2 Pricing models ...... 41 6.2.2.1 Capital Asset Pricing Model (CAPM) ...... 41 3

6.2.2.2 Fama-French three factor model (FF3) ...... 42 6.2.2.3 Fama-French five-factor model (FF5) ...... 42 6.2.3 Transaction costs ...... 42 6.3 Model diagnostics ...... 43 6.3.1 Multicollinearity ...... 43 6.3.2 Heteroskedasticity ...... 44 6.3.3 Autocorrelation ...... 44 6.3.4 Normality ...... 44 6.3.5 Results for model diagnostics ...... 45 6.4 Statistical hypothesis ...... 46 7 Results...... 47 7.1 Results for Value, Quality and QARP portfolios ...... 47 7.1.1 Pricing model regressions Value, Quality and QARP ...... 47 7.1.2 Risk adjusted performance for Value, Quality and QARP portfolios...... 50 7.2 Results for S-QARP, L-QARP and LS-QARP portfolios ...... 51 7.2.1 Pricing model regressions for S-QARP, L-QARP and LS-QARP ...... 51 7.2.2 Risk adjusted performance for S-QARP, L-QARP and LS-QARP portfolios 53 7.3 Portfolio comparison with paired sample t-test ...... 54 7.4 Possible biases and limitations ...... 55 8 Discussion ...... 56 8.1 Result discussion in comparison to previous research ...... 56 8.1.1 Implication of results ...... 57 8.1.2 Suggestions for futher research ...... 58 9 Conclusion ...... 59

APPENDICES

Appendix 1 Monthly returns ...... 66

TABLES

Table 1 Sample with exclusion steps ...... 31 Table 2 Variables summary ...... 33 Table 3 Portfolio ranking and formation for each strategy ...... 35 Table 4 Number of stock each year at portfolio formation for respective strategy 37 Table 5 Descriptive Statistics for the quintile portfolios ...... 38 4

Table 6 Descriptive statistics for market return, risk-free rate, and factors ...... 39 Table 7 Correlation between monthly returns for factors, market and Q1 portfolios 43 Table 8 Results for model diagnostics ...... 45 Table 9 Quintile portfolio regression results for Value, Quality and QARP ...... 47 Table 10 Alphas and factor analysis for Value, Quality and QARP Q1 portfolios ...... 49 Table 11 Risk adjusted performance ratios for Value, Quality and QARP portfolios . 50 Table 12 Quintile portfolio regression results for S-QARP, L-QARP and LS-QARP ..... 51 Table 13 Alphas and factor analysis for S-QARP, L-QARP and LS-QARP Q1 portfolios 52 Table 14 Risk adjusted performance ratios for S-QARP, L-QARP and LS-QARP portfolios 53 Table 15 Paired sample t-test comparison of portfolio mean returns ...... 54

FIGURES

Figure 1 Equally-weighted monthly returns for all stocks, compared to benchmark 36 5

1 INTRODUCTION

1.1 Background and motivation

Value companies are generally defined as exhibiting low market value in comparison to their book value, which thus can be viewed to be cheap in a relative way. Asness et al. (2013) define quality companies as “safe, profitable, growing and well-managed”. Quality At a Reasonable Price (QARP) refers to an investing strategy that focuses on stocks that can be categorised to be of high financial quality and of good financial health, while being simultaniously cheaply valued. In the empirical part of this study, we will also be targeting smaller companies, due to the well documented size premium, which is refered to as the size-effect. Asness et al (2018) show that small quality companies perform better in the global markets than those of larger sizes. The researches demonstrate that larger companies generally tend to be of better quality, indicating a strong relationship between quality and size.

Rasmussen and Chingono (2015) discuss that even though value investors on the public markets have traditionally steered away from leverage, the leveraged buyout industry has found great succes by applying leverage to cheaply valued small private companies. As the Private Equity-industry has grown in to its current large state by focusing on investing in these kind of companies, leveraged small-cap equities can be thought as “small-value on steroids”. The authors present a theoretical explanation for the excess returns of this kind of stocks, arguing that it can be mostly attributed to “deleveraging, a virtuous cycle of reduced interest payments, improved financial stability, and a value accrual for equity investors”. The leverage-aversion among investors is also considered as one of the factors. Also, the purchase multiple of companies, usually in terms of EV/EBITDA, is one of the key predictors of Private Equity-returns, as fund returns are generally higher in vintage years with lower purchasing multiples. This reflects that of the value premium in public markets, with higher excpected returns for companies with low fundamental book-to-market valuations.

Studies have shown that QARP investment strategies achieve excess returns in public markets in different markets and time periods. This study aims to examine how leveraged small QARP-equities perform in the Nordic stock markets and whether the returns can be explained by various factor models. We utilize the Capital Asset Pricing model, Fama-French three factor model, Fama-French five factor model, as well as risk- adjusted performance ratios (Sharpe ratio, Treynor ratio, Sortino ratio and Information ratio), to study the performance of portfolios constructed in this manner. 6

1.2 Purpose of the study

The purpose of this study is to examine whether Nordic small-cap and mid-cap equities with above average leverage and consequent debt paydown, that can at the same time be categorised as Quality At A Reasonable Price-companies, yield higher risk-adjusted returns than the market. This is tested by forming porfolios of public stocks in the Nordics based on the novel investment strategy. In a similar fashion as Rasmussen and Chingono (2015), the study focuses on, if it is possible to separate attractive leveraged small-cap and mid-cap stocks from unattractive ones.

1.3 Research questions

In order to analyze the purpose of this study, a subset of research questions is utilized, starting with the main research problem:

1. Does a Private Equity-replicating investing strategy, which focuses on leveraged small-cap and mid-cap QARP-equities in the Nordic public markets yield higher risk-adjusted returns in comparison to the market returns?

Further, the secondary research questions besides the main one are looked at, which are as follows:

2. Does Value and Quality companies, or the combination (QARP), yield higher risk-adjusted returns in comparison to the market returns?

3. Does leverage and consequently debt paydown increase risk-adjusted returns in QARP-equities?

4. Does company size affect risk-adjusted returns for QARP-equities, or leveraged QARP-equities?

1.4 Contribution

This study wishes to contribute to the limited literature on Quality and Value investing in the Nordic markets with recent market data. Few studies have specifically focused on the addition of leverage in a QARP-investing strategy, thus contributing to the previous research done in the Nordic markets in the area. Also, additional ideas for analysing stocks can also be learned from testing this method on the Nordic markets. 7

1.5 Limitations and main concerns of the study

The study is limited to OMX Helsinki, OMX Stockholm, OMX Copenhagen, and Oslo Bors. In accordance with Fama and French (1992) and Asness et al. (2013), stocks that are in the financial sector are excluded, as they cannot be compared with the rest of the sample. The final sample consists of 1692 companies, including both active and dead stocks. The portfolio performance examined is between the time period 1.6.1991– 1.6.2020. Transaction costs are excluded from the study, which account for a possible bias in the results.

1.6 Key terminology and definitions

The term QARP (Quality At a Reasonable Price) will be used as a generic term for all companies that can be classified as both being cheap in terms of value and exhibiting high financial quality. The term Nordics will be used to refer to the main stock markets of Sweden, Finland, Denmark and Norway. 8

2 LITERATURE OVERVIEW

Below, the main areas for this study’s literature overview is presented, which starts with a generic section on value investing. Second, quality investing is presented. In addition, the literature that focuses on the cross-section of value and quality, namely Quality At a Resonable Price, is reviewed. The size premium anomaly is discussed, which is relevant to our study as the study will be focusing on small- and mid-cap companies in the investing strategy. Leverage and capital structure will also be discusses, as a basis to understand the active monitoring incentive it may yield to. The litterature review is concluded with a chapter on Private Equity, where similarities are drawn between the discussed chapters.

2.1 Value investing

In this chapter, different definitions of value are discussed, in relation to the historical development of both value investing in literature and in practice. Different frameworks to implement value investing in practice, and the success of such investing staregies presented in value investing literature, are also discussed.

Graham and Dodd (1934) and Graham (1949) can be considered as one of the earliest practitioners of value investing, with their strategy for value investing in practice being based on three main theses. Value investors claim that by carefully analyzing the company's financial information and ratios, investors can find undervalued companies in the market. Graham notes that the prices of financial securities are prone to large and partly random movements depending on the market spirit and sentiment. He also claims that although securities prices fluctuate widely, many of the companies have an underlying economic value, which is somewhat stable and that also can be measured with good accuracy. Finally, he believes that a strategy of buying companies whose market value is significantly lower than the company's fundamental value, will provide a superior return with a longer investment period. One of Graham's thoughts is also that in the long run, the performance of companies and their shares tend to revert to mean.

Lee (2014) discusses value investing, and notes that several empirical studies have shown that value stocks, i.e. companies whose market value is proportionally low related to its fundamental value, have returned better than the market for many time periods and different markets. Although a number of studies have been conducted to explain the excess returns of value companies, the academics have not come to a unified answer. Fama and French (1992, 1993) are one of the first to show that value stocks tend to have 9

better performance than so-called "Glamor" or growth stocks. They measure value with the B/M multiple (Book-to-Market). Lakonishok et al. (1994) study indicates that a value oriented portfolio yields higher risk-adjusted returns, because value strategies capitalize on investor sentiment. Value investors usually divide companies into value companies and growth companies. Value companies have market value that is proportionally low related to the company's fundamental value, while growth companies have high market value in relation to the company's fundamentals. Value investors focus on finding undervalued companies as opposed to investing in growth companies.

Lee (2014) further discusses the value investment literature, and presents the academics' different views on the return premium. Some researchers argue that value stocks carry greater risk, while others explain the return premium as a result of investor behavior, where investors value certain companies higher for various reasons. They argue that the market does not have to be absolutely rational and be determined by perfect pricing mechanics. Investors may overreact to news, be overly optimistic about future prospects and get stuck in past winning stocks. This enables stocks that do not attract attention from the market to be incorrectly priced, which lays the foundation for value investment strategies based on finding undervalued companies. The value investment literature's definition of risk also differs greatly from the more academic modern portfolio theory, as value investors see risk more as the probability of a negative return on a long-term investment as opposed to temporary market fluctuations.

2.1.1 Definition of value and value metrics

Greenwald et al. (2001) state, that the value of a company is the sum of the cash flows that it will produce for investors during the company's life, discounted back to the present value. However, value estimates based on present value calculations are often prone to errors, as they are based on estimates of the future. Graham, and other value investors, choose to assess the value of a company by first considering its assets and then examining the company's strength to generate revenue. Only in rare circumstances are they inclined to consider the value of potential growth, as under many common strategic situations, increased sales or even an increase in revenue contribute nothing to the company's fundamental value, as growth under a level playing field does not create value. Growth must generally be supported by new assets.

Graham and Dodd (1934) are one of the first academics to propose a simple method for choosing stocks. Their method involves different characteristics that both consider value and quality. They score the companies based on rules, so that the companies get a total score where higher scores indicate better investment. Some of the rules will try to ensure that you only invest in companies of high financial quality, while others ensure that you buy them at reasonable prices. After Graham and Dodd, many different rankings and value scores have been proposed to measure these qualities and to improve and shape combined investment strategies.

There are many different metrics to assess the potential value of a company. Lee (2014) discusses common measures of value and highlights different ratios and studies that utilize them, such as the B/M-ratio (Stattman,1980; Rosenberg et al., 1985; Fama and French, 1992), the E/P-ratio (Basu, 1977; Reinganum, 1981), the cashflow-to-price ratio (Lakonishok et al., 1994; Desai et al., 2004), and the sales-to-enterprise-value ratio (O’Shaughnessy, 2011).

EV/EBITDA will be used as a measure of value in this study, as Rasmussen and Chingono (2015). EBITDA refers to earnings before interest, taxes, depreciation, and amortization. EV (enterprise value) is a market value of the company's operations and takes into account the interests of both shareholders and creditors. EV/EBITDA has been showed (Gray and Vogel, 2012; Loughran & Wellman, 2011) to indicate the best future price development, being the valuation multiple that returned the best, with companies with low EV/EBITDA multiples tend to have good returns in the future.

2.2 Quality investing

In this section, quality investing is discussed. Hsu et al. (2019) state that unlike many other common factors, such as value or size, quality is considerably more difficult to define. There is no agreement on the precise definition of financial quality, but many different academics have presented their variations to measure financial quality.

2.2.1 Quality definition and investing strategies

Asness et al. (2013) define a quality stock as something that is “safe, profitable, growing, and well-managed.” They claim that quality is something that all investors should be willing to pay more for if everything else being equal. They also present a quality factor and call it Quality-Minus-Junk (QMJ), which shows that high financial quality is associated with higher returns. A portfolio that takes a long position on quality stocks while at the same time selling short so-called junk stocks perform better than the market. However, the price that investors have been willing to pay for quality properties has varied and thus the size of the return premium changes depending on the market and the time period.

Definitions of quality differ, and many researchers have come up with different definitions and strategies that are based on financial quality. Piotroski (2000) constructs a financial strength score (F-score), out of four profitability measures and three that measure liquidity and two that measure operating efficiency. He shows that financially strong value firms perform better than low quality firms. Greenblatt (2010) uses return on invested capital and earnings yield as a measure of quality, whereas Sloan (1996) introduced accruals-based measure of earnings quality. Mohanram (2005) introduces GSCORE, which is another measure for measuring financial quality, and works best for measuring quality in growth companies. It is very similar to F-score, but instead of focusing on value companies, it tries to find the best growth companies. Novy-Marx (2013) uses gross margin as a better measure for quality, showing that profitable companies earn higher returns than their unprofitable counterparts. Gross profitability, which is measured by gross profit (turnover subtracted from the cost of goods sold) through the company's assets, has approximately the same degree of explanation as the B/M ratio when it comes to forecasting future returns on shares.

