LIQUIDITY AND ASSET PRICING. Evidence for the London Stock Exchange

LIQUIDITY AND ASSET PRICING Evidence for the London Stock Exchange Timo Hubers (358022) Bachelor thesis Bachelor Bedrijfseconomie Tilburg University May 2012 Supervisor: M. Nie MSc

Table of Contents Chapter 1: Introduction... 3 Chapter 2: Literature overview... 5 Chapter 3: Model specification... 9 Chapter 4: Data and empirical results... 11 4.1 Data... 11 4.2 Empirical results... 14 4.2.1 CAPM... 14 4.2.2 CAPM plus liquidity factors... 15 4.2.3 CAPM plus liquidity and Fama-French factors... 19 4.2.4 Second stage regressions... 23 Chapter 5: Conclusions... 24 Chapter 6: References... 25 2

Chapter 1: Introduction This paper studies the relationship between asset prices and liquidity. This introduction first introduces the hypothesis studied in this paper. Next the concept of liquidity will be explained, together with a deeper motivation of the hypothesis. As covered in chapter two, there have been many studies proving that there exists a relationship between asset prices and liquidity and therefore that liquidity is priced. This paper studies this relationship for stocks listed on the London Stock Exchange (LSE). The aim of this study is to investigate whether liquidity is priced on the LSE. The first hypothesis, therefore, is that there exists a relationship between liquidity and asset prices. For the second hypothesis it is necessary to explain the concept of liquidity better. Liquidity can be the costs one expects to incur when trading a share for example. That is, a brokerage fee or the costs of finding a seller or buyer. It can also be the costs of selling to a market maker, when no counterparty is available. The market maker asks a premium for bearing the risk until a buyer is found. Information asymmetry can also cause illiquidity. The counterparty could know specific private information about a stock, for example he knows that earnings are misstated, which could lead to losses. So, when an investor expects higher costs, meaning lower liquidity, he demands a higher return, which lowers the price. The second hypothesis therefore states that a higher illiquidity increases the return. Liquidity has been the subject of a lot of studies. Interestingly, there are also a lot of different measures for liquidity. This paper uses the bid-ask spread to approximate for the illiquidity of a stock. If the liquidity of a stock is lower, it is expected to be more difficult to trade. The hypotheses are tested for stocks listed on the London Stock Exchange for the period between October 1986 and December 2011. Equally weighted portfolios are formed to reduce noise in the regression analysis. This formation is done twice. The stocks are sorted on size using market value and they are sorted on liquidity using the bid-ask spread. The paper starts with the Capital Asset Pricing model, extending it first with the liquidity factor and finally extending it with the Fama and French (1993) factors. 3

The results of the regression analyses support the hypothesis that there is a relationship between liquidity and asset prices. There is not much evidence that this is also true for stocks sorted on size. The coefficients of the liquidity factor are positive, supporting the second hypothesis that the return increases when liquidity decreases. An increase in the bid-ask spread decreases liquidity and thus increases the return. The second stage regressions of the final model, including the liquidity and Fama-French factors, offer no conclusive evidence. The fit of the model for liquidity-sized portfolios is relatively low and none of the betas are significant, but the fit of the model for size-based portfolios is high. This paper proceeds as follows. Chapter 2 gives a literature overview of past research concerning asset pricing and liquidity. Chapter 3 specifies the used model and gives an interpretation. Chapter 4 contains the data specification and regression analyses. Finally, chapter 5 discusses the results and offers concluding remarks. 4

Chapter 2: Literature overview Amihud and Mendelson (1986) looked for a relationship between the bid-ask spread and the expected asset returns. They proposed that the expected asset returns are increasing in the bid-ask spread. They use risk-neutral investors who take transaction costs into account when buying and selling securities. So the individual investor values the future transaction costs, which will be incurred because of the security. Then the present value of these future transaction costs is the price discount of the security due illiquidity. They also include a clientele effect. Investors have different holding periods and therefore value the impact of transaction costs differently. Investors, who tend to hold the assets for a longer period, require a lower per-period return than investors who hold stocks for a short period. Amihud and Mendelson tested two hypotheses; expected asset return is an increasing function of illiquidity costs and the relationship between expected asset return and illiquidity costs is concave. They tested these hypotheses using data from NYSE and AMEX stocks during 1960-1980. Their data reject the alternative hypotheses, so the hypotheses are accepted. Also, they find evidence of the size effect. The capitalization of a firm has an effect on the liquidity of a stock. Stocks from firms with a higher market capitalization are less costly to trade. Eleswarapu (1997) studied a longer period. He used the same the bid-ask spread as a measure for liquidity as Amihud and Mendelson, but employed the Fama- MacBeth (1973) method for the cross-section estimation. He regressed the stock return on the stock s beta, relative spread and size. The relative spread is found to be significant for all months, whereas the beta is only significant in January and the size is found to be insignificant for every month. This raises the question about whether seasonality is a component of liquidity. Amihud (2002), discussed later in this paragraph, also studies this issue. Datar, Naik and Radcliffe (1998) used average stock turnover rate (number of shares traded divided by number of shares outstanding) to approximate for liquidity instead of the bid-ask spread, because it is difficult to obtain data about the bid-ask spread for a longer period of time and because Petersen and Fialkowski (1994) found it is not a good proxy for actual transaction costs. The 5

