The effect of liquidity on expected returns in U.S. stock markets. Master Thesis

Transcription

1 The effect of liquidity on expected returns in U.S. stock markets Master Thesis Student name: Yori van der Kruijs Administration number: address: Date: December, 2013

2 Section 1: Introduction 1.1 Relevance of the research 1.2 Summary of the findings 1.3 Paper structure Section 2: Literature review 2.1 Validity of the liquidity measures 2.2 Illiquidity proxies Price impact proxies 2.3 The origination of the Liquidity CAPM 2.4 Motivation for our research analysis Section 3: Theoretical Framework 3.1 Modern portfolio theory 3.2 The Capital Asset Pricing Model 3.3 Empirical performance of the original model 3.4 Extensions of the SLB CAPM Firm size Firm value Fama French Three Factor Model Firm momentum 3.5 Quartile Portfolio Regressions: An Introduction To The Ibbotson Analysis 3.6 Fama MacBeth Two Step Analysis 3.7 Amihud s ILLIQ Section 4: Data and Method 4.1 The Ibbotson Analysis Microcap, low liquidity sub-sample 4.2 Fama MacBeth Two Step Analysis Five Factor Model Step 1: Time-series regression Step 2: Cross-sectional regression 4.3 Evolution of illiquidity 4.4 Hypothesis summary

3 Section 5: Results 5.1 Summary statistics 5.2 Illiquidity and uncertainty in financial markets Illiquidity during the Tech Bubble Illiquidity during the Global Financial Crisis Illiquidity as an investment strategy: the conclusion 5.3 Stock liquidity and firm size 5.4 Testing the Linear Factor Models Ibbotson Analysis Fama MacBeth Two Step Analysis Step one: Time-series regressions Step two: Cross-sectional regressions Factor lambdas Comparing the results F-tests 5.5 Correlations 5.6 Evolution of illiquidity Section 6: Conclusion Section 7: Discussion Section 8: References list Appendix I

4 1. Introduction _ 1.1 Relevance of the research Over the past decades, the cross-sectional variation in expected stock returns has been explained by the Capital Asset Pricing Model, as designed by Sharpe (1964), Lintner (1965) and Black (1972). Fama and French (1993) significantly improved the model by adding size- and value-factors to the original market-risk factor. Carhart (1997) added the momentum-factor, as found by Jegadeesh and Titman (1993), to the Fama French Model, creating the Four-Factor Model. This model has often been the benchmark for portfolio managers over the past decade. Although the Four Factor Model explains the cross-sectional variation in expected returns relatively well, many researchers propose to include liquidity investment strategies in order to construct efficient portfolios (Amihud & Mendelson; 1986; Amihud, 2002; Acharya & Pedersen, 2005; Idzorek et al., 2012; Ibbotson et al.; 2013). Although the literature on the relation between liquidity and expected returns has grown dramatically, a survey conducted by Subrahmanyam (2010) showed that liquidity is rarely included as a control variable in the models. Hence, this paper investigates the average returns of liquidity investment strategies over the past fifty years, and compares these to other popular investment strategies. In this research, we mostly focus on the effects of crises on the average returns of the respective strategies. Furthermore, since many researchers suggest that the size-factor captures liquidity in the linear factor models, making the addition of the liquidity factor redundant, we investigate the extent to which size captures liquidity and vice versa. Furthermore, we attempt to improve the explanatory power of the wellknown linear factor models by adding a liquidity factor. We will use two types of analyses: the Ibbotson and Fama MacBeth Analysis, named after research of Ibbotson et al. (2013) and Fama MacBeth (1973). We use different types of liquidity portfolio strategies (i.e. moderate, aggressive, liquidity quartile, low-liquidity long, and microcap-low-liquidity long) to demonstrate the effects of risk-aversion level on returns. Finally, we investigate the evolution of liquidity and the implications on average returns. We will discuss these procedures in more detail in Section 4.

5 1.2 Summary of the findings Illiquidity explains cross-sectional differences in expected stock returns that were previously unexplained by the current linear factor models. The liquidity premium of the aggressive liquidity factor strategy is roughly equal to 2.6% per year, and is statistically significant. This suggests that the Five Factor Model is a better performance benchmark than the current linear factor models. The aggressive liquidity factor strategy outperformed the moderate strategy by 4.3% (9.6%- 5.3%) per year over the past five decades. This additional volatility of the aggressive strategy provided mostly upside potential during booms, and little extra losses during market crashes. This suggests that it is important to focus on having (dis)investments in the tails of the liquidity distribution, in order to obtain high stock returns. The liquidity quartile factor strategy outperformed the low-liquidity long and microcap-lowliquidity long strategy. The respective strategies earned significant monthly alphas of 0.49%, 0.27% and 0.37% using the Four Factor Model as benchmark. The microcap-low-liquidity long strategy performed better than the low-liquidity long strategy, as the monthly alphas show. This result is supported by Ibbotson et al. (2013). The lowest significant lambda of the constant (λ 0) (Fama MacBeth Analysis) is obtained in the regression of the aggressive liquidity factor, using the Five Factor Model as benchmark. This also suggests that the Five Factor Model explains more of the cross-sectional variation in expected stock returns than the other linear factor models. Liquidity effects hold regardless of size group. Thus, liquidity return spreads (= the difference between the low-liquidity portfolio return and the high-liquidity portfolio return) are significant across size quartiles. Analogously, size effects do not hold across all liquidity groups (quartiles). These results are supported by Ibbotson et al. (2013). The ex-post liquidity premia were lower during economic crises compared to booms, resulting from a potential flight-to-liquidity.

6 1.3 Paper structure In Section 2, we will first discuss the literature concerning stock liquidity and the implications on expected returns, followed by the theoretical framework in Section 3. Next, Section 4 summarizes our procedures regarding data acquisition and filtering, as well as outlines the regression- and analysis-procedures, followed by the hypotheses summary. Section 5 presents the results of the analyses and relates it to empirical theory. Section 6 will present the results of our hypotheses-tests. Finally, Section 7 discusses potential future research subjects and general improvements and limitations of this research.

7 2. Literature review _ Asset illiquidity has been widely discussed over the past decade, especially regarding its role in asset pricing. Constantinides (1986) defines the asset liquidity premium as the decrease in the unconditional mean return on this asset that the investor requires to be indifferent between having access to the risky asset without the transaction costs rather than with them. This means that liquidity measures have to proxy for actual transaction costs. Several measures have been introduced, relating daily return and trading volume to asset illiquidity. However, researchers have only rarely tested whether liquidity measures actually measure transaction costs experienced by investors. We will evaluate several well-known liquidity measures in this section. Finally, we will discuss whether low-frequency measures for illiquidity, measured monthly and annually, correlate strongly with high-frequency measures. Since low-frequency data is widely available for many firms and it is very costly and time consuming to obtain high-frequency data, empirical testing of hypotheses over a long time-span would be much easier if low-frequency proxies could be successfully used in models. In this section we will discuss various liquidity measures, their characteristics regarding data-requirements and whether the liquidity measure actually measures liquidity. 2.1 Validity of the liquidity measures Researchers in the field of asset illiquidity premia typically only test whether their measure is statistically related to transaction costs. However, since illiquidity is multidimensional, complex, and not directly observable, it is relevant to investigate whether the statistical measures used in empirical research are adequate proxies for transaction costs. However, data on actual transaction costs in the U.S. has only been available since 1983, and many other countries have no such data at all. This means it is difficult to assess the quality of liquidity proxies. Goyenko et al (2008) hypothesize that useful illiquidity measures can be constructed using lowfrequency (daily) return and volume data. To test this hypothesis, they compare spread proxies to effective and realized spread and compare price impact proxies to two price impact benchmarks. Their first two performance metrics are based on cross-sectional correlation and time-series

