LIQUIDITY RISK AND ASSET PRICING

Transcription

1 LIQUIDITY RISK AND ASSET PRICING DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Kuan-Hui Lee, M.A. * * * * * The Ohio State University 2006 Dissertation Committee: Approved by G. Andrew Karolyi, Adviser Kewei Hou René M. Stulz Ingrid M. Werner Adviser Graduate Program in Business Administration

2 ABSTRACT In this dissertation, I investigate the effect of liquidity ris on asset pricing. In the first essay, I test the liquidity-adjusted capital asset pricing model (LCAPM) of Acharya and Pedersen (2005) for in the US maret using various liquidity proxies. In a time-series test with a one-factor (maret model), three-factor (excess maret return, SMB, and HML) and four-factor model (excess maret return, SMB, HML and MOM) as well as in a Fama-MacBeth regression, I find that test results vary according to the liquidity measures used, to the test methodology, to the test assets, and to the weighting scheme. Tests based on the liquidity measure of Amihud (2002), Pastor and Stambaugh (2003) and zero-return proportion show some evidence that liquidity riss are priced, but in most cases, I could not find evidence that supports the LCAPM. The second essay specifies and tests an equilibrium asset pricing model with liquidity ris at the global level. The analysis encompasses 25,000 individual stocs from 48 developed and emerging countries around the world from 1988 to Though I cannot find evidence that the LCAPM holds in international financial marets, cross-sectional as well as time-series tests show that liquidity riss arising from the covariances of individual stocs return and liquidity with local and global maret factors are priced. Furthermore, I show that the US maret is an important driving force of world-maret liquidity ris. I interpret our evidence as consistent with an intertemporal capital asset pricing model (Merton (1973)) in which ii

3 stochastic shocs to global liquidity serve as a priced state variable. The third essay investigates how and why liquidity is transmitted across stocs. In a vector autoregressive framewor, I uncover a dynamic interaction of liquidity across size portfolios in that past changes of liquidity of large stocs are positively correlated with current changes of liquidity of small stocs. Furthermore, liquidity spillovers are not restricted among fundamentally-related stocs and are independent of the dynamics in return and volatility spillovers. This finding implies that the process of liquidity generation is independent of information flows and that portfolio diversification strategies should consider different patterns in return, volatility and liquidity spillovers. iii

4 to my parents iv

5 ACKNOWLEDGMENTS I don t now how to than enough for having such an exceptional doctoral committee. I wish to than Kewei Hou, G. Andrew Karolyi, René Stulz, and Ingrid M. Werner for their continual support and encouragement. I am most grateful to my advisor, G. Andrew Karolyi, for his tremendous support, guidance and encouragement. Throughout my doctoral wor he encouraged me to develop my analytical thining and research sills. His assistance guided me not only to a better researcher, but also to a better instructor. I wish to express my deep appreciation to René Stulz whose consultation, insightful comments and encouragement were continual stimulation to my research. I am deeply indebted to Ingrid M. Werner whose help, guidance, patience and encouragement tremendously helped me in all my doctoral training process. I would lie to than Kewei Hou for his insightful comments, efforts and guidance. I also than Karl Diether, Bing Han and Jean Helwege for their encouragement and friendship and than Bong-Chan Kho for being an excellent role model even from my school life in Seoul many years ago. I than my brother Tae-Hwy Lee, who is a time-series econometrician, for guiding me in pursuing academic career. I want to share my happiness and thanfulness with my friend, Jungwu Rhie, who passed away by tragic accident last year and may rest in peace in heaven. v

6 VITA November 9, Born - Taejon, Korea B.B.A. Business Administration, Seoul National University MBA, International Finance, Seoul National University M.S. Statistics, University of North Carolina, Chapel Hill 2001-present...Graduate Teaching and Research Associate, The Ohio State University. FIELDS OF STUDY Major Field: Business Administration Studies in: International Finance Empirical Asset Pricing Maret Microstructure vi