average holding period of the stock, a reciprocal of stock turnover, is an indicator for the liquidity of a stock. Investors tend to hold illiquid stocks for a longer period of time, which increases the holding period and thus decreases the stock turnover rate. Their dataset consists of data of all non-financial firms listed on the NYSE from 1962 till 1991. They used the Fama-MacBeth (1973) method for estimating the cross-section of stock returns. The data support the hypothesis that stock returns are strongly negatively related to their turnover rates. This confirms the theory that illiquidity leads to a higher return. Additionally, the turnover rate stays significant after controlling for beta, size, book-market-ratio and the January effect. So, in this study the January effect is rejected; the turnover rate was significant throughout the year. Amihud (2002) proposes that liquidity can predict future returns. He states that high illiquidity today is predictive of high illiquidity in the next period. High expected illiquidity for the next period implies a high required return, which leads to lower asset prices today. He uses an illiquidity measure that is related to the price impact coefficient (Kyle, 1985), ILLIQ. ILLIQ, the daily ratio of absolute stock return to its dollar volume, is calculated by R /(P * VOL), where R is the daily return, P is the closing daily price and VOL is the number of shares traded for that day. ILLIQ is then averaged for each stock over a year to obtain the yearly stock s ILLIQ. This measure is then used in a cross-section regression of stock returns for NYSE stocks during 1963-1996 on their previous-year ILLIQ and controlling variables: beta, size, volatility, dividend yield and past returns. The results confirm that ILLIQ has a positive and significant effect on stock returns. There is no seasonality component, because this effect is significant for all months, not just January. He further examines the time series effect of market-wide changes in stock liquidity. He uses the average of a stock s ILLIQ, AILLIQ, to test two hypotheses; expected stock return for the next period is an increasing function of illiquidity as expected in the current period and an unexpected rise in illiquidity in the current period leads to lower stock prices in the same period. The results support the hypotheses. Average stock excess return is an increasing function of lagged AILLIQ and is a decreasing function of unexpected AILLIQ. He also finds evidence that the effect of increased illiquidity 6

is stronger for smaller firms due to small firms being less liquid, consisted with the theory that liquid stocks are more attractive when liquidity worsens. Pastor and Stambaugh (2003) find evidence that market wide liquidity is important for pricing assets. They propose that the sensitivity of stock returns to market wide liquidity should be reflected in a premium. When stocks are more sensitive to market wide liquidity, i.e. have a higher exposure to market liquidity shocks, they should earn higher expected returns. For the liquidity measure they use the coefficient of the factor daily dollar volume, based on the observation by Campbell, Grossman and Wang (1993) that the coefficient capturing the change in stock price for a given trading volume in a regression of a stock s daily return on its signed lagged dollar volume is more negative for stocks with lower liquidity. They built the following model: ( ), where is the excess return of stock i on day d and is the daily dollar volume. measures liquidity, stocks with a more negative value for are perceived to be less liquid. The average of the individual stock s is the monthly market s liquidity,. Then the liquidity measure is calculated by taken the residual from an AR1 model of. The regression coefficient of this measure,, is a stock s exposure to market wide liquidity. Their dataset contains stocks listed on NYSE, AMEX and Nasdaq during 1966-1999. If liquidity risk were priced, it would mean that the return of a stock should be increasing in its liquidity beta. They indeed find that the expected return is an increasing function of a stock s sensitivity to market wide liquidity, which indicates that liquidity risk is priced. Acharya and Pedersen (2005) have developed a liquidity-adjusted capital asset pricing model (LCAPM) incorporating some of the former mentioned liquidity measures as well as new measure, the covariance between the illiquidity of a stock with the market return. They use three liquidity betas next to the market beta, and. They proposed the following model: ( ) ( ) ( ), 7