2.3 Quality at A Reasonable Price

Next, the cross-section of value and quality, namely Quality At a Resonable Price, will be discussed. There are many different strategies that can be considered value and quality- oriented, and the subject has attracted a lot of attention both in academic circles and professional investors. For instance, Novy-Marx (2015) states that although Benjamin Graham today is mainly associated with choosing shares based on ratios that measure value, such as the P/B ratio or the B/M ratio, he never suggested focusing only on low- priced companies. Graham focused on cheap and undervalued stocks, which means acquiring stocks of high-quality for cheap prices. Graham focused as much on the quality of a company's assets as the price one must pay to buy them.

Gray and Kern (2008) discuss how professional value investors make their decisions in practice. They claim that although the common view is that value investors solely focus on companies with low P/B multiples, according to research, e.g., the well-known value investor Warren Buffet can be classified as a growth investor according to Fama and French's size and value factors. By examining individual investment decisions made by professional value investors, they conclude that many of the investors spend a lot of time finding growth and value at a reasonable price as opposed to just comparing the company's book value to market value. They also claim that investors place great emphasis on analyzing the company's fundamental value as well as general market signals, such as marketing activity of major companies. Their conclusion is that the evidence shows that value investors can pick winning stocks and perform better than the market in the long run.

Other recent researcher that studies QARP-strategies include Mead at al. (2015), who find that companies that are both high quality and cheaply priced provide the highest consistent long-term returns, with the study examining both companies that are either high quality or low valued, as well as companies that fit into both categories. Li and Mohanram (2018) compare different fundamental analysis strategies, which are based on quality and value, and find better risk-adjusted performance for the combined strategy of quality and value. Novy-Marx (2015) examines abnormal returns and compares the performance of traditional value strategies and combined quality and value strategies and concludes that great benefits come from the combining of quality and value. Asness et al. (2018) build a QARP-factor and show that the Sharpe ratio for the QARP-factor is higher than the value or quality factors individually, and the authors claim that value and quality complement each other well. Maury (2017) studies QARP- 13

investing, combined with portfolio concentration, in the Finnish stock market, showing that the performance of many usual value- and quality-oriented investing strategies can be enhanced with portfolio concentration considered.

2.4 Size-effect

Several studies have shown that small companies, measured in market value, have performed, and returned historically better than large companies in several different markets. The size effect is one of the most researched market anomalies. Banz (1981) was one of the first to document the relationship between returns and the market value of companies, as he showed that small companies have, on average, larger risk-adjusted returns than large companies. Reasons for this size premium have been discussed widely, with reason ranging from asymmetric information (Zhang, 2006) to excess return due to less liquidity of the shares (Amihud and Mendelson, 1986; Acharya and Pedersen, 2005; Pastor and Stambaugh, 2003). However, it has also been discussed very much whether the effect is the result of additional risk, and the size premium has varied and even disappeared in several markets and time periods (Fouse, 1989; Chan and Chen, 1991, Reingamum, 1992). Malkiel (2003) states that many studies that have researched the size effect can also be affected by survival bias, which means that the companies listed during the research period have not been considered. Van Dijk and Hou (2018) also show in their study that the effect of the size factor has not been the same after early 1980s, addressing the disappearance to “negative shocks to the profitability of small firms and positive shocks to big firms”. Recently, Alquist et al. (2018) conclude that there is no strong and clear empirical evidence for the prominence of the size effect, but that combining size with other factors, such as value, may enhance returns.

2.5 Leverage and capital structure

Modigliani & Miller (1958) are one of the first to discuss leverage and capital structure, with their theory stating that capital structure is irrelevant in a fully efficient market (with no taxes). On the other hand, the relationship between leverage and a company's stock return is not as well explored. A strong and positive relationship between leverage and stock returns are documented in some studies (Bhandari, 1988; Fama and French, 1992) when computed from market prices, while other studies, using book leverage, shows leverage negatively affecting stock returns (Penman et al., 2007; Campbell et al, 2008; George and Hwang, 2010; Gomes and Schmid, 2010). 14

The trade-off theory (Kraus and Litzenberger, 1973) states that in a world with taxes and bankruptcy risk, companies weight the benefits of tax-shield and savings with potential bankruptcy costs, to choose the optimal capital structure. Pecking order theory states that companies have a specific preference scheme where the company primarily prefers to finance its operations through internal financing, then external financing (debt) and finally through equity (Myers & Majluf, 1984). The reason for this preferential arrangement is that there are information asymmetries between company management and investors. Agency costs, such as monitoring costs and residual losses, arise when there is a separation between ownership and control in companies. Thus, reducing the agency problem will lead to higher value of the company (Jensen and Meckling, 1976). Firms can mitigate these agency costs by issuing debt, as this incentivizes managers to avoid bankruptcy and makes them disciplined to act in favor of owners. Gompers et al. (2003) find a link between good corporate governance and stock returns, indicating that good governance yields excess returns.

2.6 Private Equity

Next, Private Equity as an asset class, the framework and workings for a leveraged buyout (LBO), historical returns for the industry and key value and return drivers are discussed. This chapter is relevant for the paper, as the empricial part of this thesis focuses on replicating a Private Equity-style investing strategy on the public markets. Possible similarities are also showcased, in terms of value and quality metrics, in the buyout targets that Private Equity-funds and traditional value investing strategies resonate towards. The addition of leverage to juice up returns, and to add monitoring incentives, is discussed from a Private Equity prespective, in order to develop a theoretical framework to understands it use in public markets as a part of the investing strategy.

2.6.1 Private Equity asset selection

Private equity funds mainly invest in stable companies with potential for operational improvements. Private equity funds strive to achieve a return on capital by investing in companies, developing them and then selling their stake in the company with the goal that the investment has increased in value. Jensen (1989) arguments that Private equity companies combine concentrated onwership with active corporate governance, performance based compensation structure and high leverage, which is done to mitigate agency problems between management and owners, and adds a clear incentive for active monitoring. This in turn leads to better operational efficiency. Kaiser and Westarp (2010) mentions seven main attributes and levers that define the activities of private 15

equity funds. First, the application for potential company acquisitions with opportunity to influence operating activities. Second, determining the price of the acquisition, focused on buying for the lowest possible price. Third, determining the structure for the financing of the acquisition including incentive for the managemenst. Fourth, value- based management of the acquired companies immediately after the investment. Fifth, value-based management of the acquired companies long-term after the investment. Sixth, potential refinancing of the acquired companies to ensure leverage ratio during the ownership of the company. And finally, negotiation of the sale price. All of these levers are used to create value in the buyout targets.

2.6.2 Private Equity and LBOs

Kaplan and Strömberg (2009) note that as private equity primarily invests in stable older companies, this enables private equity funds to raise a significant amount of debt as the expected future stable cash flow supports the interest payments the debt entails. Private equity funds often make leveraged buyouts (LBOs) where a majority share of a company is acquired, and the acquisition is financed from 60 percent to upwards of 90 percent debt. The amount of debt varies from transaction to transaction, but 60-90 percent is indicative of the amount of debt in LBOs. LBOs have been shown to incentivize the management to improve operations and add value to owners (Jensen, 1986; Kaplan, 1989). Private equity funds usually strive to acquire a majority stake in the portfolio companies. This means that private equity funds generally have a greater ability to influence decision-making within the portfolio companies, as private equity, as stated, usually invests for a majority ownership in the companies. Axelson et al. (2013) study the capital structures of private equity transactions, comparing them to public market equivalents, finding no cross-sectional relation between the structures. The study indicates that the amount of buyout leverage is mostly determined by debt market conditions, whereas leverage in public companies is mostly driven by firm charastreristics. Axelson et al. (2013) note that the private equity funds typically increase the target firms leverage from around 30 to 70 percent. Berg and Gottschalg (2005) discuss that the increased leverage provides a tax shield due to interest payments that are tax-deductible, which then leads to higher cash flows. At the same time, as Nikoslainen and Wright (2007) note, private equity funds influence the board composition at the target companies in order to have concentrated ownership, leading to better monitoring and risk management focus.

2.6.3 Private Equity returns and performance

Harris, Jenkinson, and Kaplan (2013) state the returns delivered by Private Equity buyout funds have have been significantly in excess of public equity markets since their inception in the 1980s on average. The median private equity buyout fund has outperformed the S&P 500 by 20-27% over the life of the fund, or about 3% per year. On the other hand, Cumming and Walz (2010) discuss that private equity fund managers may raport inflated valuations of companies, and that there are biases in fund performance reporting. As the valuation of the illiquid assets held by the funds is difficult, and when fund managers are incentivised to overvalue their investments, and when the disclosure rules are not standardises, the reported valuations may be biased. 17

3 THEORETICAL FRAMEWORK

In this chapter, the theoretical framework directly related to the purpose of this study are digged deeper into. The main presented literature areas are centered around the Efficient Market Hypothesis (Fama, 1970), Randow Walk Theory (Fama, 1970) and Modert Portfolio Theory (Markowitz, 1959). The presenting is continued with the main asset pricing models, which will be of relevance and provide the framework in the methodology part of the thesis, to test the risk-adjusted performance of the investing strategy.

3.1 Efficient Market Hypothesis and Modern Portfolio theory

The Effective Market Hypothesis (EMH) was developed by Eugene Fama (1970). The theory states that the markets always fully reflect the information that is available and are thus effective. Share prices are constantly adjusted in accordance with new information that enters the market. All available information must also be available to all players in the market free of charge. The players in the market are also considered to be rational. Fama presented three main variations of the hypothesis, which are the weak, semi-strong and strong form. The weak hypothesis means that asset prices already reflect entirely the previously available information to the public. The semi-strong hypothesis states that the prices reflect all publicly available information and that the changes in prices occur immediately to mirror new public information. The strong form also states that the prices mirror information unknown to the public.

Malkiel (1973) states, that there is no value in trying to analyze historical information, as all information is already reflected in the share price. However, the theory is based on three main assumptions about investors and the market; no transaction costs exist, all information is accurate and available to all investors and that all investors interpret it in the same way. The Random Walk Theory is also strongly associated with the theory of efficient markets and claims that the movement of stock prices is totally random and does not follow any pattern.

3.2 Criticism of the Efficient Market Hypothesis

Many articles have been written and debated on the effective market hypothesis. Latif et al. (2011) state that a large part of the critique of the efficient market hypothesis is based on findings of various anomalies in the stock market, which can be defined as empirical findings that conflict with established theories of financial asset pricing.

Malkiel (2003) highlights several important theories from academic research in the pricing of financial assets that conflict with and challenge the efficient market hypothesis, respectively. These include calendar anomalies, fundamental anomalies, and technical anomalies, such as for instance the size effect, value anomaly, and the January effect. Investors can also not be assumed to be completely rational because they overreact and underreact to important events, which means that the market is temporarily inefficient, and that there are always investors in the market who do not act rationally. Grossman and Stiglitz (1980) argue that if the market is to be fully efficient, trading costs and the cost of all information must be zero, and that there would be no incentive to uncover information gaps in the market prices.

Thaler (2016) discusses behavioral economics, with the main idea being that investors can overreact to news, which creates situations where stocks can be mispriced. The theory is based on the psychological and sociological aspects of investors. Behavioral economists also present explanations for many of the common market anomalies. They claim that investors can overreact or underreact to new information, which in turn creates incorrect pricing in the market. Also, Warren Buffett's phenomenal success has been much debated in the context of efficient markets. Academics who agree with the hypothesis of efficient markets believe that his long-term success can be viewed as luck. Buffet (1984) himself has defended by claiming that many other successful investors share his investment philosophy, which stems from something he calls "Graham-and- Doddsville,". These value investors base their investment strategy on Graham's lessons, and Buffet highlights several investors who have been very successful and outperformed the market, arguing that the main reason being buying low-priced value companies.

3.3 Capital Asset Pricing Model

Markowitz's (1959) presents a mean variance optimization theory, called Modern Portfolio Theory. It is used to assess and analyze different alternatives that rational investors face, wanting to get the best possible return with the least possible risk. It is based on the idea of efficient markets and claims that the optimal portfolio is the same for all investors.

Markowitz's theory of efficient markets and optimal portfolio is further developed by Sharpe (1964) for pricing individual assets and presents Capital Asset Pricing Model (CAPM), which manifests as a risk-return equation. The theory states that all assets have betas, which correspond to the asset’s movements in comparison to the market, and that the asset returns move in relation to the market returns and respective betas. The formula for CAPM and to calculate the return is:

푟 = 푟푓 + 훽(푟푀 − 푟푓)

where 푟푓 is the risk-free rate, 훽 is the company beta and (푟푀 − 푟푓) is the market risk premium. Beta is the systematic risk measure of an asset, which means the asset's tendency to react to changes in the market. The asset correlates perfectly with the market if it exhibits a beta of one. This means that the optimal combination is to hold a portion of the risk-free asset and the market portfolio, which is thus efficient. Individual assets with high risk contribute only slightly to the overall risk of the portfolio, as the unsystematic risk is diversified away. The linear equation of CAPM shows that individual assets return premium is a function of the asset's risk. According to the pricing model, due to this, incorrectly valued assets cannot exist on the market. (Fama & French, 2004).