8 correlation between the low-frequency proxy and high frequency liquidity benchmark, respectively. Their last two metrics focus on the prediction error between the proxies and the benchmark. In the first two measures, only the correlation is important. On the contrary, since their prediction error proxies focus on actual transaction costs, the scale is also important. Next, they run monthly and annual horseraces between twelve spread and twelve price impact proxies. They also test whether the measures are actually related to transaction costs and if they can replicate the high-frequency based benchmarks with measures based on low-frequency data. 2.2 Illiquidity proxies Goyenko et al (2008) distinguish two types of proxies for illiquidity: effective spread and price impact proxies. They define the effective spread of a stock in time interval i as the dollar-volumeweighted average of effective spread, computed over all trades in time interval i. And static price impact is essentially the cost of demanding additional instantaneous liquidity. They propose using the first derivative of effective spread with respect to the order size as price impact benchmark. This is intuitive, since the first derivative is the marginal effect of trading volume on bid-ask spread. Their second price impact benchmark adds a time factor to the static model. Using the second benchmark, they calculate the costs of demanding additional liquidity over five minutes. Since the liquidity proxy we use, Amihud s ILLIQ as designed by Amihud (2002), is a price-impact proxy, we focus on that category. We will briefly discuss the performance of different price-impact proxies, thus, whether the proxies are measures for actual transaction costs. They also introduce new liquidity proxies and test whether they outperform the current measures Price impact proxies For standard-size transactions, the bid-ask spread is a proxy for the price impact, whereas larger excess demand induces an additional effect on prices (see Kraul & Stoll (1972)). Easley and O Hara (1987) state that this effect is likely to be attributable to informed traders. Kyle (1985) proposes that prices are set at an increasing function of the trading volume (also known as order flow), because market makers can t distinguish trading volume generated by (liquidity) noise trading from informed trading and because greater order flow is more likely to result from informed traders. This creates a positive relationship between the order flow or transaction volume and price change, commonly called the price impact.

9 In the study by Goyenko et al (2008), the low-frequency Amihud measure has the highest crosssectional correlation with each price impact benchmark, namely Other measures such as Effective Tick Impact, Effective Tick2 Impact, Holden Impact, Lot Mixed Impact and Zeros Impact are insignificantly different from the Amihud measure. For the 5-minute price impact, Amihud is the best proxy aswell, obtaining a correlation of with the highest statistical significance. Generally, their results show that the Amihud (2002) measure is still very relevant and successful as a lowfrequency price impact proxy. The predictive power of the newly introduced measures only slightly dominates Amihud s or even differs insignificantly from it, depending on the benchmark. Surprisingly, Pastor and Stambaugh s (2001) Gamma and Amivest Liquidity ratio perform very poorly in the tests and show very little relation with illiquidity benchmarks. Since asset illiquidity is not observed directly and is multi-dimensional, there are many proxies which attempt to measure different aspects of illiquidity. For standard size transactions, liquidity is defined as the quoted bid-ask spread. Garbade (1982) and Stoll (1985) find evidence for the theory that the spread is negatively correlated with stock liquidity characteristics, such as trading volume and number of market makers trading the stock. Similarly, Amihud and Mendelson (1986) find that average portfolio risk-adjusted returns increase with their bid-ask spread. They demonstrate that the relation between asset returns and relative spread is concave, meaning that the slope of the function decreases with the spread. Their study provides supporting evidence for the theory hypothesis that long-term investors can effectively increase their risk-adjusted return by holding illiquid stocks in their portfolio. From the perspective of the firm, it is in their best interest to increase the liquidity of their stock, decreasing the required return by investors. This in turn decreases the opportunity cost of capital of the firm, which can positively influence the net present value of potential future projects. Ultimately, since the value of a firm is equal to the present value of discounted expected future cash flows, liquidity-improving financial policies could increase firm value. Empirically, when high-spread firms decrease their spread by 80% (which is to the point of low-spread firms), their firm value would increase by roughly 50% (Amihud and Mendelson, 1986). Managers should consider these implications when deliberating corporate strategies such as going public and/or increasing information disclosure in general.

10 2.3 The origination of the Liquidity CAPM Due to the empirical shortcomings of the Capital Asset Pricing Model (hereafter the SLB CAPM, SLB Model or Sharpe-Lintner Model), as developed by Sharpe (1964), Lintner (1965) and Black (1972), Fama and French (1992) and Carhart (1997) added risk-factors to improve the model s explanatory power of cross-sectional variation in expected returns. We discuss these models in more detail in Section 3. Although the explanatory power of the models improved significantly, Acharya and Pedersen (2005) suggested using a different capital asset pricing model: the liquidity CAPM. Analogic to the standard CAPM, the liquidity CAPM models the required return as being dependent on its expected illiquidity and on the covariances of its own return and illiquidity with the market return and market illiquidity. The formula for conditional expected return of security i, net of illiquidity costs, is as follows: ( ) ( ) ( ) (1) The risk premium is equal to the expectations at time t of the return on the market, minus the risk-free rate (this equals the normal market risk premium), minus the expected market illiquidity, all at time t+1. This results in the following formula for the (liquidity) market risk premium: ( ) (2) Acharya and Pedersen (2005) use the market beta and three liquidity liquidity betas, which we will explain shortly. Important is that they only use one risk-premium. In the regular CAPM, beta is equal to the covariance between the return of stock i, and the market return, divided by the variance of the market return. The three liquidity beta s work similarly and try to capture different aspects of illiquidity. Analyzing the conditional CAPM for net returns is not as straightforward, because the expected return net of illiquidity costs depends on the investor s holding period. The time period of the researchers dataset may not match the holding period of the investors. Hence, in their study, they separate the net return into gross return and illiquidity costs. The formula for the conditional expected gross returns is: ( ) ( ) ( ) (3)

11 Where ( ) ( ) (4.1) ( ) ( ) (4.2) ( ) ( ) (4.3) ( ) ( ) (4.4) Visually, the liquidity CAPM is structured as follows: Market Beta Illiq. Beta-1 Illiq. Beta-2 Risk premium Expected return Illiq Beta-3 The first beta originates from the original CAPM and measures the sensitivity of stock i s return to returns of the market portfolio. Intuitively, rational risk-averse investors would require a higher return in order to hold stocks which are relatively sensitive to market movements (i.e. high-beta stocks), since this increases the probability of default (due to increased volatility). The first liquidity beta measures the relation between expected return and the covariance between asset illiquidity and market illiquidity. They expect a positive relation, because investors would want to be compensated for holding a stock which is illiquid during times of market illiquidity. Moreover, consider an example where an investor holds multiple similar securities. When one security becomes illiquid, he may choose to sell other securities which are more liquid at that time. When the covariance between security and market illiquidity is lower, it is more likely that the