where ( ) ( ), ( ), ( ) ( ) ( ) and ( ). ( ) ( ) The model states that the required excess return depends on the risk free rate, expected illiquidity costs and the four betas. Just as in the CAPM the return on an asset increases with the market beta, the covariance between asset s return and the market return. measures the effect that return increases when the covariance between an asset s illiquidity and market illiquidity increases. Investors require a higher return for an asset that is illiquid when the market is also illiquid, so will generally be positive. measures the covariance between the return of an asset and the marked illiquidity. This beta is usually negative, because an investor is willing to accept a lower return for an asset, which has higher returns in the event that the market is illiquid. measures the covariance between the illiquidity of an asset and the market return. This beta is also usually negative, because investors will be willing to accept a lower return when a asset is liquid when the market offers a low return. The dataset consists of the daily CRSP returns and volume for NYSE/AMEX stocks during 1964-1999. The four betas are estimated from the monthly data. The results show that the market beta,, is higher for illiquid stocks. is higher, and are more negative for illiquid stocks. In comparison with the CAPM, they find that the liquidity-adjusted CAPM has a higher explanatory power. Roll and Subrahmanyam (2010) study the skewness of liquidity over time. They use the end-of-day closing bid-ask spread of stocks in the CRSP database from 1993 onwards. The find that the stock bid-ask spread is increasingly rightskewed, especially in recent years. The results hold when accounting for differences in firm size, trading volume, price and exchanges. This phenomenon can be explained by information asymmetries, as cross-section analysis indicates that there is a relationship between liquidity skewness and information proxies, such as institutional holdings and analyst following. 8

Chapter 3: Model specification This chapter explains the measure used to approximate liquidity and the model used in the cross-sectional regressions of the next chapter. This paper uses the bid-ask spread as a measure for liquidity. The bid-ask spread is the difference between the bid price and the asking price. As such, it measures the transaction costs of trading an asset. A higher bid-ask spread thus means higher costs, so liquidity decreases in the bid-ask spread. The asking price and bid price data are collected on the end of each month. The bid-ask spread is then calculated. The model that will be used to test the hypothesis is based on the Capital Asset Pricing Model (CAPM) by Sharpe (1964) and Lintner (1965). It is a single factor model and can be written down as the following equation: ( ) ( ( ), where is the return of the portfolio, the risk free rate and the return of the market. measures the systematic risk. A positive (negative) beta means that the portfolio will have a higher (lower) return than the market, when the market goes up, and a lower (higher) return than the market, when the market goes down. So, according to the CAPM, expected return depends on the risk free rate, the market risk premium ( ) and the amount of systematic risk. The CAPM has some basic assumptions. All investors have a homogenous expectation of the market return and all have access to the same information. There are no taxation or transaction costs. Markets are in equilibrium and perfectly efficient. There are no arbitrage opportunities. For a long time it was regarded as an excellent model to predict asset returns. However, research by Fama and French (1993) showed that their three-factor model did a better job at predicting asset returns by adding a size factor and a book-to-market factor. The CAPM is then extended with a liquidity factor, specifically the bid-ask spread specified in the previous section. So the equation of the model becomes: ( ) ( ( ) ( ), 9

where is the market-wide liquidity, the average of the bid-ask spreads of all stocks, and the bid-ask spread of portfolio i. then measures the change in return due to market-wide liquidity and the portion of the risk attributed to the expected liquidity. So, according to the second hypothesis either or both of the liquidity factors should increase when liquidity decreases, because they are calculated using the bid-ask spread. This means that and should be positive betas. As said before, it is common to include the Fama and French (1993) factors to models trying to explain asset prices. Including these factors improves the predicting capability of the model. These factors are the small minus big (SMB) factor and the high minus low (HML) factor. The SMB factor is included to control for size; everything else equal a small company should have lower earnings on assets than a big company. The HML factor is included to control for the book-to-market equity effect; a low book-to-market means that the company is valued more than that its assets are worth in the books and vice versa. The final equation of the model then should be: ( ) ( ( ) ( ), where and are calculated by forming 6 portfolios based on size and book-to-market ratio (BE/ME). The stocks are first sorted on market value. The cutoff is at 70%, so two groups are formed: small and big. Next, the stocks are again sorted, but this time on their book-to-market ratio. The cutoffs are at 40% and 60%, resulting in three groups: low, medium and high. These groups are now paired in order to form 6 portfolios. Then the small size portfolios are subtracted from the big size portfolios for and the lowest BE/ME ratio portfolios are subtracted from the highest BE/ME portfolios for. That is, is calculated by taking the difference of the average of small portfolios (1/3*(S/L+S/M+S/H)) and the average of big portfolios (B/L+B/M+B/H). is calculated by taking the difference of the average of high book-to-market portfolios (S/H+B/H) and the average of the low book-to-market portfolios (S/L+B/L). This leads to being mostly free of the book-to-market factor with respect to returns and being mostly free of the size factor. 10