3.4 Multifactor models

Multifactor asset pricing models will be utilized in the empirical part of this study, namely the three-factor model (Fama & French, 1993) and five-factor model (Fama & French, 2015). Below, some of the most well-known are presented.

3.4.1 Arbitrage Pricing Theory

Arbitrage Pricing Theory (Ross, 1976) states that the return on an asset depends on many different macroeconomic factors, not just the risk. He does not clearly state what these factors are but claims that the number and nature of the factors may depend on the market and the time period. This first so-called the multifactor model can be credited for popularizing the term factor.

3.4.2 Fama and French three-factor model

After Arbitrage Pricing Theory, several different studies have concluded that different factors affect asset returns. Research show that the company's size, profitability and various accounting and market-based ratios may have a correlation to returns. Fama and French (1992, 1993) present a pricing model in their paper “The Cross-Section of Expected Stock Returns”, the Fama-French three-factor model, which explains stock returns based on three factors. These are the market factor based (as in CAPM), as well as the size factor and the value factor. The size factor (SMB, or Small-Minus-Big) means the size of the company, i.e., large against small companies, while the value factor (HML, or High-Minus-Low) means the company's market value related to the book value, i.e. high or low book value in relation to market value. They show that shares of small companies and companies with high B/M ratios (Book-to-Market, reported book value divided by market value) have higher returns than their opposites. They argue that the return premiums are a result of higher risk, which is based on higher capital costs.

The formula for the Fama-French three-factor model is:

푟 = 푅푓 + 훽1(푟푚 − 푟푓) + 훽2 ∗ 푆푀퐵 + 훽3 ∗ 퐻푀퐿 + 훼

where 푟푓 is the risk-free rate, 훽 is the company beta and (푟푀 − 푟푓) is the market risk premium. SMB is the factor for company size and HML is the value factor, where 훽2 and

훽3 are the beta of these factors. This three-factor model has since become very well known in academics, and it has since been further developed. Many different additional factors have been proposed to complement the model, and factors such as momentum, volatility, yield and quality have received much attention to explain stock returns.

3.4.3 Carhart four-factor model

Carhart four-factor model (Carhart, 1997) is presented in the article “On Persistence in Mutual Fund Performance”. It considers the factor of momentum, i.e., that previously winning stocks perform better than previous losers. The formula for the Carhart four- factor model is:

푟 = 푅푓 + 훽1(푅푚 − 푅푓) + 훽2 ∗ 푆푀퐵 + 훽3 ∗ 퐻푀퐿 + 훽4 ∗ 푊푀퐿 + 훼

where WML is the momentum factor and 훽4 its beta coefficient, with the other coefficients being the same as in the three-factor model.

3.4.4 Fama and French five-factor model

Fama and French (2015) added a new factor for profitability (RMW) and investment (CMA) in their five-factor model, because of criticism of the unreliability and incompleteness of the original three-factor model. The new factors account for variation in returns due to differences in operating profitability and amount of investment between companies. The authors show that more profitable companies yield higher returns, while simultaneously companies that invest more yield lower returns. The formula for the five-factor model is:

푟 = 푅푓 + 훽1(푅푚 − 푅푓) + 훽2 ∗ 푆푀퐵 + 훽3 ∗ 퐻푀퐿 + 훽4 ∗ 푅푀푊 + 훽5 ∗ 퐶푀퐴 + 훼

where RMW is the profitability factor and 훽4 its beta coefficient, and where CMA is the investment factor and 훽5 its beta coefficient. The model’s explanatory power is tested by the authors in the study, indicating that it is more complete than the three-factor model, but fails to account well for small stock with low average returns. 22

4 PREVIOUS RESEARCH

In the following chapter, the previous research that is relevant for the purpose of this study is presented. Also, methodologies and data samples for the chosen previous research are discussed thoroughly.

4.1 Size Matters, If You Control Your Junk (2018)

Assnes et al. (2018) conclude that small quality companies have performed better than large quality companies in global markets. Small companies have historically had a return premium, which is called size effect. The researchers find a significant interplay between quality and size and find that large companies are usually high-quality companies while small companies tend to have the opposite characteristics. As a result, companies that are both small and of good financial quality have been shown to perform better over many different time periods and markets.

4.1.1 Data, method and results

The authors examinee the relationship between company size and expected returns. The authors state that the size anomaly has become one of the most discussed topics in connection with market efficiency, and that the size factor is one of the most important elements in various pricing models for assets. The researchers focus mainly on the interaction between size and financial quality. They state that the connection is interesting, as quality, value and size have strong connections to each other. Novy-Marx (2013) shows that quality, measured by profitability, has a strong connection to the value effect. Size has also been shown to interact with the value factor.

The study examines equity portfolios with both long and short positions, using data from both the US market with a longer period, and data from international markets. The sample for American companies comprises all available American shares between July 1926 and December 2012. International share data includes all available shares for 23 developed markets from January 1983 to December 2012. The 23 markets correspond to the countries in the MSCI World Developed Index in December 2012. Each individual share is allotted to the corresponding market based on the primary exchange position. The companies traded in several markets use only the primary listing, identified by the Compustat database. All figures are denominated in US dollars and abnormal returns are calculated in relation to the interest rate on one-month US government bonds. 23

The researchers use the Fama-French Small-Minus-Big factor and several different value-weighted portfolios based on different metrics for size for size portfolios. The portfolios are formed by ranking the shares each June based on their size. Value- weighted returns are calculated monthly from the beginning of July to the end of June next year. Researchers define quality for a company as characteristics that investors should be willing to pay a higher price for, i.e., stocks that are “safe, profitable, growing and well managed”. They use several different quality metrics to rank stocks in portfolios, where portfolios are created that take a long position in high-quality companies and long-short positions in low-quality companies. The researchers check for quality using Asness et al. (2014) Quality-Minus-Junk factor. They also examine other components based on profitability, profit growth, security, and payout. The researchers test whether the strong negative relationship between size and quality explains the sporadic performance of the size premium. Cumulative abnormal returns are calculated for all portfolios and different time periods. The Sharpe ratio is also calculated for the portfolios and the researchers use different factor models to control for risk.

The researchers find that previous evidence of the variability of the size effect is largely due to performance volatility of small companies that are of low financial quality. Companies of low financial quality tend to be very small, have low average returns, and are usually in risk of bankruptcy and illiquid. These qualities drive the strong negative relationship between size and quality, and the returns of these companies which are of low financial quality primarily explains the sporadic performance of the size premium. A much stronger and more stable size premium appears when the sample is controlled for poor quality, and the premium is also robust over time and significant internationally in several countries. The results are also robust with several different quality metrics, sample period, different industries and 23 international markets. The size premium is not captured by the liquidity premium, as the sample is checked for quality. The researchers' focus is on the size effect and its interaction with quality, with the aim of providing additional evidence in favor of or against different theories for the effect. The results show a significant size anomaly, and the researchers highlight it as one of the more important market anomalies, in the same weight as the value and momentum effect. According to the researchers, size, controlled for high or low quality, should be restored as one of the central empirical cross-sectional anomalies for pricing theories to explain.

4.2 Global Return Premiums on Earnings Quality, Value, and Size (2013)

Kozlov and Petajisto (2013) study the return premium of stocks that have high income quality with a wide and global data sample. The authors also test how quality works in a portfolio with exposure to value and size factors, researching how an investor can benefit from the interplay between the different factors. The results indicate that a simple strategy that takes long position in high-quality companies, and short positions in low- quality companies yields a higher Sharpe-ratio than the market, or strategies that only focus on value and quality. The results holds for the whole sample, and the authors conclude that there exist a quality premium on the market, that is also negatively correlated with the value factor.

4.2.1 Data, method and results

The researchers construct separate factor portfolios for each category, to investigate the risk and return of the portfolios with value, quality, and size emphasis. Large companies are defined as the largest companies that make up 90% of the total the market value of a market, while small businesses make up the remaining 10%. The B/M ratio (Book-to- Market) is used to classify value companies, while Accruals divided by Total Assets are used as measures of income quality. Alternative quality metrics are also used, such as return on equity ROE, CF/A (Cash Flow to Assets) and D/A (Debt to Assets). The companies are then divided into portfolios and all companies are divided into either large or small companies. The companies are divided based on the B/M ratio, to value companies, neutral or growth companies, so that the breaking points are at the 30th and 70th percentiles of the B/M ratio. The same distribution is made for quality, so that companies are divided into high, neutral, and low quality, so that the breaking points are at the 30th and 70th percentiles of the quality figure. The breakpoints are also defined according to the percentiles of the market value, so that all portfolios have equal market value for companies. The portfolios are formed at the end of June annually. The market return is built as a value-weighted return on all assets in each market. Annual abnormal returns, Sharpe ratio and volatility are then calculated for the factor portfolios. CAPM and Fama-French three-factor alphas are also counted for all factor portfolios.

The results find that a simple strategy that takes a long position in companies with high income quality and a short position in companies with low income quality results in a higher Sharpe ratio than the market or similar strategies that invest in value equities or small companies. The result holds for the entire sample. The researchers state that there is a quality return premium on the market, and that quality is negatively correlated with 25

the value factor. An investor who has exposure to both quality and value can achieve significant diversification benefits. The researchers also observe that a value-weighted global combined value and quality portfolio that invests in large companies has outperformed the market by 3.9% annually. A similar combined portfolio that has invested in small companies has outperformed the market by 5.8% per year.

4.3 A Bottom-Up Approach to the Risk-Adjusted Performance of the Buyout Fund Market (2016)

L’Her et al. (2016) observe that the relatively higher returns of Private Equity have been largely a result of the use of leverage and investing in smaller companies. The authors state that “90% of private equity buyout investments are in companies with enterprise value comparable to the bottom 10% of a small cap index such as the Russell 2000”.

4.3.1 Data, method and result

The authors use a bottom-up analysis with a comprehensive dataset to compare risk characteristics of buyout transactions to the public counterparts. The study uses data from Capital IQ, between 1993-2014, resulting to 3,492 buyout transactions. The authors also gather data on leverage and cost of leverage for 1,400 transactions between 1997- 2014. The authors then compare the distributions of portfolio companies of buyout funds and publicly listed companies, to understand the size characteristics better, with the results indicating that most of buyout investments are in companies that are very small. Next, the leverage of buyout transaction’s inception is assessed, by looking at the debt- to-enterprise value. The results indicate that buyout targets have been highly leveraged across the board than the similar public companies, with the average net debt to enterprise value being 65%. Leverage levels at the time of buyout exits is shown to be 45%, indicating that companies are deleveraged during holding period. The authors do not find evidence to indicate that the buyout target companies would have more value.

Next, the authors study the risk-adjusted performance of the buyout funds, construct public benchmarks that match the risk levels of the buyout funds, and then compare the results. The sample comprises of 752 funds between 1986 and 2008. The public market benchmark is constructed to match the leverage, size, and sector tilt of the buyout funds, and to match the risk-return levels. The results show that the buyout funds have historically outperformed the S&P500, but that no outperformance can be detected to the public market equivalents. 26

4.4 Leveraged Small Value Equities (2015)

Rasmussen and Chingono (2015) show that leverage enhances the average returns of a small-value investment strategy, indicating on a company level a positive interaction between leverage and value. The tested strategy focuses on smaller, cheaper, and more leveraged stocks, that at the same time are paying down debt and improving asset turnover. The results indicate that the average risk-adjusted returns of the strategy beat the benchmark U.S stock index between 1964 and 2014. The authors state that the well- documented pattern of leverage aversion can contribute to the excess returns to be found in leveraged small-value equities.

4.4.1 Data, method and result

The authors select companies based on size, value, and leverage. For size, companies in the first to last quartile measured in market capitalization for each year are included. This is done to try to take advantage of the size premium, at the same time as the very smallest companies are filtered out. For value, the cheapest quartile company measured in EV/EBITDA (Enterprise Value was measured as the sum of market capitalization and long-term debt) are included. The authors state that the multiple captures the value premium and works as a better measure of value today than, for example, Price-to-Book. Leverage was measured by taking long-term liabilities divided by EV (LT Debt/EV), including companies that have above median leverage, but excluding the last quartile, as the companies may have begun their debt repayment. Above median debt is used in order to allow for larger range for debt paydown.

The authors state that the leverage and consequent debt paydown leads to higher free cash flow, which in turn leads to deleveraging. At the same time, the free cash flow yield (in terms of free cash-flow/market capitalization) changes when valuation changes, indicating a potential for deleveraging. Companies can use leverage to enhance the free cash flow yield, which also lessens the need for equity, while at the same time leading to interest payments, which reduces the free cash flow. As the leverage is increased, so increases the free cash flow yield, which serves as a basis point for the interaction between valuation and leverage. A lower valuation (in terms of low EV/EBITDA multiple), combined with high leverage (in terms of Net debt to EV), leads to a high free cash flow yield, and vice versa. The authors state, that as EV/EBITDA and LT Debt/EV can be considered noisy, debt paydown serves as a good proxy for free cash flow generation. Companies which can pay down debt usually do it with positive free cash flows, indicating quality, which at the same time are better positioned for financial 27

distress, with decreasing interest payments and increased equity value. The authors discuss the Private Equity-industry, which has for decades used leverage to boost returns. Paying down debt also indicates that the management in making accountable decisions in term of capital allocation.