12 second security is not as illiquid as the first. This results in a liquidity premium for security number one, since investors have to sell that security with a larger discount for illiquidity. The second factor is an effect of covariance between asset returns and market illiquidity on expected returns. Acharya and Pedersen (2005) state that this should affect expected returns negatively because investors are required to pay a premium for holding an asset which yields a high return in an illiquid market. Supporting evidence for this theory is found in a study conducted by Pastor and Stambaugh (2001), where stocks with high sensitivity to market liquidity outperformed low sensitivity stocks by 7,5% annually, on average. This return is risk-adjusted according to Carhart s Four-Factor Model (Carhart, 1997). The third factor focuses on the relation between expected returns and the covariance between asset illiquidity and return on the market portfolio. They expect a negative effect on expected returns, because investors are willing to accept a lower return for an asset which is liquid when the market is down. It is likely that the investor s wealth is decreasing in a down market, since according to Sharpe (1964), on average, all investors hold the market portfolio. This increases the probability that the investor has to liquidate at least a part of his portfolio because of the decrease in wealth. When the assets are more liquid, buyers required illiquidity discount decreases. This is a situation where increased liquidity leads to a decrease in bid-ask spread. The sign of the third liquidity beta supports the theory from Amihud and Mendelson (1986), who suggest that quoted bid-ask spread decreases with stock illiquidity. Thus, investors can accept a lower expected return in this situation. 2.4 Motivation for our research analysis While the performance Liquidity CAPM seems very relevant to test, we did not want to exclude the size, value and momentum factors of Fama French (1992) and Carhart (1997), since these factors have explained significant variations in expected stock returns. Hence, we decided to base our analysis on the performance of the liquidity strategy on the three most well-known models, the SLB, Fama French and Four Factor Models. First, we construct liquidity strategies based on the Amihud (2002) ILLIQ measure. In our first analysis, we regress the excess returns of different liquidity strategies on the respective models and measure the risk-adjusted outperformance of each strategy, given each benchmark. In our second analysis, we run regressions on the three models, with the

13 addition of a liquidity factor, which is also based on the Amihud-measure. In order to test whether risk-aversion level affects the performance of liquidity strategies, we construct aggressive and moderate liquidity strategies and use the liquidity values of these strategies to test the crosssectional explanation of each new liquidity-adjusted benchmark. This way, we hope to thoroughly demonstrate the benefits of adding liquidity to asset pricing models. These procedures are explained in more detail in Section 3 and 4.

14 3. Theoretical Framework _ In this section, we will discuss the evolution of modern portfolio theory, the creation of and extensions to the original Capital Asset Pricing Model, followed by the theoretical background of our analysis. Finally, we will discuss our motivation for using the ILLIQ measure by Amihud (2002) to proxy for actual transaction costs. 3.1 Modern Portfolio Theory Maintaining a well-diversified portfolio should be a priority for every rational investor. This has been common knowledge for the past decades. However, the reasoning behind this is not nearly as well-known. In 1952, Harry Markowitz introduced Modern Portfolio Theory (MPT), which states that single-period asset returns are normally distributed random variables, each with its own expect return and standard deviation of returns, which are used as proxy for reward and risk, respectively. MPT suggests that all investors are rational, risk-averse, and only focus on choosing optimal mean-variance-efficient portfolios. Mean-variance-efficient portfolios maximize expected return, given a certain level of variance, or minimize variance, given a certain expected return. The efficient frontier contains the set of mean-variance-efficient portfolios. Tobin (1958) extended Markowitz s framework by adding the risk-free asset. With this addition, investors were able to lever or de-lever their optimal portfolio to fit their risk-aversion level. The line of optimal portfolios starts at the risk-free rate (for the most risk-averse investor) and is tangent to the efficient frontier. In 1964, Sharpe extended Harry Markowitz s Portfolio Theory by introducing the concepts of systematic and idiosyncratic risk. Systematic risk is non-diversifiable risk, such as macro-economic shocks resulting from natural disasters, international government policies et cetera. Idiosyncratic risk is diversifiable, firm-specific risk. He stated that since investors are able to diversify away idiosyncratic risk, they should not be compensated for bearing this type of risk. Furthermore, Sharpe (1966) introduced a measure for risk-adjusted performance using the relation between expected excess returns and portfolio risk, as proxied by standard deviation of portfolio returns. Rational investors should focus on maximizing the Sharpe Ratio (, formerly called the reward-tovariability ratio), since this maximizes their expected excess return, given a level of risk, or

15 minimizes their level of risk, given an excess return value. The formula for this tradeoff is as follows: (5) 3.2 The Capital Asset Pricing Model These additions to MPT, along with additions of Treynor (1961), Lintner (1965) and Mossin (1966), marked the birth of the original Capital Asset Pricing Model. This model attempts to explain the cross-sectional variation in expected stock return using one risk-factor, called beta. Beta relates the asset s exposure to systematic risk to the expected return: ( ) ( ( ) ) (6) Where E(R i) denotes the expected return on asset i, r f equals the risk-free rate, β i denotes the beta of asset i, and E(R m) equals the expected return on the market portfolio. The market risk-premium is denoted by E(R m)- r f. The capital asset pricing model has several strict assumptions, along with the assumptions of MPT, in order to derive equilibrium conditions: Investors are single-period mean-variance optimizers, are able to borrow and lend funds unlimitedly at a given risk-free interest rate, and have identical investment horizons. There are no market frictions, such as taxes or transactions costs. Furthermore, all investors have homogenous opinions about the parameters of the joint probability distribution of all asset returns (Jensen & Scholes, 1972), resulting from perfect market information transparency. Their individual risk-aversion level will determine their place on the capital market line, holding the tangent portfolio in combination with the risk-free asset. Relatively risk-averse investors will have a long position in the risk-free asset and invest less in the risky portfolio. Conversely, risk-seeking investors will actually short the risk-free asset (= borrow money), to invest more capital in the risky portfolio. As a result, on average, all investors will hold identical risky portfolios, the market portfolio (Fama & French, 2004).

16 3.3 Empirical performance of the original model For many years, the Sharpe Lintner Model has been the benchmark for portfolio performance. However, the simplicity of the capital asset pricing model has led to significant criticism regarding its empirical performance. Firstly, many researchers find it fundamentally difficult to empirically test the capital asset pricing model, because it may be impossible to find a perfect proxy for the market portfolio. Friend and Blume (1970) find that the relation between beta and expected return is flatter than predicted by the CAPM, which means that the cost of equity of high beta and low beta stocks are over- and underestimated, respectively. Furthermore, Jensen and Scholes (1972) proposed beta is an important determinant of stock returns. However, they emphasized that stock expected returns are not solely related to their betas. They also demonstrated that the crosssectional tests in the original model are subject to measurement error bias. Fama and MacBeth (1973) found significant residuals in their regressions. The capital asset pricing model uses the market portfolio as benchmark, and constructs the beta in relation to this benchmark. CAPM theory implies that if you invest in the market portfolio, you obtain a beta equal to one and an alpha equal to zero, by definition. The significant positive alphas from the Fama and MacBeth (1973) study imply that beta does not explain all the cross-sectional variation in expected returns. For example, Sharpe (1964) and Lintner (1965) add two assumptions to the CAPM model. One of which is that investors can borrow and lend at the risk-free rate, independent on the amount borrowed or lent. It is not likely that investors with different credit ratings and portfolio compositions are able to lend and borrow at the same rate, the risk-free rate. When investment strategies tilt towards empirical problems of the CAPM, the abnormal returns of the (passive) strategy may increase (Elton, Gruber, Das and Hlavka, 1993). In case of active management as performed by mutual funds, it is possible to obtain a positive alpha (in the original CAPM) when the mutual funds strategy focuses on low-beta stocks, value-stocks and/or small stocks, even when the fund managers have no special talent for picking winning stocks. This is because these are examples of asset classes of which the cost of equity estimated by the CAPM is too low. This means that in reality, these asset classes have higher expected returns (due to being riskier), than estimated by CAPM. As a result of these empirical problems, fake positive abnormal earnings arise.