7 TABLE OF CONTENTS Page Abstract Dedication Acnowledgments Vita List of Tables List of Figures ii iv v vi x xii Chapters: 1. Introduction Testing the Liquidity-Adjusted Capital Asset Pricing Model using Different Measures of Liquidity Introduction Liquidity-Adjusted Capital Asset Pricing Model Data and Iliquidity Measures Methodology Fama-MacBeth Regression Time-Series Tests Empirical Results Time-Series Tests Fama-MacBeth Regression Conclusion vii

8 3. The World Price of Liquidity Ris Introduction Related literature Liquidity-adjusted capital asset pricing model Data and liquidity measure Sample screening Summary statistics Is zero-return proportion a good proxy for illiquidity? Methodology Innovations of return and illiquidity Estimating predicted betas Empirical results Local and global maret betas Fama-MacBeth test results for local liquidity riss Fama-MacBeth test results for global liquidity riss Fama-MacBeth test results for local and world maret liquidity riss Do US marets drive world maret liquidity riss? Time series tests Subperiod analysis Robustness tests Different innovation Two-way sorts Conclusion Liquidity Spillovers Introduction Literature Review Theories Empirical Studies Hypotheses Data and Liquidity Measure Liquidity Spillovers Vector Autoregression VAR Estimation Results Are Liquidity Spillovers Related to Correlated Fundamentals or Information Flow? Intra-Industry Liquidity Spillovers Intra- vs Inter-Industry Liquidity Spillovers viii

9 4.6.3 Does Information Flow Contribute in Liquidity Spillovers? Does Style Investing Contribute to Liquidity Spillovers? Robustness Checs Alternative Lags Value-Weighted Average Discussion Conclusion Conclusion Bibliography Appendices: A. Tables B. Figures ix

10 LIST OF TABLES Table Page A.1 Summary Statistics A.2 Betas by Size Group A.3 Intercepts from the Maret Model Regression A.4 Intercepts from the Three Factor Model Regression A.5 Intercepts from the Four Factor Model Regression A.6 Fama-French Regression of Size Portfolios with Value-Weighted Maret Illiquidity A.7 Fama-French Regression of Size Portfolios with Equal-Weighted Maret Illiquidity A.8 Fama-French Regression of Illiquidity Portfolios with Value-Weighted Maret Illiquidity A.9 Fama-French Regression of Illiquidity Portfolios with Equal-Weighted Maret Illiquidity A.10 Summary Statistics (Liquidity and Return in World Financial Marets) 145 A.11 Correlation of Liquidity Measures by Size in US Maret A.12 Coefficients from the estimation of predicted betas A.13 Mean of Portfolio formed based on Predicted Betas x

11 A.14 Fama-French Regression by Predicted Betas (Local Maret) A.15 Fama-French Regression by Predicted Betas (World Maret) A.16 Fama-French Regression by Predicted Betas (Local and World Maret) 152 A.17 Fama-French Regression by Predicted Betas with respect to US maret and Non-US World Marets A.18 Time-Series Tests A.19 Fama-French Regression by Global Predicted Betas (Subperiod) A.20 Fama-MacBeth regression with 25 portfolios for US maret A.21 Fama-MacBeth regression with post-raning betas (2-way sorts) A.22 Descriptive Statistics A.23 VAR Estimation Results A.24 Zero-Bloc Exclusion Tests A.25 Summary Statistics for Industry-Size Portfolios A.26 Within-Industry Liquidity Spillovers A.27 Intra- vs Inter-Industry Liquidity and Volatility Spillovers A.28 Spillovers in Size-B/M Style A.29 Style vs Industry xi

12 LIST OF FIGURES Figure Page B.1 Maret Illiquidity and Return B.2 Intercepts from Maret Model Regression (Liquidity Net Beta) B.3 Intercepts from Maret Model Regression (Net Beta) B.4 Intercepts from Three Factor Model Regression (Liquidity Net Beta) 184 B.5 Intercepts from Three Factor Model Regression (Net Beta) B.6 Intercept from four factor model regression (liquidity net beta) B.7 Intercept from four factor model regression (net beta) B.8 Correlation of Liquidity Measures in US Maret B.9 Intercepts from Maret Model Regression B.10 Daily Quoted Spread xii