The authors perform a regression analysis to identify which factors separated attractive investments from the less attractive ones, categorizing the factors as deleveraging factors, technical factors, and quality factors. To measure free cash flow generation (deleveraging metrics), the authors balance the use of EBITDA/EV and LT Debt/EV with Debt Paydown. Debt Paydown is defined as 퐿푇 퐷푒푏푡푌퐸퐴푅 푇−1 < 퐿푇 퐷푒푏푡푌퐸퐴푅 푇−2. The authors state that the use of cash flow to deleverage impacts the risk of financial distress positively, by reducing interest payments while increasing equity value. Company size, share turnover and prior-year return are used as technical factors in the regressions. For quality factors, Improving Asset Turnover, Gross Profitability, and low-to-medium LT Debt/Assets are used as metrics. The improved rate of asset turnover was measured by looking at whether a company's sales growth was higher than asset growth in the past year (% Revenue growth > % Asset growth). Gross profitability was measured as gross profits divided by assets.

The regression results (evaluating the average effect of the factors on Next 1 Year Return among universe of stocks) indicate the importance of deleveraging in a leveraged small- value strategy. Companies that are paying down long-term debt yield average returns of 3.6% higher than companies who do not. Lastly, equally weighted, and value-weighted annual portfolios based on the significant factors were formed between the years 1965 and 2013 on U.S stocks (NYSE/AMEX/NASDAQ). The portfolios were formed as the 25 highest-ranked companies, the 50 highest-ranked companies and portfolios dividing the companies into quartiles (Q1-Q4). The results indicate that the risk-adjusted return was significantly higher for the equally weighted portfolios with the 25 and 50 highest-ranked companies, with Sharpe ratio for these portfolios being 0.53 and 0.46, respectively. The portfolio of top 25 stocks has an average annual return of 27.3% with 41.8% standard deviation during the period. The value-weighted top 25 portfolios exhibit CAPM alpha of 9.6% and beta of 1.66 and controlled for Fama-French factors (including momentum and liquidity) an average risk-adjusted return of 13.1% annually. 28

4.5 Replicating Private Equity with Value Investing, Homemade Leverage, and Hold-to-Maturity Accounting (2017)

Stafford (2017) shows that Private Equity-funds are prone to invest in small companies with low EBITDA-multiples, and that public equities with similar characteristics have high risk-adjusted returns, controlled for common factors. A passive Private Equity- replicating strategy produces an unconditional return distribution that resembles heavily with that of the pre-fee aggregate private equity index, with estimated fees of 3.5% to 5% annually. The author states that the EBITDA multiple is a highly indicative variable for finding value premium during the sample period.

4.5.1 Data, method and results

The author examines if returns and risks of a Private Equity allocation can be reproduced on public markets with passive investing, by replicating the investment selection, holding periods, leverage and use of conservative estimates of portfolio net asset value used by PE. The approach utilized aims to identify the key characteristics of the private equity investment process and apply it passively on public equities.

First, the author studies the asset selection, by utilizing a dataset of private equity public- to-private transactions (between 1983 and 2014 in the U.S), by utilizing OLS and logistics regressions on firm characteristics of private equity selected firms. In addition, companies with an operating cash flow of less than $ 1 million have been excluded from the study. The results indicate that PE-investors generally tend to target small firms, and firms that can be categorized as “value” companies, measured by EBITDA multiples. The author states that the premise behind such value investing are due to market mispricing of non-systematic risk exposures, which leads to high risk-adjusted returns. Also, low net equity issuance (the amount of share repurchases) indicates of being a strong predictor of potential buyout. Market beta and leverage levels are found not to be reliable predictors of private equity selection.

Second, the study focuses on replicating private equity returns with the combination of size and value, using small companies with low EV/EBITDA multiples, between 1981 to 2015 with all publicly traded companies on CRSP. Leverage is applied to the portfolio in similar levels (target portfolio level of 2.0x by utilizing margin account) that Private Equity companies use in buyouts, where market debt to firm value usually are increased from around 30% to 70%. The study uses a so-called homemade leverage (adding leverage through brokerage margin account, with borrowing rates close to risk-free rate) 29

to identified companies, to match the leverage levels. The author points that this homemade leverage does not produce and match the incentive, tax effect, and cost of financial distress that firm-level leverage does, but that the effects on risk and return are altered. Both equally weighted and value-weighted portfolios are formed monthly, based on information assumed to be known in the beginning of the month. The study uses monthly, quarterly, annual, two-year, three-year, and four-year portfolios, as the long holding periods are characteristics of private equity investment process.

The author's results showed that a multiple that measures operating cash flow (EBITDA) was a better measure of value than the classic Book-to-Market multiple for the period examined. Both equally weighted and value-weighted monthly rebalanced portfolios comprised of low EBITDA multiple companies have high risk-adjusted returns, averaging 18% per year and 13% per year, respectively. For longer holding periods, CAPM beta falls from 1.18 to 0.05 as the holding period increases from monthly to 4-years. The Value Replicating Strategy yields a yearly mean return of 18.6% and the Private Equity- Replicating Strategy a yearly mean returns of 20.0%. On the other hand, the risks for both strategies are high, with large drawdowns during 2008, with value losses of upwards 90% compared to peak value. Furthermore, the study showed that the risk- adjusted return for the portfolios during the period was significantly higher than the compared Private Equity companies' funds after fees.

4.6 Other relevant papers

Frazzini et al. (2013) show in their article “Buffets Alpha”, that the famed Warren Buffet’s returns can mostly be attributed as a reward for his use of leverage (with 1.6-to-1 on average) combined with a focus on cheap, safe, quality companies. His portfolio consists mainly of companies that are safe, with both low volatility and low beta, which are cheap, i.e. value companies with low P / B ratios, and of high quality, i.e. companies that are profitable, stable, growing and that pay significantly in dividends. An investment strategy that uses these factors is in line with Graham's and Dodd's ideas, which highlights both value and quality when making investment decisions. Part of his performance can also be considered due to his use of leverage in the form of debt, which enhances his return. Although Buffet can be considered an exceptional value investor, it turns out that his focus on secure quality companies may have had a major impact on his return. Buffet himself has stated that it is much better to buy a wonderful company at a good price than a good company at a wonderful price. 30

5 DATA

In the following chapter, the framework for the data used in the empirical research is presented.

5.1 Overview of data sample, description and restrictions

The data sample is downloaded from Thomson Reuters Datastream (TRD). The data consist of data between the period 1.6.1990-1.6.2020. The sample includes all listed and dead stocks on the Nordic main stock markets, which are defined as OMX Stockholm, OMX Nordic Copenhagen, OMX Nordic Helsinki and Oslo Bors. The inclusion of dead stocks, which are stocks that have e.g. delisted under the period, is done in order to minimize survivorship bias. The main motivation with the fairly large sample and long time period, is to try to ensure that the largest possible universe of listed Nordics stocks are included in the sample and are tested in different market conditions with a long enough timespan. Financial data is downloaded in Euros from the TRD database for all the companies in the sample.

5.1.1 Exclusions

Due to missing information and other relevant factors, some companies are excluded from the final data sample.

1. Firstly, only majority notes are included, which means that if a company has both “A” and “B”-stocks listed, only “B”stocks are included.

2. Second, all financial companies are excluded, as according to Fama and French (1992). This includes all financial companies, insurance companies and real estate investment companies. This is done, because these companies have special accounting standards and thus the researched variables will not match with the rest of the companies and are not comparable. Also, companies with industry classification as “NA” are excluded.

3. Thirdly, companies that lack data in the TRD database for the research period are excluded from the sample.

5.1.2 Summary of data and exclusions

Table 1 Sample with exclusion steps

Step Excluded Sampel size 1. Only majority notes 3308 2. Industry classification, excluding financials and “NA” 2155 3. Missing financial data => final sample 1692

Sample Active Dead 1692 companies 947 745

5.2 Variables

This section discusses the different variables that are chosen for the study, in order to form the porfolios that will be studied. The variables for the study are chosen from previous research on the topic, mainly in line with the variables presented of Rasmussen and Chingono (2015), with some alterations.

5.2.1 Value variables

EBITDA/EV (Earnings Before Interest, Taxes and and Amortizatio, divided by Enterprise Value, definded as the sum of market capitalization and long term debt) is used as the value indicator and purchase multiple. Companies with a low valuation in terms of EBITDA/EV are prefered.

5.2.2 Quality variables

Improving asset turnover (% Revenue Growth > % Asset Growth) is used as one of the factors to indicate quality. The variable takes value 1 if Asset turnover is improving, and zero otherwise. Improving asset turnover indicates better asset efficiency, or increasing sales. Gross profitability (Gross Income / Total Assets) is also looked at, in accordance with Novy-Marx (2012), as companies with high gross profitability are using their asset base more productively. Companies with high Gross profitability are prefered.

5.2.3 Size

As we want to focus on small-cap and mid-cap companies, we also screen for market capitalization. We define size classification according to the definitions of Nasdaq (2020) in the Nordic markets. Nasdaq uses the market capitalization of the listed stocks to divide the companies to small-cap (with market capitalization <=150 million euros), mid-cap 32

(with market capitalization >150 million euros but <=1 billion euros), and large-cap (with market capitalization over 1 billion euro). Market capitalization is defined as the number of common shares at the end of the calendar year, multiplied by the stock price at the date of portfolio formation. Companies that have a market cap >1 billion euros at the time of portfolio formation are excluded, for our small company portfolios, which thus include small-cap and mid-cap companies.

5.2.4 Leverage variables

LT Debt/EV (Long Term debt, divided by Enterprise Value) is used as the leverage ratio, showcasing values in the interval between 0 and 1. In accordance with Rasmussen and Chingono (2015), above-median leverage is used to qualify the companies, as this allows for a greater scope for debt pay-down in our leveraged portfolios. LT Debt/EV is used, as a higher value indicates a lower valuation, making it more attractive from a value stand point. LTDebt/EV takes a value of 1 if above median, and zero otherwise. At the same time, companies with low-to-moderate LT Debt/Assets are preferred, as they will be in a stronger position to endure financial distress, with less borrowing in relation to their asset base. LTDebt/Assets takes a value of 1 if below median, and zero otherwise. We also control for Debt Paydown (퐿푇 퐷푒푏푡푌푒푎푟 푇−1 < 퐿푇 퐷푒푏푡푌푒푎푟 푇−2), as cheap and leveraged companies that are deleveraging are increasing equity value, and are also better suited for financial distress. Debt Paydown takes a value of 1 if company has deleveraged, and zero otherwise.

5.2.5 Variable summary

Table 2 Variables summary Variable name Category Definition Ranking

EBITDA/EV Value Highest to lowest

Improving Asset Quality % Revenue Growth > % Yes=1, No=0 -> Ranked turnover Total Assets Growth

Gross profitability Quality Gross Profits / Total Assets Highest to lowest

Q-score Quality Joint rank of Quality Lowest to highest variables Z-score QARP Joint rank of Value and Lowest to Highest Quality Market cap Size Shares * Stock price > 1b euros excluded

LT Debt/EV Leverage Above median Above median=1 (included), below median=0 (excluded)

LT Debt/Assets Leverage Below median Below median=1, above median=0 -> Ranked

Debt paydown Leverage LT Debt T-1 Ranked

L-score Leverage Joint rank of Leverage- Lowest to highest variables

5.3 Portfolio formation and ranking

The following section is divided into two parts, first discussing the ranking of companies based on the different variables. Second, how the portfolios are formed on basis of the ranking of the variables is discussed.

5.3.1 Ranking of variables

On the basis of the discussed and chosen variables, a ranking system to divide the companies into portfolios is created. The ranking is done each year, at 1st of June. The ranking of the variables is as follows:

1. The companies are ranked by the Value-variable, with higher EBITDA/EV values yielding better Value-score. The companies are divided to Q1-Q5 Value portfolios based on the Value-score.

2. The companies are ranked by the Quality-variables. First, companies are ranked based on Gross Profitability. Second, companies with Improving Asset Turnover are assigned 1, whereas companies with decreasing Asset Turnover are assigned 0, and then the companies are ranked, so that 1 yields better score. The Q-score is formed as the average of the Quality-rankings, with higher values yielding 34

lower score. The companies are then ranked on basis of the Q-score, and divided to Q1-Q5 Quality portfolios.

3. A combined Z-score for QARP-metric is formed for each company on the basis of the ranking of the Value – and Quality-scores. The Z-score is the average of sum of the values for the scores. The companies are then ranked on basis of the Z- score, with the lowest score being the most admirable, and divided to Q1-Q5 QARP portfolios.

4. For small company portfolios, companies with market cap > 1 billion euros are excluded. Q1-Q5 S-QARP portfolios are formed on the basis of Z-score, with large companies excluded.

5. The leveraged QARP-portfolios are ranked based on Z-score and L-score, which is created on the basis of Leverage-variables. First, only companies with above median LTDebt/EV are included. Second, companies with below median LTDebt/Assets are assigned 1, and companies with above median are assigned 0, and then the companies are ranked, with 1 yielding higher ranking. Third, deleveraging companies are assigned 1, otherwise 0. Then the companies are ranked, with score of 1 yielding higher ranking. A joint L-score is created as the average of sum of the values for the ranks based on LTDebt/Assets and Debt Paydown. Lastly, the companies are ranked on basis of the average of Z-score and L-score, with the lowest score being the most admirable. Companies are then divided to Q1-Q5 L-QARP portfolios based on the ranking.

6. LS-QARP portfolios (Private Equity-replicating) are formed based on L-QARP portfolio ranking, and large-cap excluded.

5.3.2 Formation and rebalancing of portfolios

The portfolios are constructed as long only and are equally-weighted between stocks. The stocks will be divided into five quintile portfolios (Q1-Q5 portfolio) based on their respective rank each year for each metric.