17 3.4 Extensions of the SLB CAPM Over the years, researchers have demonstrated that there were several aspects of cross-sectional variation in expected stock returns that were not accounted for in the original model. As a result, there have been several additions to the original model. In this section, we will explain three additions that have been covered extensively in empirical research Firm size Reinganum (1981) demonstrated that firm size was negative related to abnormal returns. For NYSE-AMEX firms, these abnormal returns persisted for at least two years, leading to the suggestion that either the one-period capital asset pricing model was misspecified, or that capital markets were inefficient. After thorough investigation, the abnormal returns did not seem to arise from market inefficiencies such as information lags or transaction costs. Thus, they concluded that the abnormalities are a result of risk factors being omitted from the CAPM. Banz (1981) finds that small NYSE stocks (, as measured by total market value,) have higher risk-adjusted returns than large stocks. Similar to the research of Reinganum, he first attributed part of this effect to a lack of market efficiency. However, since this effect has been persistent for multiple decades, it is evident that the capital asset pricing model does not explain all the cross-sectional variation in expected stock returns. Banz noted that size is not necessarily the omitted factor, but could be a proxy for one or more true but unknown factors correlated with size. Hence, because the SLB Model underestimated (overestimated) the expected returns for small (large) stocks, investors were able to obtain significant positive alphas by investing in small stocks. This suggested that they were earning high risk-adjusted abnormal returns using this investment strategy. On the contrary, these abnormal returns were earned on an inadequate benchmark, which did not account for the size premium. This means that the additional return was simply a compensation for bearing extra size risk Firm value Research from Stattman (1980) and Rosenberg, Reid and Lanstein (1985) showed that book-tomarket equity for U.S. stocks is positively related to average returns. A possible explanation for this phenomenon is that investors view stocks with high book-to-market ratios (= value stocks) as more

18 risky, since the market value of the assets is close to the book value. This indicates that historically, the firm has created little value with its assets. Investors require a premium to compensate for the additional uncertainty about future earnings, which could lead to defaults or bankruptcy. Similar to the size premium, the original SLB Model does not account for the value premium. The higher positive alphas generated by the value-strategy, on average, are not risk-adjusted abnormal returns but compensation for bearing value risk Fama French Three Factor Model Fama and French (1992, 1993) supported the previous research on the positive size- and valuepremia. They extended the SLB Model by adding the size and value factors, resulting in the wellknown Fama French Three Factor Model: ( ) ( ( ) ) (7) This new model accounts for the size and value abnormalities which resulted in incorrect riskadjusted abnormal returns in the SLB Model. The size and value factors are constructed as follows: Small-minus-big, or SMB, denotes the portfolio with a long (short) position in the bottom (top) 5 size decile portfolios. The cutoff point is the median NYSE market equity in year t. This investment strategy reaps the size premium and has a zero net position (e.g. the long position is financed by the capital obtained from shorting the large cap portfolios). High-minus-low, or HML, refers to the outperformance of high-btm stocks compared to low-btm stocks. The value portfolio is formed by having a long (short) position in the top (bottom) three book- and market-value-decile portfolios, reaping the value premium, on average. The result of these new factors is that the positive risk-adjusted abnormal returns that were previously earned using size- and value-investment strategies will no longer be obtainable using these strategies. Similar to beta, which was already implemented in the SLB Model, s and v determine the extra return an investor requires for bearing more size- and value-risk, respectively. This means that in empirical tests, the Fama French Model will result in lower alphas and higher adjusted R-squared values, since this new benchmark model explains the cross-sectional variation in expected returns better than the SLB Model.

19 3.4.4 Firm momentum Although the Fama French Model performed much better than the SLB CAPM in explaining the variation in expected returns, there was still room for an improved benchmark, according to Jegadeesh and Titman (1993). They found that past winners, on average, outperform past losers in the short-term future. This is called short-term momentum. Carhart (1997) introduced the momentum factor as an extension to the Fama French Model, called the Four Factor Model : ( ) ( ( ) ) (8) Winners-minus-losers, or WML, represents the short-term outperformance of winning stocks compared to losing stocks. The factor portfolio is constructed by having a long (short) position in the top (bottom) three performing decile portfolios, measured over the past 11 months. This, on average, reaps the momentum premium which is roughly equal to 1% per month (Jegadeesh & Titman, 1993). Carhart (1997) emphasizes that the momentum-factor is not entirely similar to the size- and value-factors. While the size- and value- factors can clearly be interpreted as risk-premia, the momentum-factor simply denotes the outperformance of winning firms compared to losing firms. Empirically, the Four Factor Model has performed relatively well in explaining the cross-sectional variation in expected stock returns. Nevertheless, we propose adding a fifth factor, stock liquidity, to the current benchmark model. We expect that relatively liquid stocks earn lower average returns than illiquid stocks (Amihud, 2002). We will use two different types of regression analysis in order to investigate the explanatory power of the liquidity power in the current benchmarks: The Ibbotson Analysis (referring to the paper of Ibbotson et al. (2013)) and the Fama MacBeth Analysis (Fama & MacBeth (1973). 3.5 Quartile Portfolio Regressions: An Introduction to the Ibbotson Analysis This procedure is based on the work of Ibbotson et al. (2013), which proposes to include liquidity with the current investment styles (size, value and momentum), with stock liquidity being negatively related to expected returns. They also suggest that liquidity is an economically significant indicator of long-term returns that is not yet accounted for in the current benchmarks. While many researchers state that stock liquidity is already proxied for by the size-factor, they find that size