Chapter 4: Data and empirical results The first section describes the data. The second section describes the regression analyses and discusses the results. 4.1 Data The data used in the regression consists of all stocks listed on the London Stock Exchange (LSE) during the period October 1986 and December 2011. These data are obtained from Datastream. A total number of 4340 stocks were listed on the LSE during this period. However, the bid and ask price statistics are not available for all these stocks. The first month has data on 414 stocks and the last month has data on 1514 stocks regarding the bid and ask price. Some months, specifically during 2006-2007, have around 2100 stocks with bid and ask price data. The statistics obtained from Datastream are the monthly return index, bid price, ask price and market value. Because the return index starts for each stock at 100 in the first month listed in the dataset, these indexes cannot be readily compared with each other. For example, in a random month the return index of one stock could be 350 (indicating that the return in that month is 350 times as high in comparison to the return in the month that the stock first appeared) and of another stock 3000. To obtain the monthly return, these return indexes are recalculated to show a percentage, that is, the return index of a stock of, say, March 1990 is subtracted from the return index of April 1990 and then divided by the return index of March 1990. The market return is obtained by taking the weighted average of these returns of all stocks in a month. The bid-ask spread is calculated by subtracting the bid price from the asking price. The risk free rate is obtained from Fama trough CRSP Monthly Treasury Fama Risk Free Rates. The Fama and French factors, and, are downloaded from Kenneth French s website. Portfolios are needed for the regression itself, because using the returns of the individual stocks creates a lot of noise in the regression. Two different sets of portfolios will be created, one sorted on size (market value) and the other sorted on liquidity (bid-ask spread). The stocks are divided in 10 equally weighted 11

portfolios. In effect, the regressions on the three different models will each be run twice, once for the size-sorted portfolios and once for portfolios sorted on liquidity. The average number of stocks in each portfolio amounts to 148 stocks, while the lowest number of stocks in a portfolio is 42 stocks and the highest number of stocks is 218. Table 1 gives an overview of the variables of the size-sorted portfolios and Table 2 gives an overview of the variables of the liquidity-sorted portfolios. Table 1 The mean and standard deviation for the return and bid-ask spread of portfolios sorted on size for the months 10/1986 31/12/2011 Portfolio mean return st.dev. return mean spread st.dev. spread 1-0.015 0.063 939.013 2648.158 2-0.003 0.059 118.011 194.280 3 0.003 0.059 104.210 191.468 4 0.005 0.059 32.867 104.975 5 0.011 0.060 66.581 151.021 6 0.015 0.061 16.802 18.664 7 0.018 0.071 14.221 15.153 8 0.017 0.060 28.628 47.769 9 0.017 0.059 6.539 4.847 10 0.015 0.052 9.666 45.326 12

Table 2 The mean and standard deviation for the return and bid-ask spread of portfolios sorted on liquidity for the months 10/1986 31/12/2011 Portfolio mean return st.dev. return mean spread st.dev. spread 1 0.004 0.066 1.009 0.573 2 0.008 0.062 1.608 0.599 3 0.007 0.060 2.186 0.845 4 0.009 0.059 2.699 0.817 5 0.011 0.065 3.104 0.910 6 0.009 0.055 3.941 1.479 7 0.007 0.053 4.665 1.094 8 0.011 0.051 6.048 1.745 9 0.011 0.053 9.546 4.013 10 0.007 0.070 1259.191 2433.697 The mean bid-ask spread of size-based portfolios is in accordance with economic theory, that is, stocks in the smaller size portfolios are more difficult to trade and therefore have a higher bid-ask spread. The mean return, however, is lower for the smaller size stocks. This is in contrast with the economic intuition that the return is higher for the smaller size stocks. Looking at the standard deviation of the return it is possible that this is caused by the relatively short span of 1986-2011. Portfolios sorted on liquidity show, naturally, an increase in the bid-ask spread. The returns of these portfolios do not indicate that the return is dependent on the bid-ask spread. 13

4.2 Empirical results This section tests the three models: (1) CAPM, (2) CAPM with a liquidity factor and (3) CAPM with a liquidity factor and the Fama-French factors. The size and liquidity sorted portfolio returns are regressed on each model. For the final model, second stage regressions on both the portfolios will be run. That is, the average return per portfolio will be regressed on the five betas found in the first regression. The models, for which the Ordinary Least Squares (OLS) time-series regressions will be run, are presented in Table 3. Table 3 OLS time-series models 1 ( ) 2 ( ) 3 ( ) 4.2.1 CAPM The dependent variable in the first test is the return of each size-based portfolio and in the second test the return of each liquidity-based portfolio. The independent variable is the same in both tests: the market premium. The results of these regressions are displayed in tables 4 and 5 on the next page. In both the size-based and the liquidity-based portfolios the market premium is significant and explains a minimum of 67,4% and maximum of 86,5% of the variance of the excess return of the size-based portfolios, and 69,0% and 88,0% for the liquidity-based portfolios. However, the constants are significant for all portfolios but two portfolios, indicating that the constant also captures some of the variance. The smallest and highest portfolios (1 and 10) have a lower fit of the model (R 2 ) than the portfolios in the middle. Outliers in the dataset, which distort the data, could cause this. 14