Table 3 Portfolio ranking and formation for each strategy

Strategy Definition Portfolios

Value Ranked based on Value Q1-Q5

Quality Ranked based on Quality Q1-Q5

QARP Ranked based on Z-score Q1-Q5

Small QARP (S-QARP) Ranked based on Z-score & large-cap excluded Q1-Q5

Leveraged QARP (L-QARP) Ranked based on Z-score & L-score Q1-Q5 Ranked based on Z-score, L-score & large-cap Leveraged small QARP (LS-QARP) Q1-Q5 excluded

Rebalancing of the weights of the companies in the constructed portfolios happens every month, but the holding period is 1-year for respective companies in the portfolios. This means that the portfolios are equally-balanced monthly, but that the holding period is 1- year, whereafter new companies are included. As many recent research (DeMiguel et al, 2009; Plyakha et al, 2015; Malladi and Fabozzi, 2017) state, equal-weighted portfolios (naive 1/N) can be assumed more robust than value weighted, and that equal-weighted portfolios outperform value weighted, even after accounting for higher portfolio turnover costs and even on a monthly basis, making more economic sense. The first potfolios are formed on 1.6.1991 and the last porfolios 1.6.2019, so that the studied time period is between 1.6.1991-1.6.2020. In the same line as Fama and French (1992) and Chan et al. (1991), the portfolios are formed using the accounting information from the end of previous calender year. This is done in order to ensure that the financial information was available for investors at the time, in order to mitigate look-ahead bias.

5.4 Return data for companies

Stock return data is calculated on a monthly basis as arithmetic returns from the variable Total Return Index “RI” from TRD database. The “RI” variable accounts for dividends and stock splits. The return data is downloaded in Euros for all companies and benchmark index. The monthly returns are calculated with the formula:

푅퐼푡 푅푡 = − 1 푅퐼푡−1

Where 푅푡 stand for monthly return, 푅퐼푡 for the stockprice at t and 푅퐼푡−1 for the stock price at t-1. 36

If a stock delists during the holding period, the funds are distributed to the rest of the stocks. Additionally, if a company declares bankcrupty, the return for the company is calculated as -100%.

5.5 Market benchmark index, risk-free rate and market factors data

MSCI Nordic countries is used as the market index, as it is generally used as a proxy for the market by e.g. Financial Times and Bloomberg when returns for the Nordic markets are asessed. The risk-free rate used for the study is the 1-month Euro Interbank Offered Rate (EURIBOR) for 1999-2020. The 1-month Stockolm Interbank Offered Rate (STIBOR) is used between 1990-1999, due to lacking data availability of EURIBOR rates for the previous period. In order to calucalte excess risk-adjusted returns with the method presented in the next chapter, the market data for the factors SMB, HML, RMW and CMA is needed. The monthly factor data for the research period is downloaded from Kenneth French’s webside. The European factors are used, as they resemble most closely the Nordic sample.

5.6 Descriptive statistics

Next, descriptive statistics will be presented for the sample. The equally-weighted average monthly returns for all the stocks in the sample is checked in comparison to the return of the benchmark market index, as seen in Figure 1.

Figure 1 Equally-weighted monthly returns for all stocks, compared to benchmark

The correlation between the two time series is calculated as 0.795, which indicates a high correlation. Higher correlation could probably be obtained with value-weighted returns for the stock sample, as the benchmark index is calculated as value-weighted. 37

Table 4 Number of stock each year at portfolio formation for respective strategy

QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small).

Value Quality QARP S-QARP L-QARP LS-QARP

Year Q1-Q5 Q1 Q1-Q5 Q1 Q1-Q5 Q1 Q1-Q5 Q1 Q1-Q5 Q1 Q1-Q5 Q1

1991 264 53 256 52 252 52 238 51 126 26 120 26 1992 281 57 283 57 277 56 259 54 138 28 132 28 1993 309 62 310 62 308 62 289 60 154 31 148 31 1994 330 66 315 63 314 64 287 60 157 32 146 30 1995 348 70 335 67 334 67 301 61 167 34 150 33 1996 356 72 348 70 348 70 316 60 174 35 159 30 1997 415 83 355 71 354 71 312 67 177 36 155 35 1998 482 97 383 77 382 77 325 68 191 39 161 35 1999 524 105 384 77 382 77 340 69 191 39 177 37 2000 554 111 356 72 352 71 292 62 175 35 152 32 2001 606 122 427 86 422 85 364 76 211 43 184 36 2002 607 122 438 88 436 88 380 78 218 44 192 39 2003 600 120 567 114 564 113 519 106 282 58 256 52 2004 575 115 569 114 564 114 509 101 282 57 244 49 2005 583 117 575 115 570 115 497 94 285 58 239 47 2006 618 124 582 117 575 115 475 100 287 58 217 51 2007 673 135 656 132 646 132 532 97 323 66 249 49 2008 727 146 734 147 706 142 597 113 353 72 282 56 2009 732 147 745 149 718 144 656 133 359 74 322 69 2010 729 146 731 147 717 147 629 119 358 72 298 61 2011 734 147 735 147 723 145 613 116 361 73 286 51 2012 719 144 731 147 714 145 630 127 357 72 305 68 2013 683 137 702 141 679 136 582 119 339 68 274 64 2014 671 135 696 140 665 133 558 119 332 67 263 61 2015 687 138 713 143 676 136 565 128 338 68 262 62 2016 723 145 761 153 713 143 586 123 356 72 276 57 2017 738 148 811 163 734 147 597 126 367 74 275 60 2018 825 165 893 179 816 164 669 132 408 82 307 62 2019 874 175 936 188 864 174 727 143 432 87 342 75

As one can see from Table 3, companies in the sample have grown each year, starting from 26 companies (1991) to 75 companies (2020) for LS-QARP Q1-portfolio. The differences in the number of stocks in the portfolios for respective strategy each year are due to exclusions and data availability. 38

5.6.1 Portfolios, market, risk free rate, factor returns

A normally distributed sample has a skewness close to zero and kurtosis close to 3. Asymmetry in the distribution around the mean can be read from the skewness, while kurtosis indicates the distribution thickness of the tails. (Day, 2005)

Table 5 Descriptive Statistics for the quintile portfolios

All values are on monthly basis, between 1.6.1991-1.6.2020, in excess of risk-free rate. Jarque-Bera shows the t-statistic of the test (1980), indicating if the null hypothesis of normality is rejected.

Mean Median SD Min Max Skewness Kurtosis Jarque-Bera Value Q1 0.0109 0.0145 0.0480 -0.2389 0.2009 -0.5321 3.5095 199.0 Q2 0.0084 0.0130 0.0469 -0.2124 0.2030 -0.5283 3.4422 191.9 Q3 0.0070 0.0102 0.0481 -0.1892 0.1886 -0.5951 2.6417 124.4 Q4 0.0041 0.0064 0.0595 -0.2077 0.1848 -0.3402 1.5552 43.0 Q5 0.0086 0.0018 0.0851 -0.2252 0.6282 1.5962 9.4321 1458.7 Quality Q1 0.0083 0.0103 0.0475 -0.1833 0.2063 -0.2956 2.6429 108.9 Q2 0.0095 0.0110 0.0503 -0.2187 0.1774 -0.2863 2.3054 83.9 Q3 0.0087 0.0094 0.0615 -0.1904 0.5855 2.0178 22.0592 7386.9 Q4 0.0083 0.0087 0.0592 -0.2141 0.4158 0.7313 7.1761 790.2 Q5 0.0055 0.0068 0.0603 -0.2068 0.2073 -0.2314 1.3269 29.6 QARP Q1 0.0100 0.0118 0.0461 -0.2293 0.2176 -0.4998 4.5055 314.7 Q2 0.0074 0.0103 0.0468 -0.2080 0.1779 -0.6468 2.6742 130.7 Q3 0.0091 0.0124 0.0495 -0.1776 0.1892 -0.2312 1.8868 56.3 Q4 0.0073 0.0074 0.0671 -0.2177 0.6041 1.7956 17.9799 4939.5 Q5 0.0053 0.0006 0.0723 -0.2230 0.3965 0.4385 3.4577 188.4 Small-QARP Q1 0.0100 0.0115 0.0455 -0.2278 0.2234 -0.4562 4.3060 286.3 Q2 0.0075 0.0103 0.0462 -0.2182 0.1659 -0.6659 2.8381 145.5 Q3 0.0092 0.0108 0.0497 -0.1800 0.2001 -0.1119 1.7883 48.5 Q4 0.0068 0.0057 0.0709 -0.2160 0.7196 2.7394 28.9300 12729.8 Q5 0.0052 0.0007 0.0729 -0.2316 0.4191 0.5203 3.9602 247.9 Leveraged-QARP Q1 0.0102 0.0093 0.0496 -0.2362 0.2176 -0.2536 3.7018 206.6 Q2 0.0085 0.0119 0.0529 -0.2061 0.3152 0.2374 5.2416 408.9 Q3 0.0076 0.0098 0.0542 -0.2074 0.2284 -0.4503 2.8923 136.0 Q4 0.0061 0.0078 0.0560 -0.2282 0.2509 -0.2111 2.5191 97.0 Q5 0.0043 0.0059 0.0763 -0.2635 0.7720 2.6329 28.8796 12653.6 Leveraged Small-QARP Q1 0.0104 0.0102 0.0491 -0.2340 0.2201 -0.2142 3.7548 211.4 Q2 0.0082 0.0111 0.0528 -0.2109 0.3331 0.2687 5.5711 462.3 Q3 0.0067 0.0097 0.0540 -0.2163 0.2088 -0.4178 2.8537 131.1 Q4 0.0060 0.0067 0.0571 -0.2279 0.2543 0.0435 2.5777 98.9 Q5 0.0039 0.0036 0.0842 -0.2634 0.9830 4.2917 51.3541 39786.2 39

In Table 5, we can see that the Value Q1 portfolio has had the highest average monthly return (1.09%), with the LS-QARP Q1 portfolio exhibiting the second largest with 1.04%. We also see that in general, the Q1 portfolios for all strategies have lower volatility than the Q5 portfolios, in terms of standard deviations. The Value Q1 portfolio has a SD of 0.0480, whereas the Q5 portfolio has a SD of 0.0851. In Table 5, we also see from the Jarque-Bera test statistics, that none of the return time series for portfolios are normally distributed at 1% significance level. We see from the return graphs in Appendix, that some of the portfolios have heavy outliers. The swings have been relatively drastic in contrast to the rest of the time series, which may explain the high kurtosis value for the portfolios. These extreme values could be reduced by Winsorizing, however, this is decided not to be done as these returns can be considered features of the time series.

Table 6 Descriptive statistics for market return, risk-free rate, and factors

All values are on monthly basis. Jarque-Bera shows the t-statistic of the Jarque-Bera test (1980) of the normality of the variables, indicating if the null hypothesis of normality is rejected.

Mean Median SD Min Max Skewness Kurtosis Jarque-Bera Rm 0.0099 0.0121 0.0620 -0.1859 0.2034 -0.1861 1.0849 19.8 Rf 0.0026 0.0021 0.0029 -0.0004 0.0221 1.6497 5.3048 574.7 Rm-Rf 0.0073 0.0101 0.0622 -0.1896 0.2005 -0.2030 1.0851 20.2 SMB 0.0007 0.0014 0.0214 -0.0741 0.0881 -0.0477 1.0055 15.5 HML 0.0022 0.0030 0.0249 -0.1096 0.1115 0.0485 3.1783 149.9 RMW 0.0039 0.0044 0.0158 -0.0484 0.0608 -0.2501 0.6964 11.1 CMA 0.0012 -0.0001 0.0182 -0.0733 0.0875 0.3645 3.5261 191.9

In Table 6 we see the descriptive statistics for market return, risk-free rate, and the factors. The same can be concluded for the factors, risk-free rate, and market return, as seen in the table below. We can see that the market has risen by 0.99% on average on a monthly basis, and 0.73% in excess of the risk-free rate. 40

6 METHODOLOGY

In this chapter, the methodology used in conducting the empricial part of this study is presented. Abnormal returns with different pricing models are tested, as well performance measurement tests of risk-adjusted returns for the quintile portfolios are conducted.

6.1 Main Hypothesis formulation

The main hypothesis of this study is that the portfolio formed with the Private Equity- replicating leveraged small QARP-strategy (LS-QARP Q1 portfolio) will yield abnormal returns, which is consistent with the previous research. Thus, the hypothesis, with previous research as the base, follows:

H1a: Private Equity-replicating portfolio performs in line with the market without exhibiting abnormal returns.

H1b: Private Equity-replicating portfolio exhibits abnormal returns in comparison to the market.

6.2 Perfomance measurement of risk-adjusted returns

6.2.1 Sharpe ratio, Treynor-ratio, Sortino ratio and Information ratio

The portfolio returns are tested with the Sharpe ratio, Treynor ratio, Sortino ratio and Information ratio. Sharpe ratio (Sharpe, 1966) is used to calculate the risk-adjusted returns of the portfolios. Sharpe-ratio for a portfolio is calculated by:

푅푝,푇 − 푅푓 푆ℎ푎푟푝푒 푟푎푡𝑖표 = 휎푝

where 푅푝,푇 is the return for the period, 푅푓 the riskfree rate and 휎푝 the portfolio standard deviation. The approach by Ledoit and Wolf (2008) is used to test the difference of portfolio Sharpe ratios to the market ratios, using heteroscedastic-autocorrelation consistent standard errors.