20 does not capture liquidity altogether. In their sample, they use equally-weighted double-sorted quartile portfolios based on liquidity and size to measure the differences in average returns across quartiles. If liquidity adds no explanatory power to the current benchmarks, the average returns should be equal across size quartiles (i.e. given a size quartile, the level of liquidity should not influence the realized return). They find, however, that across size quartiles, the return is negatively related to stock liquidity. This suggests that size does not capture all aspects of firm liquidity. Furthermore, they regressed the returns of the liquidity factor long-short portfolio, which is constructed analogously to the Fama French and Carhart factors, and the low-liquidity long portfolio, on the SLB, Fama French, and Four Factor Models. This resulted in significantly positive alphas across all models. The long-short strategy significantly outperformed the low-liquidity long strategy, resulting in statistically and economically significant monthly alphas of 0,31% and 0,16% in the Four Factor Model, respectively. This led to their conclusion that the liquidity strategy is not easily beaten. Finally, they constructed a microcap-low liquidity portfolio to investigate the additional effect of only including small, illiquid firms. This strategy performed slightly better than the low-liquidity long strategy, but significantly worse than the long-short factor strategy. We use the same double-sorting procedure to investigate the liquidity implications in our sample, as well as run regressions of the returns of the liquidity factor, low-liquidity long and microcap-lowliquidity long strategy on the SLB, Fama French and Four Factor Model. 3.6 Fama MacBeth Analysis The Fama MacBeth Analysis includes two steps: time-series regressions followed by cross-sectional regressions. In the first step, the coefficients for each risk-factor (s, h, m, and i) are calculated. These coefficients of step one can be interpreted as the sensitivity of each portfolio to the respective riskfactor. We use these coefficients as input for the second step: the cross-sectional regressions. In the step, we attempt to calculate the respective premium for each risk factor (market-, size-, value-, and liquidity-risk). Note that momentum-risk is not included, since momentum is not interpretable as a risk-factor (Carhart, 1997), but only measures the outperformance of past winners compared to past losers. Since we run a cross-sectional regression for each month, we average the lambdas (e.g. the coefficient for each risk-factor in each cross-sectional regression) over time, giving us average lambdas. The averages lambdas are equal to the respective premia. If the liquidity lambda/premium is statistically and economically significant, this suggests that liquidity explains part of the

21 unexplained cross-sectional variation in expected returns and should be considered as a new risk factor. The Ibbotson and Fama MacBeth Analysis will be discussed in more detail in Section 4. Now, we will elaborate upon our choice for the liquidity proxy. 3.7 Amihud s ILLIQ We use the ILLIQ-measure, as developed by Amihud (2002), as liquidity proxy in our sample. Goyenko et al (2008) tested the extent in which popular liquidity proxies were related to actual transaction costs. They demonstrated that the Amihud measure is an adequate low-frequency proxy for stock price impact. The formula is as follows: (9) Where and are the return and dollar volume on day d of month t, respectively. is the number of valid observations in month t of stock i. Finally, for empirical analysis, the proxy is multiplied by one million. An advantage of this measure compared to other liquidity measures is that inputs are readily available for most markets and for long periods of time. This allows us to study the time-series effect of illiquidity. When compared to the liquidity ratio (which is the ratio of the sum of the daily volume to the sum of absolute return), as used by Cooper et al. (1985) and Khan and Baker (1993), the liquidity ratio does not have the intuitive interpretation of measuring the average daily association between a unit of volume and the price change, as does ILLIQ. The intuition behind this measure is as follows. Stocks are considered to be relatively illiquid (e.g. have a high value for ) when the stock price moves a lot as a result of a relatively low amount of trades. Amihud (2002) defines illiquidity costs,, as the cost an investor incurs when selling a stock. This means that investors can buy securities at price but must sell at. In this model, liquidity risk originates from uncertainty about the illiquidity costs. Short-term investors are, by nature, generally not suited for investing in illiquid stocks. Their goal is to achieve a high return in a short investment period. The relative illiquidity costs compared to rate of return (over the whole investment period),, is expected to be relatively high for short-term investment

22 strategies. This is because, on average, in a short time-period, we expect the difference between and to be smaller than over larger periods. Driessen and De Jong (2013) state that if investors have homogeneous investment horizons, the optimal investment strategy (accounting for liquidity effects) is the value-weighted market portfolio. When liquidity risk and transaction costs are accounted for in the model, the risk-adjusted return is equal to the net-return of the value-weighted market portfolio. Thus risk adjusted abnormal return, as denoted by alpha, is equal to zero. Rational short-term investors would only invest in illiquid stocks if they have superior information compared to the market, assuming semistrong market efficiency. Naively speaking, this would imply insider trading, which is illegal. Hence, we assume that rational short-term investors do not invest in illiquid stocks, since they do not want to incur the relatively high illiquidity costs associated with this asset class. This means that in a rational economy, only long-term investors will invest in illiquid stocks to reap the diversification and additional return benefits. Amihud and Mendelson (1986) refer to this phenomenon as the clientele effect. However, when only long-term investors invest in a certain asset class, the liquidity premium may disappear altogether, because all investors are willing to hold the stocks for a long time period.

23 4. Data and Method In order to construct our illiquidity measure, we used the CRSP database to obtain daily return and volume data for all common shares of the AMEX and NYSE for the period January 1st, 1963 to December 31st, We used this time period because since 1963, the simple relation between beta and expected returns disappeared (Reinganum, 1981; Lakonishok & Shapiro, 1986; Fama & French, 1992), suggesting that there are omitted variables in the SLB Model which could explain the cross-sectional variation in expected returns better. Secondly, this sample period includes the Tech Bubble and the Global Financial Crisis; periods with strong liquidity implications. Prior to exclusions of firms, we obtained data on 6530 individual firms, and on average, 4806 firms are in the sample each month. We then filtered the complete dataset to only keep stocks with CRSP share code equal to 10 or 11 (common shares) and exchange code equal to 1 or 2 (AMEX and NYSE). With regard to the illiquidity measure, we use the ILLIQ-proxy of Amihud (2002). Considerations about eligibility of stocks is analogous to the procedure of Amihud (2002), Pastor and Stambaugh (2001) and Acharya and Pedersen (2005), who construct price, return and volume requirements for stocks. Only stocks with return and volume data for more than 150 days during year y-1 are eligible. Also, the stock price has to be greater than $5 at the end of year y-1, since returns on low-priced stocks are greatly affected by the minimum tick of $1/8. This increases the noise of the estimator. In order to maintain a consistent measure for illiquidity, we exclude NASDAQ stocks since this data includes inter-dealer trades and is only available from 1982 (Acharya & Pedersen, 2005). After performing these exclusions, we have an average of 1678 firms in our dataset each month. Finally, we normalize the illiquidity measure by controlling for the ratio of the capitalizations of the value-weighted market portfolio at month t-1 and at the end of These procedures reduce the measurement error in the illiquidity measure. We use two regression procedures in order to test whether investors need to include liquidity with the other investment styles to form efficient portfolios. However, our analysis will start by investigating the summary statistics. Along with the conventional method of evaluating the statistics of the full sample, we investigate the effect of liquidity and firm size on geometric mean returns using equally-weighted double-sorted quartile intersection portfolios based on liquidity and size. If