Table 4 Regression of excess return of size-based portfolios on the market premium. * indicates that the coefficient is significant at the 0.05 level Table 5 Regression of excess return of liquidity-based portfolios on the market premium. * indicates that the coefficient is significant at the 0.05 level Portfolio R 2 Portfolio R 2 (size) (t-value) (t-value) (liquidity) (t-value) (t-value) 1-0.015 1.187 0.723 1 0.007 1.308 0.747 (-6.418)* (28.006)* (2.895)* (29.777)* 2-1.262 0.843 2 0.011 1.295 0.791 (-0.899) (40.165)* (5.059)* (33.792)* 3 0.005 1.297 0.865 3 0.009 1.283 0.822 (3.056)* (43.836)* (4.583)* (37.322)* 4 0.006 1.249 0.822 4 0.009 1.251 0.840 (3.147)* (37.294)* (5.446)* (39.752)* 5 0.014 1.312 0.863 5 0.012 1.254 0.690 (8.477)* (43.566)* (4.552)* (25.867)* 6 0.019 1.334 0.849 6 0.009 1.216 0.866 (10.661)* (41.098)* (5.777)* (44.183)* 7 0.022 1.341 0.674 7 0.003 1.094 0.795 (7.340)* (24.963)* (1.676) (34.157)* 8 0.019 1.273 0.817 8 0.009 1.172 0.894 (9.790)* (36.674)* (7.126)* (50.409)* 9 0.017 1.210 0.762 9 0.010 1.185 0.880 (8.042)* (31.012)* (7.344)* (46.975)* 10 0.008 0.993 0.669 10 0.013 1.408 0.748 (3.805)* (24.691)* (4.865)* (29.863)* 15

4.2.2 CAPM plus liquidity factors The liquidity factor, the bid-ask spread, will be added to the CAPM model. Before the regressions are run, it is necessary to check for collinearity. This means that two or more variables could explain the same variance, which causes the coefficients estimates of these variables to change significantly when data is added or removed. In order to test for collinearity, the correlation between the market beta and the bid-ask spread of every portfolio is calculated in Table 6 for the size-based portfolios and in Table 7 for the liquidity-based portfolios. Table 6 Correlation between market premium, market-wide liquidity and portfolio liquidity of size-based portfolios. The significance is displayed under the correlation (a correlation is significant at the 0.05 level) Table 7 Correlation between market premium, market-wide liquidity and portfolio liquidity of liquidity-based portfolios. The significance is displayed under the correlation (a correlation is significant at the 0.05 level) 1-0.313-0.278 0.981-0.075-0.008 0.204 0.892 0.046-0.039 0.438 0.512-0.083 0.029 0.157 0.629-0.108-0.058 0.066 0.328-0.063-0.084 0.284 0.155-0.048-0.124 0.413 0.035-0.105-0.077 0.075 0.194-0.123-0.092 0.037 0.12-0.026 0.021 0.663 0.72 1-0.313-0.11 0.157 0.063 0.008-0.261 0.237-0.271 0.173 0.003-0.205 0.196-0.305 0.146 0.013-0.095 0.052 0.107 0.374-0.105-0.046 0.075 0.44-0.159-0.015 0.007 0.805-0.165 0.027 0.005 0.647-0.303 0.944 16

The market premium and the market-wide liquidity risk are significantly correlated. Also, the correlation between the market premium and expected liquidity risk is more significant for liquidity-based portfolios, where the bid-ask spread of 8 out of 10 portfolios has a significant correlation with the market premium in comparison to only two size-based portfolios. Table 8 contains the results of the regressions for the model on the size-based portfolios and Table 9 contains the results on the liquidity-based portfolios. Table 8 Regression of excess return of size-based portfolios on the market premium and liquidity factor. * indicates that the coefficient is significant at the 0.05 level Portfolio R 2 (size) (t-value) (t-value) (t-value) (t-value) 1-0.018 1.244 0.733 (-5.976)* (27.147)* (1.310) (-0.727) 2-0.004 1.305 0.850 (-1.903) (39.040)* (3.694)* (-0.173) 3 0.003 1.338 0.869 (1.503) (42.445)* (4.137)* (-0.047) 4 0.004 1.266 0.829 (2.028)* (35.983)* (3.063)* (-0.210) 5 0.012 1.332 0.864 (6.823)* (40.888)* (3.024)* (-0.697) 6 0.017 1.360 0.848 (7.347)* (38.551)* (2.785)* (0.298) 7 0.022 1.354 0.665 (5.506)* (22.733)* (0.859) (-0.473) 8 0.014 1.281 0.827 (6.873)* (35.520)* (1.928) (2.692)* 9 0.010 1.230 0.765 (3.010)* (29.253)* (1.541) (2.727)* 10 0.008 0.983 0.664 (3.546)* (22.475)* (-0.159) (0.360) 17