Treynor ratio (Treynor, 1966) measures the return of the portfolio in comparison to the beta of a portfolio. It is calculated as following:

푅푝,푇 − 푅푓 푇푟푒푦푛표푟 푟푎푡𝑖표 = 훽푝 41

where 훽푝 is the beta coefficient for the portfolio.

Sortino ratio (Sortino et al., 1991) is generally used for sampels that are not normally distributed, and avoids Sharpe ratios penalty for extremely high values. It is calculated as:

푅푝,푇 − 푅푓 푆표푟푡𝑖푛표 푟푎푡𝑖표 = 푁푅푝

where 푁푅푝 represent the downside deviations. Downside deviations eliminates positive returns when calculating risk, using Minimum Acceptable Return (MAR) as the target of which subset of returns that are less than the target are used to calculate the differences to the target. The risk-free rate is used as MAR.

Information ratio (Sharpe, 1994) calculates to which degree the portfolio has beaten the benchmark (Active Premium), relative to the volatility of the active returns i.e. the difference between 푅푝,푇 − 푅푚,푇, namely Tracking Error. Its is calculated as the Active Premium divided by the Tracking Error.

푅푝,푇 − 푅푚,푇 퐼푛푓표푟푚푎푡𝑖표푛 푟푎푡𝑖표 = 푇푟푎푐푘𝑖푛푔 퐸푟푟표푟

where 푅푚,푇 represent the market benchmark return.

6.2.2 Pricing models

6.2.2.1 Capital Asset Pricing Model (CAPM)

CAPM is used as the base regression model, which includes only the market excess returns. The abnormal returns in the CAPM-model are called Jensen’s alpha (Jensen, 1968). The model takes the following form:

푅푝 − 푅푓 = 훼푝 + 훽1푝(푅푚 − 푅푓) + 휀푝

where ∝푝 is the Jensen’s alpha, 훽1푝 is the beta coefficient of the portfolio and 푅푚 − 푅푓 the market risk premium.

6.2.2.2 Fama-French three factor model (FF3)

Fama-French 3-factor regression (FF3) are conducted, which includes market excess returns, the size-factor Small-Minus-Big (SMB) and value-factor High-Minus-Low (HML). The formula for the regression of the factor model is as follows:

푅푝 − 푅푓 = 훼푝 + 훽1푝(푅푚 − 푅푓) + 훽2푝푆푀퐵 + 훽3푝퐻푀퐿 + 훽4푝푀푂푀 + 훽5푝퐿퐼푄 + 휀푝

where 푅푚 − 푅푓 is the market risk premium and the alpha, denoted as ∝푝, is the abnormal returns of the portfolio, indicated by the regression model.

6.2.2.3 Fama-French five-factor model (FF5)

A factor analysis with the Fama-French five-factor model (FF5) is also conducted, which includes the market excess returns, the factors SMB, HML, the profitability factor Robust-Minus-Weak (RMW) and investment factor Conservative-Minus-Aggressive (CMA). This model is used, because it tends to have more explanatory power in comparison to models with less factors (Fama and French, 2015).

The formula for the Fama-French five-factor regression model is as follows:

푅푝 − 푅푓 = 훼푝 + 훽1푝(푅푚 − 푅푓) + 훽2푝푆푀퐵 + 훽3푝퐻푀퐿 + 훽4푝푅푀푊 + 훽5푝퐶푀퐴 + 휀푝

All the models are used to calculate the alpha values for the portfolios, by using ordinary- lest square (OLS) regressions.

6.2.3 Transaction costs

As the scope of this study is more theoretical, transactions costs, capital gain taxes, or other types of costs are not accounted for in this study. These can be substantial, as the portfolios are balanced frequently, and as small stocks are often very expensive to trade due to their illiquid trading volumes. This means that investors wishing to replicate the performance and return would have to pay transaction costs, which lessens returns.

6.3 Model diagnostics

In this chapter, the model diagnostics are discussed. Heteroskedastic robust standard errors are used to estimate t-statistics in the regressions, which is done to mitigate autocorrelation and heteroscedasticity, as Newey-West (1987). As the sample of the study is fairly large, I find it safe to account in line with the customs in financial research that the Central Limit Theorem holds, and that Gauss Markow assumptions hold, and that an anasymptotic normal distribution of the residuals can be assumed (Wooldridge, 2012).

6.3.1 Multicollinearity

An assumption for the linear regression model is that multicollinearity does not exist, i.e., the independent variables should not have a linear relationship. Multicollinearity is examined with a correlation matrix.

According to Rockwell (1975), correlation above 0.6 can lead to misleading results. The results in the table below indicate that all correlations between independent variables used in the regressions are below this level.

Table 7 Correlation between monthly returns for factors, market and Q1 portfolios

Correlation of monthly returns between factors, market and Q1 portfolios of respective strategy. Q1 portfolios consist of top 20% companies in each category, and QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small). Market and portfolio returns are excess of risk-free rate. The grey area indicates the independent variables used in factor regressions.

Value Quality QARP S-QARP L-QARP LS-QARP SMB HML RMW CMA Rm-Rf Q1 Q1 Q1 Q1 Q1 Q1 SMB 1 HML 0.02 1 RMW -0.01 -0.55 1 CMA 0.01 0.57 -0.20 1 Rm-Rf -0.18 -0.02 -0.18 -0.44 1 Value Q1 0.19 0.25 -0.21 -0.20 0.72 1 Quality Q1 0.15 0.14 -0.23 -0.29 0.80 0.89 1 QARP Q1 0.19 0.25 -0.19 -0.21 0.72 0.96 0.94 1 S-QARP Q1 0.22 0.24 -0.19 -0.20 0.69 0.95 0.93 0.99 1 L-QARP Q1 0.17 0.28 -0.20 -0.18 0.69 0.93 0.88 0.95 0.95 1 LS-QARP Q1 0.20 0.28 -0.20 -0.17 0.65 0.92 0.87 0.94 0.95 0.99 1

6.3.2 Heteroskedasticity

Another assumption for the linear regression model is homoskedasticity, i.e., the variance of the error terms must be constant. This is tested with the Breusch-Pagan test (Breusch & Pagan, 1979) for all regression models. The null hypothesis is that the variance of the error terms is constant, i.e., the model is homoscedastic, the counter- hypothesis states that the variance is not constant, and the model thus suffers from heteroskedasticity. The results indicate that heteroscedasticity is not a concern in majority of the models.

6.3.3 Autocorrelation

Furthermore, it is assumed that the covariance between the error terms is equal to zero, meaning that there is no autocorrelation and no systematic pattern in the error terms. This is being tested with a Breush-Godfrey test (Wooldridge, 2013). The null hypothesis is that there is no autocorrelation, with the opposite hypothesis being that there is autocorrelation. The results indicate that autocorrelation is not a concern in the majority of the FF3 and FF5 regression models, but that most CAPM regressions exhibit significant (0.1% level) autocorrelation.

6.3.4 Normality

To test hypotheses of the parameters, it is also necessary that the residuals in the models are normally distributed. This is tested with the Jarque-Bera test (1980). The results indicate (on a 0.1%-5% level) that the residuals are not normally distributed for respective regressions. However, the central limit value theorem states that when the sample is large enough, the sample average will approach the normal distribution and the negative effects of non-normality will decrease. The study thus leans on this econometric assumption and independent and identically distributes probability distribution is assumed, with finite mean and standard deviation.

6.3.5 Results for model diagnostics

Table 8 Results for model diagnostics

Results for tests for heteroscedasticity, autocorrelation, and normality in the residuals for all portfolios with CAPM, FF3 and FF5 regressions. The values indicate the value of the test statistics of respective test. Test statistics for Breusch-Pagan follow a chi-squared distribution. Q1 portfolios consist of top 20% companies, and QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small).

Breusch-Pagan Breusch-Godfrey Jarque-Bera for residuals CAPM FF3 FF5 CAPM FF3 FF5 CAPM FF3 - FF5 Value Q1 0.4 2.5 3.8 25.6*** 1.6 1.9 89.3*** 17.6*** 17.2*** Q2 0.2 14.5** 14.9* 18.4*** 3.8 3.2 116.2*** 38.2*** 36.3*** Q3 1.0 12.9** 14.4* 9.7** 2.8 3.0 37.4*** 11.5** 9.0* Q4 0.0 1.6 3.2 1.9 0.0 0.0 95.5*** 301.2*** 269.3*** Q5 0.7 1.1 1.1 0.0 0.6 0.4 9363.6*** 16841.5*** 19779.4*** Quality Q1 0.6 14.4** 15.1* 11.6** 1.4 1.3 67.2*** 59.9*** 61.3*** Q2 0.0 1.4 3.0 11.7** 2.3 2.3 148.4*** 411.3*** 399.1*** Q3 0.0 1.3 1.3 2.3 0.1 0.2 97756.3*** 182974.7*** 188032.3*** Q4 0.6 4.5 6.3 1.5 0.2 0.1 6045.7*** 16508.2*** 17898.8*** Q5 0.7 2.9 7.5 10.4** 1.5 1.6 66.5*** 75.6*** 64.8*** QARP Q1 1.2 5.7 7.6 19.3*** 2.8 2.6 175.1*** 49.1*** 42.4*** Q2 1.1 9.5* 9.5 24.4*** 3.6 3.1 60.2*** 20.0*** 23.2*** Q3 0.1 3.3 4.3 14.6*** 3.4 3.9 144.9*** 620.6*** 615.3*** Q4 0.0 1.2 1.3 1.1 0.0 0.0 76640.8*** 146493.7*** 150722.0*** Q5 1.1 3.7 4.6 1.8 0.1 0.2 978.6*** 1520.1*** 2190.4*** S-QARP Q1 0.7 3.6 4.7 17.5*** 2.1 2.0 193.0*** 85.1*** 66.7*** Q2 0.9 9.4* 10.5 23.0*** 3.4 3.2 67.5*** 25.4*** 26.9*** Q3 0.2 4.0 4.8 11.3** 1.6 2.2 145.2*** 610.3*** 610.7*** Q4 0.0 1.2 1.2 0.5 0.0 0.0 112674.1*** 201988.3*** 207700.2*** Q5 1.1 3.7 4.8 1.9 0.2 0.4 1149.1*** 1855.2*** 2648.6*** L-QARP Q1 0.7 0.3 2.2 16.9*** 1.9 2.7 476.0*** 949.3*** 930.3*** Q2 0.2 1.2 2.2 4.7 0.1 0.1 1505.2*** 6998.5*** 6751.3*** Q3 0.7 3.6 10.0 23.2*** 2.6 2.3 52.4*** 37.9*** 38.7*** Q4 0.0 4.6 7.0 14.0*** 0.2 0.1 43.9*** 49.2*** 52.2*** Q5 0.2 2.3 3.6 2.1 0.3 0.4 49530.4*** 83440.5*** 84278.4*** LS-QARP Q1 0.7 0.3 1.9 15.3*** 1.0 1.6 495.3*** 1069.9*** 1014.6*** Q2 0.1 1.1 1.4 3.8 0.1 0.1 1509.4*** 6547.7*** 6278.5*** Q3 0.4 4.0 12.9* 21.0*** 2.7 2.6 60.1*** 80.8*** 74.4*** Q4 0.1 3.3 4.9 10.4** 0.0 0.0 127.2*** 226.7*** 237.3*** Q5 0.2 2.3 3.7 0.7 0.0 0.1 112486.8*** 166597.5*** 166691.3*** *) Significant at 5% level, **) at 1% level, ***) at 0.1% level 46

6.4 Statistical hypothesis

The factual hypotheses are transformed into statistical hypotheses in accordance with the purpose of the study. The statistical tests will test the hypothesis by utilizing the alpha values from the different asset pricing models presented in the theoretical framework, which will be the main assessment tool for assessing the performances of the portfolios. The statistical null hypothesis and the corresponding reversed hypothesis based on the chosen regression for the different factor models will be as following:

1. H0 = The alpha values exhibited from the regression results will not significantly differ from zero for the formed portfolios -> 훼𝑖 = 0

H1 = The alpha values exhibited from the regression results will significantly differ from zero for the formed portfolios -> 훼𝑖 ≠ 0

Furthermore, we also examine whether the risk-adjusted return is significantly higher than the market return. For the risk-adjusted returns (and corresponding ratios), the following statistical hypothesis is presented:

2. H0 = The difference between the risk-adjusted perfomance measures for the portfolios and the market will not significantly differ from zero -> 푆𝑖 − 푆푚 = 0

H1 = The difference between the risk-adjusted perfomance measures for the portfolios and the market will significantly differ from zero -> 푆𝑖 − 푆푚 ≠ 0

7 RESULTS

In this chapter, the results from the study will be discussed. Results for Value, Quality and QARP, and for S-QARP, L-QARP and LS-QARP portfolios will be presented separately.

7.1 Results for Value, Quality and QARP portfolios

In the following section, results for Value, Quality and QARP-strategies are evaluated. We start by presenting the pricing model regression results, followed by the risk adjusted performance results.

7.1.1 Pricing model regressions Value, Quality and QARP

In the table below, the pricing model regression results for Value, Quality and QARP portfolios are presented.

Table 9 Quintile portfolio regression results for Value, Quality and QARP

Results from factor model regressions, using monthly data for the period 1.6.1991-1.6.2020. Average monthly alphas, t-statistics and Adjusted R2 for respective portfolio. We use heteroskedastic robust standard errors (HAC). Q1 portfolios consist of top 20% companies in each category, and QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small).