13 CHAPTER 1 INTRODUCTION In classical asset pricing models, perfect financial marets without frictions, especially no trading costs, are assumed and thus the diverse features of liquidity are ignored. 1 However, considering liquidity in investment is important since liquidity affects portfolio investment performance (Holthausen, Leftwich, and Mayers (1991), Keim (2004), Lesmond, Schill, and Zhou (2004), Korajczy and Sada (2004)) and it has a significant implication for portfolio diversification strategies (Domowitz and Wang (2002), Harford and Kaul (2005)). In addition, it has been shown that liquidity affects the cross-sectional differences of asset returns as a characteristic (Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), Amihud (2002)) or as a ris factor (Pastor and Stambaugh (2003), Sada (2004), Acharya and Pedersen (2005)). This dissertation consists of three essays devoted to investigating the effect of liquidity ris on asset pricing. In the first essay, I test the liquidity-adjusted capital asset pricing model (LCAPM) of Acharya and Pedersen (2005) for in 1 Liquidity is a concept used to capture the various trading costs and it has many, and potentially overlapping dimensions arising from adverse selection (Bagehot (1971), Copeland and Galai (1983), Kyle (1985), Glosten and Milgrom (1985)), and needs for immediate trading (Demsetz (1968), Tinic (1972), Stoll (1978), Ho and Stoll (1980), Cohen, Maier, Schwartz, and Whitcomb (1981), Ho and Stoll (1981), Ho and Stoll (1983), Grossman and Miller (1988)). Broadly, it is used to describe the ease of trading a large amount of shares in a given amount of time without a significant impact on prices. 1

14 the US maret using various liquidity proxies. The LCAPM is attractive in that it covers various channels through which liquidity may affect asset prices in one model while incorporating traditional maret ris as well. Liquidity ris that arises from the covariance of individual stoc return with maret liquidity, which is investigated by Pastor and Stambaugh (2003), is present in the LCAPM as one source of ris through which liquidity affects asset prices. Commonality in liquidity, which denotes the comovement of individual stoc liquidity with maret liquidity (Chordia, Roll, and Subrahmanyam (2000), Hasbrouc and Seppi (2001), Huberman and Hala (2001)), is also captured in the LCAPM. In addition, the LCAPM proposed a new source of liquidity ris, which arises from the covariance of individual stoc liquidity with maret returns. While the LCAPM covers liquidity as a ris factor, it also encompasses liquidity level in the model. Hence, the test of the LCAPM gives us an opportunity to investigate the effect of liquidity on asset prices through various channels. In a time-series test with a one-factor (maret model), three-factor (excess maret return, SMB, and HML) and four-factor model (excess maret return, SMB, HML and MOM) as well as in a Fama-MacBeth regression, I find that test results vary according to the liquidity measures used, to the test methodology, to the test assets, and to the weighting scheme. Tests based on the liquidity measure of Amihud (2002), Pastor and Stambaugh (2003) and zero-return proportion show some evidence that liquidity riss are priced, but in most cases, I could not find evidence that supports the LCAPM. The second essay extends the study of liquidity ris and asset pricing to international financial marets by testing the LCAPM at the global level. The analysis encompasses 25,000 individual stocs from 48 developed and emerging countries around 2

15 the world from 1988 to Though I cannot find evidence that the LCAPM holds in international financial marets, cross-sectional as well as time-series tests show that liquidity riss arising from the covariances of individual stocs returns and liquidity with local and global maret factors are priced. Furthermore, I show that the US maret is an important driving force of world-maret liquidity ris. I interpret our evidence as consistent with an intertemporal capital asset pricing model (Merton (1973)) in which stochastic shocs to global liquidity serve as a priced state variable. The third essay investigates how and why liquidity is transmitted across stocs. In a vector autoregressive framewor, I uncover a dynamic interaction of liquidity across size portfolios in that past changes of liquidity of large stocs are positively correlated with current changes of liquidity of small stocs. Furthermore, liquidity spillovers are not restricted among fundamentally-related stocs and are independent of the dynamics in return and volatility spillovers. This finding implies that the process of liquidity generation is independent of information flows and that portfolio diversification strategies should consider different patterns in return, volatility and liquidity spillovers. 3