24 size explains all the cross-sectional variation in expected returns that liquidity does, we would see no difference in expected returns across size quartiles. Analogously, we would see no significant differences in returns across liquidity quartiles if liquidity captures the size effect. We will first discuss our procedure based on the recent work of Ibbotson et al. (2013). Next, we will use the famous Fama MacBeth (1973) Two-Step Analysis. At the end of this section, we will briefly discuss our hypotheses. 4.1 Ibbotson et al. (2013) Analysis We downloaded monthly Fama French and momentum factor data from the website of Kenneth French. We also obtained daily data on stock characteristics, such as stock price, return, dollar trading volume, and total shares outstanding from the CRSP database. Next, using the daily CRSP data, we constructed the monthly Amihud (2002) ILLIQ measure as proxy for asset illiquidity. The procedure for constructing this measure is discussed in Section 3.7. Note that Ibbotson et al. (2013) use stock turnover as proxy for stock liquidity. Haugen and Baker (1996) and Datar, Naik and Radcliffe (1998) found a negative relation between stock turnover and future returns in the U.S. equity market. The intuition behind their measure is that a stock is relatively liquid when turnover is high. In equilibrium, the more illiquid stocks are allocated to investors with lower trading frequency. They amortize the illiquidity cost over a longer period, thus mitigating the loss due to the asset s illiquidity costs. Thus in equilibrium, there is a negative relationship between stock illiquidity costs and trading frequency (Amihud & Mendelson, 1986). We divide our dataset into equally-weighted double-sorted quartile portfolios, sorted first on stock liquidity, subsequently on firm size, as proxied by market capitalization. We first use the summary statistics per double sorted quartile to give an intuition about the underlying data. Our expectation is that both stock liquidity and firm size are negatively related to expected returns. Next, we compute the monthly returns of a long-short illiquidity portfolio, where the returns of the most liquid quartile were subtracted from the returns of the most illiquid quartile (Ibbotson et al., 2013). This gives us a dollar-neutral liquidity factor, which is regressed on the models including factors for market, size, value and momentum, as obtained from Kenneth French s website. We will use the SLB CAPM (Sharpe, 1964; Lintner, 1965; Black, 1972), which includes only beta as risk-factor, the Fama-

25 French model, which added book-to-market ratio and firm size, and the Four Factor Model, which also includes momentum, as benchmark models. Finally, as a comparison, we will also regress the excess returns of the portfolio which is only long in stocks of the most illiquid quartile, as well as the excess returns of the enhanced low-liquidity strategy, on the three models. The first strategy is called the low-liquidity long strategy. The second strategy is enhanced because we only include stocks from the low-liquidity-microcap intersection portfolio. Essentially, since you already have a long position in the least liquid quartile portfolio, the biggest difference between the first and second strategy is the extra short position the large cap quartile portfolio. If this strategy adds value to the original low-liquidity long strategy, we should see higher values for alpha (=risk-adjusted abnormal return) in the regression for the enhanced liquidity strategy. The first regression, where the returns of the long-short portfolio are regressed on the SLB CAPM, is as follows: ( ) (10) Where R it denotes the return on the long-short portfolio, α denotes the risk-adjusted excess return, β im denotes the sensitivity of the portfolio to market swings, R Mt is the return on the market portfolio and r ft is the risk-free rate, as proxied by the one-month Treasury bill rate, retrieved from Ibbotson Associates.. In the Fama French regression, the returns of the long short portfolio are regressed on the size and value factors, which are essentially returns of long short value and size portfolios, respectively: ( ) (11) The final regression also includes the momentum factor: ( ) (12) Note that since we use the returns of the long-short strategy in the regressions, we don t need to subtract the risk-free rate from the returns on the left-hand-side of the equation. This is because the

26 long-short position strategies, by definition, have a zero net position. On the contrary, as will be made clear in the following section and formula, the risk-free rate will have to be subtracted from the returns of the low-liquidity long and enhanced liquidity strategy. This is because an investor would have to borrow money (= short position in the risk-free asset) to have a long position in these portfolio strategies. Thus, on the left-hand-side of the equation, the risk-free rate needs to be subtracted from the returns of the investment strategies. The left-hand-side of the following SLB CAPM equation contains the adjustment: ( ) (13) The equations for the Fama French and Four Factor regressions on the returns of the low-liquidity long portfolio are similar to Equation (11) and (12), except with the adjustment on the left hand side for excess returns. Finally, in Fama MacBeth regressions which we will discuss in the following section, the returns we use as dependent variables are portfolio returns obtained from Kenneth French s website. The portfolios are 5x5 intersection portfolios sorted, first on size, subsequently on book-to-market ratio. These portfolios are not zero in net position; these are similar to the lowliquidity long and microcap-low liquidity long strategy. Hence, we also subtract the risk-free rate from the monthly portfolio returns in these regressions Microcap, low liquidity sub-sample We use the double-sorted liquidity-size intersection portfolios: specifically the intersection quartile portfolio of low-liquidity, microcap for this sub-sample Market capitalization of each stock at month t is calculated in order to determine the cut-off points for each size quartile. Our hypothesis is that the size factor explains part of our illiquidity factor and vice versa, since it is intuitive that relatively small firms are expected to be less liquid and more risky than large firms. Also, small firms are less likely to be transparent, publicly listed, and have standardized processes than large firms. This means that cross-sectional differences in expected returns resulting from asset illiquidity are difficult to investigate, since size and illiquidity factors could be driven partly by the same factors. Consider a month t where, on average, small firms outperformed large firms, thus SMB is positive. On average, small firms are expected to be less liquid than large firms. Since the illiquidity factor (based on quartiles) on month t is equal to the return of the least liquid quartile portfolio minus the return of the most liquid quartile portfolio, it is likely that the liquidity factor is positive as well. We

27 would like to separate the size effect from the illiquidity effect. If this strategy significantly outperforms the low-liquidity long strategy, as denoted by a significantly higher alpha, there is still value in (dis)investing in small (large) cap stocks, parallel to the liquidity strategy. Table 1 (Section 5.1) shows the cut-off points of the market capitalization quartiles (in billion US dollars) before dropping the small, medium and large cap stocks. This suggests the distribution is skewed to the right, since the median value for market capitalization ($0.30b) is significantly lower than the mean ($2.62b). This means a small number of stocks account for a large percentage of the total market capitalization. We will use this sample to run the Ibbotson Analysis using the standard CAPM, the Fama French and the Four Factor Model as benchmarks and test whether the signs and/or significance of the coefficients change compared the other strategies in the analysis. When analyzing the results, we will compare the effectiveness of the investment strategies based on the coefficient and significance of the monthly alpha and adjusted R-squared of the model. The best strategy, in terms of expected returns, is the one which has the highest statistically significant monthly alpha, since this denotes the monthly outperformance of the strategy compared to the benchmark, in percentages. Results of this analysis will be discussed in Section Fama MacBeth (1973)-analysis For the Fama MacBeth Analysis, we use the same data as that used in the Ibbotson analysis. However, we also obtain monthly returns on 5x5 portfolios based on size and book-to-market ratio from the website of Kenneth French to create our benchmark models: the SLB CAPM, Fama French and the Four Factor Model. After the illiquidity factor is constructed based on Amihud s ILLIQ measure (Amihud, 2002) and added to the models, we will run Fama MacBeth two-pass regressions, in order to determine the risk premia of the factors. Using this procedure, we can compare signs and economical and statistical significance of the factors, as well as the adjusted R-squares of the models. This way we can investigate whether asset illiquidity explains a significant part of expected asset returns, which is not yet explained by the current risk factors, and should be considered to be added as a fifth factor to the well-known models. The next section will explain the complete process.