CAPM FF3 FF5 Obs. Alpha t-stat Adj. R2 Alpha t-stat Adj. R2 Alpha t-stat Adj. R2 Value Q1 0.0068*** 2.71*** 0.518 0.0048*** 3.07*** 0.694 0.0030* 1.75* 0.703 348 Q2 0.0041* 1.92* 0.597 0.0023 1.57 0.741 0.0013 0.83 0.744 348 Q3 0.0024 1.23 0.660 0.0009 0.65 0.780 0.0007 0.46 0.783 348 Q4 -0.0017 -0.85 0.680 -0.0027 -1.56 0.742 0.0004 0.21 0.757 348 Q5 0.0021 0.64 0.413 0.0010 0.34 0.483 0.0051* 1.67* 0.495 348 Quality Q1 0.0038* 1.94* 0.638 0.0024* 1.68* 0.752 0.0021 1.43 0.752 348 Q2 0.0049** 2.38** 0.612 0.0034** 2.17** 0.710 0.0030** 1.98** 0.709 348 Q3 0.0037 1.36 0.492 0.0020 0.93 0.572 0.0031 1.38 0.572 348 Q4 0.0033 1.42 0.508 0.0017 0.89 0.610 0.0028 1.46 0.610 348 Q5 0.0002 0.07 0.569 -0.0015 -0.79 0.676 0.0004 0.18 0.681 348 QARP Q1 0.0061** 2.58** 0.523 0.0042*** 2.69*** 0.698 0.0022 1.41 0.711 348 Q2 0.0031 1.47 0.608 0.0014 1.00 0.748 0.0008 0.57 0.747 348 Q3 0.0045** 2.17** 0.643 0.0030** 1.93** 0.729 0.0034** 2.09** 0.729 348 Q4 0.0017 0.59 0.514 -0.0001 -0.04 0.592 0.0012 0.55 0.592 348 Q5 -0.0007 -0.25 0.503 -0.0019 -0.77 0.585 0.0018 0.72 0.599 348 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level

The results (in Table 9) indicate significant positive alpha values for Q1-portfolios for all strategies with CAPM and FF3 regressions (at 5% significance level). The results indicate that the Value Q1-portfolio has the highest monthly alpha of 0.68% with CAPM, dropping to 0.3% with FF5. The Q1 portfolios for Quality and QARP have monthly alphas of 0.38% and 0.61%, respectively with CAPM, dropping to 0.24% and 0.42% with FF3, respectively. The results indicate that the naive Value strategy seems to yield higher alphas than the market, and that the Value effect in the sample is strong. The results also indicate that there seems to be a quality premium on the market, and that the cross- section of value and quality yields excessive returns.

The alpha values for Quality portfolios are the most significant with the Q2-portfolio, exhibiting 0.49% monthly alphas with CAPM (1% significance level) and 0.34% with FF3 (1% significance level). The Q2-porfolios for Quality show an alpha of 0.3% (on a 1% significance level) with FF5, with a R^2 of 0.709.

Interestingly, the Q5 portfolio for Value exhibits a monthly alpha of 0.51% (on a 5% significance level) with the FF5. This indicates that so called “glamour” stocks would outperform Value stocks. On the other hands, the monthly alphas for the Q5 portfolio are not significant with CAPM and FF3, but still positive, with monthly values 0.21% (CAPM) and 0.10% (FF3). These results seem contradictory and can be due to the Q5- portfolios exposure towards RMW and CMA factors.

Table 10 Alphas and factor analysis for Value, Quality and QARP Q1 portfolios

Value Quality QARP Q1 Q1 Q1 CAPM FF3 FF5 CAPM FF3 FF5 CAPM FF3 FF5

MKT 0.5559*** 0.6061*** 0.6156*** 0.6105*** 0.6550*** 0.6505*** 0.5371*** 0.5854*** 0.5883*** α_p 0.0068*** 0.0048*** 0.0030* 0.0038* 0.0024* 0.0021 0.0061** 0.0042*** 0.0022 SMB 0.7313*** 0.7350*** 0.6723*** 0.6696*** 0.7044*** 0.7044*** HML 0.5167*** 0.6801*** 0.3056*** 0.3576*** 0.4927*** 0.7031*** RMW 0.3771** 0.0731 0.4278*** CMA -0.0719 -0.0631 -0.1422 R^2 0.517 0.697 0.707 0.637 0.755 0.755 0.521 0.700 0.715 Adj. R^2 0.515 0.694 0.703 0.636 0.752 0.752 0.520 0.698 0.711 Obs. 348 348 348 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level

The Table 10 reports the regression results for Q1 portfolios. The alpha estimates from CAPM indicate a significant (0.1% level) average monthly risk adjusted return of 0.68% for Value Q1-portfolio, 0.38% for Quality Q1-portfolio (1% level) and 0.61% for QARP Q1-portfolio (1% level). The monthly alpha drops to 0.48%, 0.24% and 0.42% with FF3, respectively (all significant on 5% level). The monthly alpha drops to 0.3%, 0.21% and 0.22% with FF5, respectively (only Value Q1 significant 1% level). This is expected, as the explanatory power is increased with the additional factors of the model, and thus the alpha decreases. Accordingly, we can reject our statistical null hypothesis on a high significance level for Value portfolio with all regressions, and for Quality and QARP with FF3 and FF5.

The factor coefficients indicate high bias towards market factor, SMB and HML for all Q1-portfolios. SMB captures the size factor, whereas HML the value factor. The CMA factor in FF5 is not significant for any of the portfolios, indicating that the portfolios do not have exposures towards stocks with aggressive investment strategy.

The explanatory power of the models (Adjusted R-squared) for Value Q1 ranges from 0.517 (CAPM) to 0.703 (FF5) for Value Q1. Similarly, the explanatory power for QARP Q1 is 0.636 with CAPM and 0.752 with FF5. Still, the two additional factors (RMW and CMA) in FF5 do not seem to add much explanatory power, with adjusted R^2 values very close for all Q1 portfolios for FF3 and FF5. 50

7.1.2 Risk adjusted performance for Value, Quality and QARP portfolios

Next, the risk adjusted performance is evaluated for Value, Quality and QARP-portfolios with the different measures.

Table 11 Risk adjusted performance ratios for Value, Quality and QARP portfolios

Results for monthly risk adjusted performance measures, using monthly data for the period 1.6.1991- 1.6.2020. We use heteroskedastic robust standard errors (HAC). Ledoit-Wolf test measures the difference between the Sharpe ratios of respective portfolio and the comparable ratio of market. Q1 portfolios consist of top 20% companies in each category, and QARP (=Quality At a Reasonable Price).

Sharpe ratio Qi - Market Treynor ratio Sortino ratio Information ratio Diff. T-stat

Value Q1 0.227 0.110 2.72** 0.158 0.196 0.382 Q2 0.179 0.061 1.71 0.097 0.116 0.181 Q3 0.145 0.028 0.84 0.060 0.072 0.045 Q4 0.068 -0.049 -1.55 -0.006 -0.011 -0.307 Q5 0.101 -0.016 -0.41 0.035 0.081 -0.008 Quality Q1 0.175 0.057 1.70 0.090 0.115 0.180 Q2 0.189 0.072 2.06* 0.108 0.148 0.279 Q3 0.142 0.025 0.74 0.075 0.111 0.126 Q4 0.140 0.023 0.60 0.070 0.099 0.098 Q5 0.092 -0.026 -0.70 0.017 0.023 -0.140 QARP Q1 0.217 0.100 2.50* 0.144 0.173 0.315 Q2 0.159 0.042 1.17 0.076 0.086 0.092 Q3 0.184 0.067 2.02* 0.100 0.138 0.255 Q4 0.109 -0.008 -0.24 0.039 0.066 -0.011 Q5 0.073 -0.044 -1.13 0.001 0.017 -0.181 Market 0.117 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level

We see that Value Q1 exhibits the highest monthly Sharpe ratio of 0.227, which is significantly different (1% level) by 0.110 of market. The Value Q1 portfolio also exhibits the highest Treynor, Sortino and Information ratio. This means that the Value Q1- portfolio clearly has the highest risk-adjusted return of the portfolios. The combined QARP-strategy, with the Q1 portfolio, exhibits a Sharpe ratio of 0.217, whilst the Q1 portfolio for Quality exhibits a Sharpe ratio of 0.175. This indicates that the Quality companies are slightly lessening the risk-adjusted performance in the combined strategy. Still, the Quality Q1 portfolio has a higher Sharpe ratio than the market by 0.057 (whilst not significant) and Q2 of 0.072 (significant on 5% level), indicating that focusing purely on high quality companies seems to yield higher returns than the market on a 51

risk-adjusted basis. The Q5 portfolios for respective strategies have worse Sharpe ratios than the market, but these are not statistically significant. The Value Q5-portfolio has a negative Information ratio (-0.008), and clearly lower Treynor and Sortino ratio than the Q1-portfolio, indicating that “glamour” stocks have worse risk-adjusted returns than value stocks. This seems to be the case for both Quality and QARP-portfolios too, with Q5-portfolios exhibiting clearly worse ratios than Q1-portfolios.

7.2 Results for S-QARP, L-QARP and LS-QARP portfolios

In the following section, results for S-QARP, L-QARP and LS-QARP-strategies are evaluated. We start by presenting the pricing model regression results, followed by the risk adjusted performance results.

7.2.1 Pricing model regressions for S-QARP, L-QARP and LS-QARP

In the following table, the regression results for S-QARP, L-QARP and LS-QARP portfolios are presented.

Table 12 Quintile portfolio regression results for S-QARP, L-QARP and LS-QARP

CAPM FF3 FF5 Obs. Alpha t-stat Adj. R2 Alpha t-stat Adj. R2 Alpha t-stat Adj. R2 S-QARP Q1 0.0063*** 2.64*** 0.475 0.0044*** 2.78*** 0.661 0.0026 1.62 0.672 348 Q2 0.0035 1.59 0.549 0.0017 1.15 0.712 0.0015 0.93 0.710 348 Q3 0.0048** 2.15** 0.560 0.0033* 1.93* 0.667 0.0038** 2.20** 0.667 348 Q4 0.0014 0.43 0.433 -0.0005 -0.21 0.515 0.0009 0.38 0.515 348 Q5 -0.0007 -0.25 0.476 -0.0020 -0.78 0.564 0.0018 0.69 0.579 348 L-QARP Q1 0.0062** 2.33** 0.469 0.0040** 2.33** 0.643 0.0019 1.08 0.656 348 Q2 0.0042* 1.74* 0.489 0.0022 1.28 0.622 0.0008 0.46 0.627 348 Q3 0.0028 1.03 0.571 0.0007 0.39 0.712 -0.0003 -0.16 0.713 348 Q4 0.0014 0.05 0.506 -0.0009 -0.54 0.678 -0.0019 -1.09 0.678 348 Q5 -0.0009 -0.26 0.345 -0.0027 -0.82 0.412 -0.0023 -0.74 0.408 348 LS-QARP Q1 0.0067** 2.49** 0.421 0.0045** 2.58** 0.608 0.0025 1.41 0.620 348 Q2 0.0043* 1.68* 0.411 0.0023 1.21 0.552 0.0014 0.73 0.553 348 Q3 0.0022 0.78 0.501 0.0001 0.04 0.658 -0.0005 -0.23 0.657 348 Q4 0.0016 0.55 0.438 -0.0008 -0.44 0.623 -0.0019 -0.95 0.623 348 Q5 -0.0013 -0.33 0.273 -0.0031 -0.80 0.330 -0.0029 -0.86 0.326 348 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level 52

The results indicate significant positive alpha values for Q1-portfolios for all strategies with CAPM and FF3 regressions (at 1% level). None of the Q1 portfolios are statistically significant with FF5 regression. Interestingly, the S-QARP Q3-portfolio exhibits the highest alpha, of 0.38% monthly (on a 1% significance level) with FF5. The Q1-portfolio with S-QARP strategy has a higher monthly alpha (0.26%, not significant) than the Q1- portfolio for LS-QARP (0.25%, not significant) with FF5. On the other hand, LS-QARP Q1-portfolio exhibits the highest alpha with both CAPM and FF3 (0.67% and 0.45%, respectively), indicating that the Private Equity-replicating strategy yields the highest alpha. The Q5-portfolios exhibit negative alphas for S-QARP with CAMP and FF3, and for L-QARP and LS-QARP with CAPM, FF3 and FF5, but these are not statistically significant.

Table 13 Alphas and factor analysis for S-QARP, L-QARP and LS-QARP Q1 portfolios

Results from factor model regressions for Q1 portfolios, using monthly data for the period 1.6.1991-1.6.2020. We use heteroskedastic robust standard errors (HAC). Q1 portfolios consist of top 20% companies in each category, and QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small).