16 CHAPTER 2 TESTING THE LIQUIDITY-ADJUSTED CAPITAL ASSET PRICING MODEL USING DIFFERENT MEASURES OF LIQUIDITY 2.1 Introduction Trading activity incurs trading costs, which are explicit (e.g. broerage commission) and implicit (e.g. price impact, price of immediacy). While prior studies have focused on the impact of liquidity level on asset prices (Amihud and Mendelson (1986), Brennan and Subrahmanyam (1996), Amihud (2002)), recently have researchers begun to investigate liquidity as an undiversifiable source of ris (Pastor and Stambaugh (2003), Acharya and Pedersen (2005)). Acharya and Pedersen (2005) propose a theoretical model, the liquidity-adjusted capital asset pricing model (the LCAPM, henceforth), that encompasses liquidity as a stoc characteristic as well as a source of various undiversifiable riss. However, they tested the model using a specific proxy and a particular test methodology. In this paper, I test the LCAPM for in the US maret and investigate the robustness of their conclusion using various liquidity proxies and test methodologies. While explicit trading costs are easy to measure, this is not so for implicit trading costs. For example, it is hard to measure price impact cost, which is defined as the 4

17 difference in price when the trading occurs and that when the trading does not occur, since it requires a benchmar price which could have been determined in the absence of trading. Liquidity (or illiquidity) is a concept that captures these trading costs. Previous studies in the asset pricing field have devoted a lot of effort to suggest valid measures of such trading costs. Liquidity proxies based on high frequency data have received a lot of attention as desirable measures (Amihud and Mendelson (1986), Huang and Stoll (1997), Chordia, Sarar, and Subrahmanyam (2005), among others). However, high frequency data is available only for a relatively short period of time as data from the Institute for the Study and Securities Marets (ISSM) starts in Hence, many researchers have suggested proxies of liquidity based on daily return and trading volume since they give longer time-series of liquidity. Roll (1984), for example, suggested a proxy of spread based on serial correlation of daily returns. Turnover, which is defined as daily share trading volume divided by the number of total shares outstanding, has also been a popular measure of liquidity. The theoretical motivation for using turnover as a liquidity proxy goes bac to Demsetz (1968) and Glosten and Milgrom (1985). Demsetz (1968) shows that the price of immediacy would be smaller for stocs with high trading frequency since frequent trading reduces the cost of inventory controlling. On the other hand, Glosten and Milgrom (1985) shows that stocs with high trading volume would have lower level of information asymmetry to the extent that information is revealed by prices. Amihud (2002) proposed a simple and intuitive liquidity measure, which is defined as the absolute daily return divided by daily trading volume. Pastor and Stambaugh (2003) proposed a liquidity measure based on return reversal. More recently, Lesmond, Ogden, and 5

18 Trzcina (1999) proposed an liquidity measure based solely on daily returns relying on the idea that informed traders would not trade on a day when the stoc is highly illiquid. 2 While these measures have many benefits in that they provide relatively long timeseries of liquidity for researchers and more importantly, in that they are simple, there have been arguments questioning the reliability of these liquidity measures (Hasbrouc (2005), Goyeno, Holden, Lundblad, and Trzcina (2005)). Given the limitations of various liquidity measures, I construct each of these measures using daily returns and trading volume data from CRSP for 1962 to Acharya and Pedersen (2005) used the liquidity proxy of Amihud (2002) and found evidence validating the model in the US maret for This paper examines whether this empirical result is unique to the specific measure used. For comprehensive tests of the model, we employ two different test methodologies of Fama-MacBeth cross-sectional regression and time-series test. The LCAPM is attractive in that it covers various channels through which liquidity may affect asset prices in one model while incorporating traditional maret ris as well. Liquidity ris that arises from the covariance of individual stoc return with maret liquidity, which is investigated by Pastor and Stambaugh (2003), is present in the LCAPM as one source of ris through which liquidity affects asset prices. Commonality in liquidity, which denotes the comovement of individual stoc liquidity with maret liquidity (Chordia, Roll, and Subrahmanyam (2000), Hasbrouc and Seppi (2001), Huberman and Hala (2001)), is also captured in the LCAPM. In addition, the LCAPM proposed a new source of liquidity ris, which arises from the 2 All of these measures will be introduced in detail in section