28 4.2.1 Five Factor Model The following formula illustrates the Four Factor Model, as designed by Carhart (1997), with the addition of the illiquidity factor. ( ) ( ( ) ) (14) We will use two liquidity factors in this analysis: the moderate and aggressive liquidity strategy. The moderate strategy is comparable with the momentum and value strategies, since they use the same cut-off points for their long and short-portfolios. This liquidity factor strategy is constructed as follows: We sort stocks based on illiquidity, construct illiquidity decile portfolios and compute the historic average excess return of the 30% most and least liquid portfolios. Since we expect illiquid stocks to outperform liquid stocks, we subtract the average excess return of the three most liquid decile portfolios from the average excess return of the three most illiquid decile portfolios. If illiquidity is a risk-factor that is not already completely explained by other risk-factors in the Four Factor Model, this, on average, should yield a significant positive value (Amihud, 2002; Ibbotson et al., 2013). The aggressive liquidity strategy uses only the top and bottom decile portfolios instead of the top and bottom three. Because this strategy has long (short) position in the most illiquid (liquid) portfolio (of stocks), we expect the liquidity premium to be higher than in the moderate strategy. Note that these are comparable investment strategies to the one used in the previous section, where an investor would long the most illiquid quartile portfolio, and short the most liquid quartile portfolio. In the following sections, we will demonstrate the Fama MacBeth Two Step Analysis using the Five Factor Model Step 1: Time-series regression First, we run a time-series regression for all N portfolios (N=25). ( ) (15) The first step gives us 25 coefficients for each risk-factor (s, h, m, i). The coefficients of step one can be interpreted as the sensitivity of each portfolio to the respective risk-factor. Since we investigate

29 the implications of liquidity on asset returns, and because the theory of the Four Factor Model has already been extensively reviewed, we will only focus on the first-step output of the illiquidity factor. Since we want to investigate whether illiquidity explains cross-sectional variation in expected stock returns, the second step of the Fama MacBeth-regression is much more important, as this is where we can test whether the risk premia are supported by the empirical evidence Step 2: Cross-sectional regression We use the 25 betas, s s, h s, m s and i s obtained in step one as input for this step. Here we run a cross-sectional regression for each month (T=50x12=600). r it r ft ˆ t t i t sˆ i t vˆ i t mˆ i t ii (16) it ˆ After the cross-sectional regression, we have obtained 600 λ 0, λ 1,.., λ 5 (one for each month). We average the lambdas over time, resulting in the premium for each risk-factor. The estimated liquidity premium is equal to the average of 600 λ 5 s. The final step is to determine the economical and statistical significance of each risk-factor. We can also compare the value of adjusted R-squared of the original Four Factor and Five Factor Model. This is the ratio of explained variation by the model to total variation, but is also a function of the number of regressors in the model. Hence, if an extra explanatory variable does not add any value to the model, adjusted R-squared decreases. Furthermore, since the perfect benchmark is characterized by an alpha equal to zero (or not statistically different from zero), we would conclude that the liquidity factor improved the current benchmark if the alpha is significantly lower than the alpha of the Four Factor Model. On the contrary, if we observe statistical insignificance of the liquidity factor, a decreasing adjusted R-squared and/or a significantly higher alpha, we can conclude that the illiquidity factor did not improve the Four Factor Model. Finally, we will also conduct partial F-tests in order to test the null hypotheses that all coefficients of the models are zero. This means that none of the factors have explanatory power. We will conduct these tests for the Sharpe Lintner, Fama French, Four Factor and Five Factor Model.

30 4.3 Evolution of illiquidity It seems relevant to test whether the implications of illiquidity on asset expected returns have changed over the past decades. Globalization of financial markets has significantly decreased illiquidity for many asset classes. Each decade, we regress portfolio excess returns on the five riskfactors to investigate the evolution of illiquidity. Our hypothesis is that, due to the globalization of the markets over the past decades, the liquidity premium has decreased over time. Especially in the last decade, where there have been many innovations at the level of exchanges (i.e. electronic order book, decrease in minimum price changes), we expect the value for ILLIQ (Amihud, 2002) to be at its lowest level. Furthermore, we will run the Fama MacBeth two-pass regressions each decade. The lambdas obtained from the second step as denoted above will inform us about the illiquidity premium during crises and booms. We expect the liquidity premium (which is equal to the lambda of illiquidity from step 2) to be low, or even negative during crises, since it is likely that liquid stocks outperform illiquid stocks during times of uncertainty. Conversely, during booms, the investor can reap the benefits of the liquidity premium, leading to a relative outperformance of illiquid stocks to liquid stocks Hypothesis summary We summarize our hypotheses as follows: Hypothesis 1: Illiquidity explains part of the cross-sectional differences in expected stock returns that is yet to be explained by the current linear factor models. The cross-sectional predictive power is investigated in step 2 of the Fama MacBeth Analysis. We expect a statistically significant positive liquidity lambda and an increase in adjusted R-squared. Hypothesis 2: The aggressive liquidity factor strategy outperforms the moderate liquidity factor strategy in our sample, in terms of average returns. The monthly geometric means in the summary statistics and the cumulative returns in the return-time plots will provide the evidence. Hypothesis 3: The liquidity quartile factor strategy outperforms the low-liquidity long and microcaplow-liquidity long strategy in our sample, in terms of risk-adjusted returns (= alpha). Note that we test this hypothesis to investigate whether the extra return earned by the aggressive liquidity factor

31 strategy is not just a compensation for bearing additional risk with regard to the respective benchmark [Ibbotson Analysis]. Hypothesis 4: The lowest significant lambda of the constant (λ 0) is obtained in the regression of the aggressive liquidity factor, using the Five Factor benchmark model [Fama MacBeth Analysis]. Hypothesis 5: Liquidity effects hold regardless of size group. Thus, liquidity return spreads (= the difference between the low-liquidity portfolio return and the high-liquidity portfolio return) are significant across size quartiles. The geometric mean returns of the equally weighted double-sorted intersection quartile portfolios will be used testing this hypothesis. Hypothesis 6: Size effects hold regardless of liquidity group. Thus, size-return spreads (= the difference between the microcap-portfolio return and the large-cap-portfolio return) are significant across liquidity quartiles. The geometric mean returns of the equally weighted double-sorted intersection quartile portfolios of Table 2 will be used testing this hypothesis. Hypothesis 7: During crises, the ex-post liquidity-lambda decreases (or becomes negative), because we expect to perceive a flight-to-liquidity, leading to a periodical outperformance of liquid stocks compared to illiquid stocks. Conversely, during booms, we expect the ex-post lambda to be positive, since long-term investors could have reaped the liquidity premium.