S-QARP L-QARP LS-QARP Q1 Q1 Q1 CAPM FF3 FF5 CAPM FF3 FF5 CAPM FF3 FF5

MKT 0.5051*** 0.5556*** 0.5565*** 0.5469*** 0.5959*** 0.6009*** 0.5131*** 0.5646*** 0.5672*** α_p 0.0063*** 0.0044*** 0.0026 0.0062** 0.0040** 0.0019 0.0067** 0.0045** 0.0025 SMB 0.7443*** 0.7433*** 0.7020*** 0.7029*** 0.7438*** 0.7436*** HML 0.4707*** 0.6640*** 0.5811*** 0.8025*** 0.5725*** 0.7884*** RMW 0.3811*** 0.4618*** 0.4361*** CMA -0.1406 -0.1395 -0.1482 R^2 0.474 0.664 0.676 0.468 0.646 0.661 0.420 0.611 0.625 Adj. R^2 0.472 0.661 0.672 0.466 0.643 0.656 0.419 0.608 0.620 Obs. 348 348 348 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level

We can that all the Q1-portfolios exhibit significant exposures to the market proxy, SMB, HML and RMW factors, with all the regressions. The LS-QARP portfolio shows a not significant monthly excess return of 0.25% with FF5 regression (0.67% with CAPM and 0.45% with FF3 at 1% level). The CMA factor is not statistically significant with any of the portfolios. We can also see that the explanatory power (measured by adjusted R^2) only slightly increases with FF5, compared to FF3, in all regressions. 53

7.2.2 Risk adjusted performance for S-QARP, L-QARP and LS-QARP portfolios

Next, the risk adjusted performance is evaluated for S-QARP, L-QARP and LS-QARP portfolios with the different measures. As we see from the table below, the Sharpe ratio for the market and Q1 portfolios for respective strategies are significantly (5% level) different, with differences of 0.103 for S-QARP, 0.088 for L-QARP and 0.096 for LS- QARP.

Table 14 Risk adjusted performance ratios for S-QARP, L-QARP and LS-QARP portfolios

Sharpe ratio Qi - Market Treynor ratio Sortino ratio Information ratio Diff. T-stat

S-QARP Q1 0.220 0.103 2.43* 0.154 0.177 0.301 Q2 0.163 0.046 1.19 0.084 0.092 0.099 Q3 0.184 0.067 1.81 0.108 0.143 0.234 Q4 0.096 -0.021 -0.59 0.030 0.054 -0.053 Q5 0.071 -0.046 -1.16 -0.002 0.014 -0.186 L-QARP Q1 0.205 0.088 2.10* 0.142 0.171 0.293 Q2 0.161 0.044 1.11 0.092 0.117 0.148 Q3 0.140 0.023 0.60 0.063 0.080 0.067 Q4 0.108 -0.009 -0.22 0.034 0.039 -0.069 Q5 0.057 -0.060 -1.46 -0.017 -0.004 -0.207 LS-QARP Q1 0.213 0.096 2.17* 0.159 0.184 0.305 Q2 0.156 0.039 0.89 0.094 0.109 0.114 Q3 0.124 0.007 0.17 0.050 0.057 -0.010 Q4 0.105 -0.012 -0.27 0.034 0.038 -0.071 Q5 0.046 -0.071 -1.69 -0.031 -0.013 -0.220 Market 0.117 *) Significant at 5% level, **) at 1% level, ***) at 0.1% level

S-QARP Q1 exhibits the highest monthly Sharpe ratio of 0.220. LS-QARP Q1 exhibits largest Treynor, Sortino and Information ratio (0.159, 0.184 and 0.305, respectively).

7.3 Portfolio comparison with paired sample t-test

A paired t-test is used for testing the significance between a portfolio's mean with an other portfolio’s mean, which in this case means that we test whether there is a difference between the mean returns of the portfolios. The results of the tests can be seen in Table 15. The null hypothesis is that the mean return is the same for the portfolios. The mean returns are tested for statistical significance by using the t-statistics of the returns. Then a p-value is calculated to examine whether the mean returns differ significantly from zero.

Table 15 Paired sample t-test comparison of portfolio mean returns

Paired sample t-test comparison of portfolio returns (excess of market return), using monthly data for the period 1.6.1991-1.6.2020. Q1 portfolios consist of top 20% companies in each category, and QARP (=Quality At a Reasonable Price), S (=Small), L (=Leverage) and LS (=Leveraged Small).

Mean Qi-Qi Mean Diff. T-stat Df p-value Value Q1 0.01089 0.0023 0.678 347 0.4891 Value Q5 0.0086 Quality Q1 0.0083 0.0028 1.676 347 0.0947 Quality Q5 0.0055 QARP Q1 0.0100 0.0047 1.7855 347 0.0751 QARP Q5 0.0053 S-QARP Q1 0.0010 0.0048 1.7939 347 0.0737 S-QARP Q5 0.0052 L-QARP Q1 0.0102 0.0058 1.9092 347 0.0571 L-QARP Q5 0.0043 LS-QARP Q1 0.01045 0.0066 1.8286 347 0.0682 LS-QARP Q5 0.0037 Value Q1-Quality Q1 0.0026 2.1856 347 0.02951 Value Q1 – QARP Q1 0.0009 1.1650 347 0.2448 Value Q1 – S-QARP Q1 0.0009 1.1469 347 0.2522 Value Q1 – L-QARP Q1 0.0008 0.7326 347 0.4643 Value Q1 – LS-QARP Q1 0.0004 0.4268 347 0.6698 Quality Q1 – QARP Q1 -0.0017 -1.9093 347 0.0571 Quality Q1 – S-QARP Q1 -0.0017 -1.811 347 0.0170 Quality Q1 – L-QARP Q1 -0.0019 -1.4734 347 0.1415 QARP Q1 – S-QARP Q1 0.0002 0.0786 347 0.9374 QARP Q1 – L-QARP Q1 -0.0001 -0.1794 347 0.8577 QARP Q1 – LS-QARP Q1 -0.0004 -0.4923 347 0.6229 S-QARP Q1 – L-QARP Q1 -0.0001 -0.1983 347 0.843 S-QARP Q1 – LS-QARP Q1 -0.0004 -0.5430 347 0.5875 L-QARP Q1 – LS-QARP Q1 -0.0003 -0.9567 347 0.3394

As seen in Table 15, the differences for the portfolio mean returns are not statistically significant on a 5% level for any of the comparison combinations with paired sample t- test. Still the differences range from 0.23% to 0.66% for the Q1-Q5 comparisons for all strategies, indicating that Q1 portfolios have higher mean returns.

7.4 Possible biases and limitations

The main possible biases in the data and corresponding results will most likely be due the exclusion of transaction costs in the study, possible survivorship bias due to missing or excluded companies in the sample and some problems with data from the TRD database. Small stocks are often very expensive to trade due to their illiquid trading volumes. The use of equally weighted portfolios can also add to the transaction costs, as portfolio weights are monthly rebalanced. The issue of selecting the right and appropriate benchmark can also skew the results. 56

8 DISCUSSION

This analysis has described the performance of a novel investment strategy, focusing on leveraged small QARP-companies in the public Nordic markets. The study is conducted between 1.6.1991 to 1.6.2020. The study contributes to the scarce existing literature on QARP investment in the Nordic stock market. In this chapter, I will analyse the results in comparison to previous studies.

8.1 Result discussion in comparison to previous research

The primary purpose of this study is to investigate the performance of leveraged small- QARP equities in the Nordic markets. In relation to the benchmark index (MSCI Nordic Countries), the Private Equity-replicating portfolio exhibited excess returns, even with volatility considered. The risk adjusted performances of the portfolio is higher than for the benchmark index, which shows that the return increases disproportionately in relation to volatility.

Previous studies on the subject by Chingono and Rasmussen (2015) show that leverage yielded positive abnormal returns for small value companies in the United States. The results in this study support the hypothesis that high leverage and debt paydown leads to positive excess return for small QARP companies. This is shown by performing regressions of the sample with the return as a dependent variable against CAPM and the three- and five-factor models. The regressions are performed for the whole time period, indicating significant abnormal returns for the Private Equity-replicating portfolio (Leveraged Small-QARP Q1). Assnes et al. (2018) show that small quality companies have performed better than large quality companies. The results of this study are aligned with the results, with Small-QARP Q1-portfolio yielding sligthly higher monthly alphas than QARP Q1-portfolio. Kozlov and Petajisto (2013) show that a combined value and quality portfolio, that has invested in small companies, has outperformed the market by 5.8% per year. The results of this study show that the Small-QARP Q1-portfolios have had an monthly alpha of 0.63% with CAPM and 0.26% with FF5, which translates to 7.83% and 3.17% on an annual basis, respectively. This seems to be in-line with the previous study, considering the differences in portfolio weights and other limitations. Stafford (2017) shows that equally weighted and monthly rebalanced portfolios comprised of low EBITDA/EV companies yield yearly returns of 18.0%. He also shows that the Private Equity-replicating strategy in his study has a yearly mean return of 20.0%. In this study, the Value Q1-portfolio exhibits a monthly alpha of 0.68% (CAPM) and 0.3% (FF5), which translates to an yearly alpha of 8.47% (CAPM) and 3.66% (FF5). 57

Furthermore, the Leveraged Small-QARP Q1-portfolio exhibits a monthly alpha of 0.67% (CAPM) and 0.25% (FF5), which translates to an yearly alpha of 8.34% (CAPM) and 3.0% (FF5). The results from this study thus seem to be moderately in line with the study by Stafford (2017), when accounted for the differences in portfolio formations and the used metrics. L’Her et al. (2016) show that buyout funds have historically outperformed their benchmark index, and that this has been largely a result of the use of leverage and investing in smaller companies. This study indicates that a similar strategy on the Nordic markets seems to also outperform its benchmark.

8.1.1 Implication of results

In conclusion, the results in this thesis are interesting, given as many previous studies exhibit similar results, which indicates that the phenomenon has been prominent in global stock markets during different time periods. This study indicates that small QARP-companies with high leverage have had higher returns in Nordic countries compared to the benchmark index, meaning that debt has worked as a lever for the returns of these companies. The hypothesis of efficient markets suggests that an investor cannot perform better than the market by picking stocks, and notes that the only way to get a higher return is by taking more risk. However, according to the weak form of the theory, one can possibly analyze companies' fundamental signals, to choose better companies. The leveraged small QARP strategy studied focuses on the companies' fundamental signals, so the results may be in line with the weak form of the theory.

However, it is important to consider the limitations of the data sample. The study is done for a limited period of time, so the results may also be due to sheer luck. Transaction cost, capital gain taxes and other costs are also excluded. To really reject the hypothesis of efficient markets on the Nordic main exchanges, a larger data sample would be needed. This means that the study has only been an interesting introduction to further research. A positive bias can occur due to survivorship bias, which may distort returns. It can also be pointed out that the MSCI Nordic Countries index contains companies that are large or medium-sized, which can also affect the results of the return in relation to the market. Past returns do not reflect future returns and it is thus impossible to know about the strategy in the future as well will be equally favorable.

8.1.2 Suggestions for futher research

The study has focused on examining whether leverage and debt paydown strengthens the return for small QARP companies. Still, the reasons behind the phenomenon could be studied even more thoroughly. Given the study’s economically significant results regarding active investment management, the first proposal for further research is to increase the statistical robustness of the observations, by looking for instance at a longer time period and more markets. As a note, it would also be of interest to study whether there are more underlying variables, such as ownership concentration, that have a positive effect on returns or whether it is only leverage that influences this. One could delve deeper on the active monitoring incentive this strategy entails. Different factor- models could also be utilized, such as the one used in the study by Chingono and Rasmussen (2015). It could also be interesting to see if the results differ by market. As there are many ways of constructing portfolios, it would therefore also be interesting to see variations of similar strategies studied, with different metrics for value, quality and size. Also, a further deep dive could be conducted into different leverage and debt paydown measures. It would also be interesting to see how a value-weighted strategy would perform in relation to the currently used equally weighted, or how changes in the holding period affect the return of the portfolios. Holding periods of to two, three or five years could reflect more that of the holding periods used by Private Equity-funds. One could possibly also combine ESG factors, or momentum with the strategy. 59

9 CONCLUSION

The purpose of this study is to examine whether Nordic small-cap and mid-cap equities with above average leverage and consequent debt paydown, that can at the same time be categorized as Quality at A Reasonable Price-companies, yield higher risk-adjusted returns than the market. This has been done by studying and examining portfolios that are formed of public stocks in the Nordics based on the novel investment strategy. The performance has been studied by using Capital Asset Pricing Model, Fama-French three- factor model, Fama-French five-factor model, and different risk adjusted performance measures. The study was conducted between 1.6.1991-1.6.2020, utilizing data for 1692 public companies on OMX Stockholm, OMX Nordic Copenhagen, OMX Nordic Helsinki and Oslo Bors.

First, the results of the study show that value companies have outperformed the market, when measured by EV/EBITDA. Second, the results show that high quality companies outperform low quality, and that high quality companies exhibit excess returns in comparison to the market. Furthermore, companies at the cross-section of value and quality, namely QARP, seem to have yielded higher returns than purely Quality- companies. Third, the results show that the returns can further be juiced with the addition of leverage and consequent debt paydown. This is most prominent in small- and mid-cap companies. The results thus support the hypothesis of the thesis, stating that the Private Equity-replicating portfolio, consisting of leveraged small QARP-equities, exhibits statistically significant abnormal returns in comparison to the market.

This would support the mispricing hypothesis but could not reject the assumption of efficient markets. The strategy presented to emphasize the results of the work provides indications that financial quality is an important factor that should be considered by value investors. Also, the results indicate that small-cap and mid-cap companies yield higher returns, when combined with a QARP-strategy, and that these returns can further be juiced up with the addition of leverage and debt paydown in the target companies. This may be a result of leverage aversion, as Chingono and Rasmussen (2015) point out. In summary, it can thus be stated that leveraged small QARP equities, i.e., the targets of the Private Equity-replicating investing strategy, seem to have yielded excess returns in the Nordic markets, in comparison to the benchmark index, on a risk-adjusted basis.

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APPENDIX 1 MONTHLY RETURNS

Value portfolios

Quality portfolios

QARP portfolios

Small QARP portfolios

Leveraged QARP portfolios

Small Leveraged QARP portfolios

Factors