The coefficient of expected liquidity risk for the size-based portfolios is for all but one portfolio () and is only significant 2 out of 10 times. Thus even when the factor is significant, its coefficient is or. Market-wide liquidity performs a little better, being significant 5 times, but the beta is always. An explanation for these results on size-based portfolios can be found in Table 1. The bid-ask spread does vary for every portfolio, but it does not a show a consistent decline. In some portfolios the bid-ask spread is higher than the previous portfolio. The model explains 66,4% till 86,9% of the variance, with the standard market beta contributing most. The standard market beta is significant for all portfolios. Still, the highly significant constants show that the model can be improved by adding more variables. Table 9 Regression of excess return of liquidity-based portfolios on the market premium and liquidity factors. * indicates that the coefficient is significant at the 0.05 level Portfolio R 2 (liquidity) (t-value) (t-value) (t-value) (t-value) 1-0.003 1.361 0.007 0.757 (-0.715) (29.268)* (3.373)* (2.124)* 2-1.341 0.006 0.813 (-0.254) (34.088)* (3.535)* (2.026)* 3 1.325 0.003 0.828 (0.198) (35.408) (3.283)* (1.444) 4-0.004 1.282 0.005 0.839 (-0.806) (37.175)* (1.865) (2.597)* 5 1.287 0.003 0.681 (0.034) (23.282)* (1.438) (1.328) 6 1.226 0.868 (0.569) (41.800) (2.170)* (1.618) 7-0.10 1.126 0.003 0.807 (-1.509) (33.177)* (1.769) (2.031)* 8-0.005 1.197 0.898 (-1.171) (47.781)* (1.769) (3.658) 9 0.004 1.200 0.878 (1.208) (43.039)* (0.921) (2.210)* 10 0.012 1.431 0.743 (4.156)* (27.540)* (-0.434) (0.585) 18

The results of the liquidity-based portfolios show that the coefficient for the bidask spread is significant for 5 portfolios and that these significant coefficients are higher than zero. The market-wide liquidity risk is for every portfolio. In comparison to the previous CAPM regressions and the CAPM plus liquidity factor regression on size-based portfolios, the constant is insignificant for every portfolio except the last. This means that the CAPM adjusted with a liquidity factor does indeed a better job at explaining the variance of excess returns of liquidity-based portfolios. The fit of the model ranges from 74,3% till 89,8%. 4.2.3 CAPM plus liquidity and Fama-French factors Finally, for the third model the Fama and French (1993) factors, SMB and HML, are added to the model. As before, tables 10 and 11 check for collinearity between the factors. The correlations between the market premium, marketwide liquidity and expected liquidity have remained the same, so they will not be displayed here. For reference, see tables 6 and 7. The correlation between the SMB factor and the market premium is relatively high and it is significant. This could lead to these coefficients not being significant. The correlations between the SMB factor and the bid-ask spread are for both the size-based and the liquidity-based portfolios insignificant. Several correlations between the HML factor and bid-ask spread are significant, yet not high enough to have an impact on the regression. Market-wide liquidity does not seem to be correlated with either of the Fama-French factors. 19

Table 10 Correlation between Fama-French factors and previously used variables of size-based portfolios. The significance is displayed under the correlation (a correlation is significant at the 0.05 level) Table 11 Correlation between Fama-French factors and previously used variables of liquidity-based portfolios. The significance is displayed under the correlation (a correlation is significant at the 0.05 level) 0.344 0.019 0 0.744-0.034 0.065 0.564 0.272 1-0.178-0.017 0.046 0.768 0.44-0.021-0.007 0.716 0.91 0.011 0.099 0.858 0.094-0.055 0.071 0.35 0.23 - -0.124 0.975 0.035-0.027 0.132 0.646 0.024 0.098 0.059 0.098 0.317-0.008 0.077 0.896 0.189-0.013 0.159 0.822 0.007 0.045-0.079 0.447 0.181 0.344 0.019 0 0.744-0.034 0.065 0.564 0.272 1-0.178-0.068 0.045 0.247 0.446-0.059 0.04 0.315 0.495-0.038 0.038 0.515 0.517-0.029 0.078 0.628 0.186-0.023 0.05 0.701 0.395 0.126 0.985 0.032 0.089 0.121 0.13 0.04 0.075 0.083 0.206 0.157 0.028 0.115 0.63 0.05-0.023 0.048 0.696 0.414 20