32 5. Results _ 5.1 Summary statistics Table 1 provides monthly and annual summary statistics on the five factors of the liquidity CAPM, as well as firm characteristics, for period Illiquidity (10%) denotes the illiquidity factor constructed using the returns of a long portfolio of the ten percent most illiquid stocks and shorting the portfolio of the ten percent most liquid stocks. The illiquidity (30%) factor is constructed analogous to the other illiquidity factor portfolio, but also includes stocks with less extreme values for (il)liquidity. Portfolios are rebalanced each month. Finally, Figure 5-8 (Appendix I) show the evolution of monthly CAPM factors as well as 12-month lagged moving averages. Figure 1 shows this for the 10% illiquidity factor. These figures give an intuition about the volatility of factor returns. Figure 5 depicts the evolution of the median value for Amihud s (2002) illiquidity measure. We will discuss this in more detail in Section 5.2. Noteworthy are the mean values of the illiquidity factors. Since we have monthly factor-data, this is the average monthly outperformance of the illiquid stocks compared to liquid stocks, and equals a return on the long-short portfolio of 0.44% per month for the 30% factor (or 5.32% per year), with an annual return of 6.68%. The values for the mean monthly and annual return for the 10% illiquidity factor are 0.80% and 9.61%, respectively. This factor has a median annual return of 10.48%. This means that in our sample period, on average, the returns of illiquid stocks have been significantly higher than the returns of relatively liquid stocks. The summary statistics also show that the distribution is not very skewed, since the median and mean values are similar. The positive values confirm our expectations. We hypothesized that investors would require a higher return in order to invest in an illiquid portfolio (of stocks), due to the extra illiquidity costs and risks associated with selling illiquid assets (Amihud, 2002; Acharya & Pedersen, 2005; Ibbotson et al., 2013).

33 Table 1: Monthly and annual descriptive statistics of five factors, Monthly factor descriptive statistics Quartiles Variable Observations Mean (%) S.D. (%) Min (%) 25th pct (%) Median (%) 75th pct (%) Max (%) Market risk premium Small Value Momentum Illiquidity (10%) Illiquidity (30%) N (portfolios) 25 T (months) 600 Annual factor descriptive statistics Market risk premium Small Value Momentum Illiquidity (10%) Illiquidity (30%) N (portfolios) 25 T (years) 50 Firm characteristics Observations Mean S.D. Min 25th pct Median 75th pct Max Market capitalization ($ billions) Trading volume ($ millions) , Shares outstanding (* 1000 shares) ,144.68

34 Furthermore, we introduced two long-short illiquidity strategies to further clarify the difference in return and risk between the moderate (30%) and aggressive (10%) illiquidity investment strategy. We hypothesized that the aggressive strategy would yield a higher return than the moderate illiquidity strategy, since the investor has a long position in the illiquid decile portfolio that is expected to be performing best (in terms of returns), and a short position in the most liquid decile portfolio, which is expected to be performing the worst, ex ante. It seems intuitive that since the aggressive strategy only includes the most extreme stocks of the distribution, especially in the illiquid area, the standard deviation of the returns are expected to be higher than that of the moderate strategy. Finally, we notice that the minimum value for the monthly momentum factor in our sample is - 34,74%, while the maximum value is 18,39%, with a standard deviation of 4,28%. The momentum factor is constructed as the realized return of the 30% best performing firms (e.g. firms above return percentile 70 in the previous year) minus the return of the 30% worst performing firms (e.g. firms below return percentile 30 in the previous year). The large discrepancy, in absolute terms, between the maximum and minimum value of the momentum factor suggests that in extreme cases of outperformance between past winners and losers, past losers have actually performed much better than past winners. A potential explanation for this effect is that when the stock price of past winners has increased significantly in a short time-period, as a result of good performance in the market, investors may become overconfident that this good performance will continue in the future. Managers may also be inclined to think that their managerial qualities are significantly better than the market. This overconfidence drives up the demand, and in turn, the price of the stock (Barber & Odean, 2001). This can lead to overvaluation. Assuming efficient markets, rational (institutional) investors will short the overvalued stock, until the price has reached the equilibrium price (Bondt & Thaler, 1985). Consequently, when the firm value declines to the actual equilibrium price the next time periods, this has resulted in a significant negative realized return for the overconfident investors. 5.2 Illiquidity and uncertainty in financial markets During uncertain times (i.e. crises), many researchers perceived a flight to liquidity (Vayanos, 2004). This is because during these times, the probability that performance drops below a certain exogenous threshold increases, making withdrawals more likely. Liquid assets offer managers easier access to immediate capital, improving their position to pay off debt holders, thus avoiding bankruptcy. The resulting increase in demand of liquid stocks would lead to an increase of the

35 liquidity premium, ceteris paribus. Acharya and Pedersen (2005) find that investors have to pay a premium for buying a stock that is liquid during crises or when market in general is illiquid. However, they also expect illiquid assets to perform especially poor during crises, since these stocks provide managers and investors no safety net. In the following section we will compare the (10%) illiquidity strategy to the size, value, and momentum strategy. Though, since the (10%) illiquidity investment strategy and the momentum strategy outperformed the other strategies significantly, we will mostly focus on these Illiquidity during the Tech Bubble The hypothesis that investors prefer liquidity during uncertain times is supported by our data, as can be seen in Figure 1 and 2, where the period of shows a significant increase in illiquidity, leading to a large decrease in (moving average) returns of the long-short portfolio. Figure 3 and 4 also show this effect. The value of $1,00 invested in the illiquidity (10%) strategy in January 1 st, 1963 grew to about $105 in the period However, in the following years, the value of the strategy dropped by over 33% to $70. While the interpretation of cumulative returns over the whole period is valid in the Figure 3, interpreting differences between the investment strategies is more difficult due to the effect of high dollar values for the illiquidity (10%) and high momentum strategy on the scale of the graph. Hence, Figure 4 shows the cumulative returns using a logarithmic scale. The tech bubble lead to a significant negative return of illiquid stocks, depicted by the downward sloping lines of illiquidity 10% and 30% during the period shortly after the year The momentum strategy showed slight drops in return during the tech bubble. Figure 3 shows that the $1,00 invested in January 1 st, 1963 grew to approximately $48 in the period until The following years showed to be very volatile with ups and downs, yielding a net return of about zero percent in the years 2000 through Again, this is best visible in Figure 8, which shows the growth adjusted for the amount of capital invested. While the lack of significant negative returns seems hard to understand, it lies in the very nature of the momentum factor to yield positive returns. When returns of the original momentum portfolio decrease, the poor-performing stocks originally included in the portfolio are replaced by better performing stocks. In this case, tech stocks will be quickly moved from the buy-side (long position) of the investment strategy, to the sell-side (short position). This means that if bad performance is not extremely sudden and short-term, the strategy will correct itself by rebalancing the portfolios. Jegadeesh and Titman (1993) find that this strategy yields average returns of 1% for the following 3-12 months. Vayanos and Woolley (2013) investigated the optimum portfolio rebalancing frequency for the momentum factor and find that

36 Figure 1-2: Evolution of monthly ILLIQ factor (Amihud, 2002) and constructed monthly CAPM-based high-minus-low ILLIQ factor. Monthly Amihud (2002) ILLIQ factor is constructed using daily data. The ILLIQ factor is the sum of the absolute values of the ratio of daily returns and dollar volume on days d of month t, divided by the number of valid observations in month t. A high value for ILLIQ denotes high illiquidity for stock I in month t, meaning relatively high return movements caused by relatively low dollar trading volume. We computed the monthly median of the ILLIQ measure to account for individual outliers. The evolution of the high-minus-low illiquidity CAPM factor as shown in Figure 2 is analogous to that of Figure 5 through 8 (Appendix I). The value of the factor on month t is equal to the return of the portfolio with the 10% most illiquid stocks minus the return of the portfolio with the 10% most liquid stocks. The moving average is lagged by 12 months Date Illiquidity (%) MA_ILLIQ (%)