The results of the regression of the complete model are shown in tables 12 and 13, for respectively, the size-based portfolios and the liquidity-based portfolios. Table 12 Regression of excess return of the size-based portfolios on the market premium, liquidity factors, SMB and HML factor. * indicates that the coefficient is significant at the 0.05 level Portfolio (Size) (t-value) (t-value) (t-value) (t-value) (t-value) (t-value) R 2 1-0.017 1.270 0.740 (-5.601)* (26.167)* (1.229) (-0.630) (1.229) (1.433) 2-0.004 1.312 0.851 (-1.774) (36.630)* (3.661)* (-0.168) (-0.645) (0.783) 3 1.302 0.874 (1.001) (39.233)* (3.774)* (-0.265) (2.808)* (2.233)* 4 0.003 1.225 0.836 (1.390) (33.120)* (2.687)* (-0.310) (2.835)* (2.421)* 5 0.012 1.308 0.866 (6.338)* (37.696)* (2.839)* (-0.789) (2.069)* (-0.009) 6 0.016 1.298 0.860 (6.814)* (35.576)* (2.336)* (0.070) (4.769)* (1.529) 7 0.021 1.273 0.003 0.679 (5.315)* (20.215)* (0.451) (-1.001) (3.483)* (0.718) 8 0.013 1.215 0.841 (6.232)* (32.669)* (1.364) (2.352)* (4.667)* (2.703)* 9 0.009 1.158 0.003 0.781 (2.882)* (26.443)* (0.964) (2.138)* (4.212)* (2.524)* 10 0.008 0.953 0.668 (3.107)* (20.432)* (-0.380) (0.363) (1.647) (1.198) As is clear in Table 12, the betas for the liquidity factors are again for almost all portfolios. The beta for market-wide liquidity risk is significant for 5 portfolios. It does not seem that the bid-ask spread can explain the variance in the excess return well. Whenever it is significant, the coefficient is most of the time. The beta of the SMB factor ranges from to 0.003 and is significant for 7 portfolios. The HML factor is for 8 portfolios, for the other 2, and only significant in 4 portfolios. This model explains 66,8% till 87,4% of the 21

variance in the excess returns of the size-based portfolios, again with the standard market beta of CAPM as major contributing factor. However, the constant is also significant for 8 out of 10 portfolios, indicating that there is still variance left that can be explained by other variables. Table 13 Regression of excess return of the liquidity-based portfolios on the market premium, liquidity factors, SMB and HML factor. * indicates that the coefficient is significant at the 0.05 level Portfolio (Spread) (t-value) (t-value) (t-value) (t-value) (t-value) (t-value) R 2 1-0.004 1.337 0.007 0.763 (-0.854) (27.088)* (3.123)* (2.086)* (1.068) (2.426)* 2-1.312 0.005 0.821 (-0.300) (31.732)* (3.244)* (1.897) (1.507) (3.381)* 3 1.276 0.841 (0.161) (32.963)* (2.870)* (1.160) (2.908)* (4.267)* 4-0.003 1.251 0.004 0.853 (-0.602) (35.224)* (1.509) (2.241)* (1.591) (5.012)* 5 1.233 0.003 0.689 (0.130) (20.921)* (1.142) (1.029) (2.271)* (1.814) 6 0.003 1.190 0.876 (0.767) (38.795) (1.743) (1.098) (2.817)* (3.446)* 7-0.007 1.083 0.814 (-1.081) (29.962)* (1.353) (1.368) (3.045)* (1.630) 8-0.003 1.166 0.910 (-0.856) (43.611) (1.378) (3.063)* (2.849)* (1.690) 9 0.003 1.157-0.892 (0.946) (40.740)* (0.751) (2.185)* (4.782)* (-2.559)* 10 0.011 1.403-0.003 0.767 (3.878)* (26.404)* (-0.046) (0.215) (2.297)* (-4.304)* 22

Table 13 shows that the expected liquidity risk beta varies from till 0.007 and is significant for 4 portfolios. The market-wide liquidity risk factor does not perform any better, being significant only 3 times and constantly. The Fama-French factors add explanatory power to this model. Both the SMB and the HML betas are significant in 7 portfolios and are mostly higher than zero. The constant factor is only significant for the last portfolio, indicating that this model explains the variance in the excess return well. As usual, the market beta is significant for all portfolios. The fit of the model ranges from 76,3% till 91,0%. 4.2.4 Second stage regressions For the cross-section regression the betas found in the previous subparagraph will now be regressed on the average return of the portfolios using the following model: ( ), where the lambdas take the values of the betas found in the size-based and liquidity-based portfolios return regressions on the market premium, liquidity and Fama-French factors. Table 14 Regression of excess return of the size-based and liquidity-based portfolios on the betas of the market premium, liquidity factors, SMB and HML factor. * indicates that the coefficient is significant at the 0.05 level (t-value) (t-value) (t-value) (t-value) (t-value) (t-value) R 2 Size - -0.024-93.196 5.480 6.530-8.311 0.970 (-0.055) (-1.330) (-0.460) (1.266) (3.314)* (-1.973) Liquidity -0.024-0.005-196.757 0.285 1.859 0.856 0.425 (-1.580) (-0.401) (-0.797 (0.277) (0.556) (0.690) Table 14 presents the results. The fit of the model for the size-based portfolios is quite high, 97,0%, but only the beta of the SMB factor is significant. The liquiditybased portfolio betas perform even worse, explaining only 42,5% with no single beta significant. 23

Chapter 5: Conclusions The purpose of this paper was to investigate whether liquidity is priced and whether the return increases when liquidity decreases. This was done by regressing the excess returns of size-based and liquidity-based portfolios using the CAPM, the CAPM extended with the bid-ask spread and finally the CAPM extended with the market-wide liquidity risk, the expected liquidity risk and the Fama-French factors, SMB and HML. Second stage regressions have been run on this final model, for both the size-based and liquidity-based portfolios. While the CAPM does explain a lot of the variance in the excess return, the liquidity factors do add value to the model for liquidity-based portfolios. Adding the SMB and HML factors to the model does not negate the effect of the liquidity on the return and increases the explanatory power of the model. Results of the second stage regressions are positive for the size-based portfolios, but are not conclusive for the liquidity-based portfolios. This paper thus finds evidence in support of the hypothesis that there is a relationship between liquidity and asset prices. If the stocks are sorted on market value however, then the evidence is mixed. For some portfolios the liquidity betas are significant, but they take a low value, often zero, for all sizebased portfolios. With respect to the second hypothesis, this study finds evidence that the return increases when liquidity decreases, as evident in the positive coefficients of the liquidity factor in the second and third model for liquidity-based portfolios. A positive coefficient for the bid-ask spread indicates that an increase in the bidask spread, which decreases liquidity, increases the return. However, in comparison with the standard market beta of the CAPM, neither the liquidity factors, SMB nor HML have a high coefficient, which could be a subject for further research. The Fama-French factors could be extended with a momentum factor, further increasing the explanatory power of the model. Furthermore, stocks were admitted to the dataset when their data was available, possibly leading to a distortion of the bid-ask spread data due to beginning stocks having a relative high bid-ask spread as compared to some years later. 24

Chapter 6: References Acharya, V.V. and Pedersen, L.H., 2005. Asset pricing with liquidity risk. Journal of Financial Economics, 77(2), pp.375-410. Amihud, Y. and Mendelson, H., 1986. Asset pricing and the bid-ask spread. Journal of Financial Economics, 17(2), pp.223-249. Amihud, Y., 2002. Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets, 5(1), pp.31-56. Amihud, Y., Mendelson, H. and Pedersen, L.H., (2005). Liquidity and Asset Prices. Foundation and Trends in Finance, 1(4), pp.269-364. Campbell, J.Y., S.J. Grossman and Wang, J., (1993). Trading volume and serial correlation in stock returns. Quarterly Journal of Economics, 108(4), pp.905-939. Datar, V.T., Naik, N.Y. and Radcliffe, R., 1998. Liquidity and stock returns: An alternative test. Journal of Financial Markets, 1(2), pp.203-219. Eleswarapu, V.R., (1997). Cost of transacting and expected returns in the Nasdaq market. Journal of Finance, 52(5), pp.2113-2127. Fama, E.F. and French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), pp.3-56. Fama, E.F. and MacBeth, J.D., 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy, 81(3), pp.607-636. Kyle, A.S., (1985). Continuous auctions and insider trading. Econometrica, 53(6), pp.1315-1335. 25

Lintner, J., (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), pp.13-37. Pastor, L. and Stambaugh, R.F., 2003. Liquidity risk and expected stock returns. Journal of Political Economy, 111(3), pp.642-685. Petersen, M.A. and Fialkowski, D., 1994. Posted versus effective spreads. Journal of Financial Economics, 35(3), pp.269-292. Roll, R. and Subrahmanyam, A., (2010). Liquidity skewness. Journal of Banking and Finance, 34(10), pp.2562-2571. Sharpe, W., 1964. Capital asset prices: A theory of capital market equilibrium under conditions of risk. Journal of Finance, 19(3), pp.425-442. 26