19 covariance of individual stoc liquidity with maret returns. While the LCAPM covers liquidity as a ris factor, it also encompasses liquidity level in the model. Hence, the test of the LCAPM gives us an opportunity to investigate the effect of liquidity on asset prices through various channels. In time-series tests with one-factor (maret model), three-factor (excess maret return, SMB, and HML) and four-factor models (excess maret return, SMB, HML and MOM) as well as in Fama-MacBeth cross-sectional regression tests, we find that the results are sensitive to the liquidity measures, to the test assets used, to the weighting scheme and to the test methodologies. Tests based on liquidity measure of Amihud (2002), Pastor and Stambaugh (2003) and zero-return proportion suggested that liquidity riss are priced, but in most cases, we could not find evidence supporting the LCAPM. Given the findings in this paper, an important question may arise. Why some of the measures show supporting evidence of the LCAPM while others do not? Is it because of the different level of goodness of each measure? Or, is it because each measure proxies different aspect of liquidity? I thin both can be at least the part of the answer. First, proxies of trading costs used in this paper are, as manifested in the previous studies (Goyeno, Holden, Lundblad, and Trzcina (2005), Hasbrouc (2005), Lesmond (2005)), noisy measures. In a recent paper of Korajczy and Sada (2006), common factors across eight different liquidity measures 3 are shown to be strongly priced. This result may come from reducing noise of each liquidity measure by principal component analysis as well as from capturing common systematic aspects of liquidity that each liquidity measure jointly proxies for. Second, and more 3 Those measures are Amihud (2002), turnover, quoted spread, effective spread, and four measures from Sada (2004). 7

20 importantly, I did not consider the impact of different holding periods on liquidity in the empirical tests (Amihud and Mendelson (1986), Constantinides (1986), Atins and Dyl (1997), Chalmers and Kadlec (1998)). By using monthly return and liquidity, we implicitly assume that the investors holding period is one month, which may be a strong assumption. This paper is organized as follows. In section 2.2, Acharya and Pedersen (2005) s LCAPM is introduced. Data and liquidity proxies are illustrated in section 2.3 and the test methodology is shown in section 2.4. Empirical results are summarized in section 2.5 separately by different methodologies. I conclude in section Liquidity-Adjusted Capital Asset Pricing Model It has been empirically shown that liquidity is a priced factor both as a characteristic and as a systematic ris factor. However, a theoretical asset pricing model that includes both of these aspects of liquidity was proposed only recently. The liquidityadjusted capital asset pricing model of Acharya and Pedersen (2005) is derived from a framewor similar to the CAPM in that ris-averse investors maximize their expected utility under a wealth constraint, but by replacing the cost-free stoc price, P i,t, with a stochastic trading-cost-adjusted stoc price, P i,t Ψ i,t, where Ψ i,t is a trading cost in absolute amount, in an overlapping-generations economy. The LCAPM is presented as, Cov t (R i,t+1 C i,t+1, R M,t+1 C M,t+1 ) E t (R i,t+1 C i,t+1 ) = R f + λ t. (2.1) V ar t (R M,t+1 C M,t+1 ) R i is a gross return of stoc i, R f is a gross ris-free rate and C i,t is a trading cost per price at time t (C i,t Ψ i,t /P i,t 1 ). Subscript t in expectation, covariance, and variance denotes that these operators are conditional on the information set available 8

21 up to time t. Subscript M denotes that the variable is defined in terms of the maret portfolio. As a result of the study of the liquidity-adjusted price, LCAPM has three additional covariance terms related to stochastic trading costs other than the traditional maret ris component. It is clear that without the trading cost terms, C M and C i, the LCAPM in (2.1) is equivalent to the traditional CAPM. By assuming constant conditional variance or constant premia, the unconditional version of the model is derived as: E (R i,t R f,t ) = E (C i,t ) + λβ 1 i + λβ2 i λβ3 i λβ4 i (2.2) where, 4 β 1 i = Cov (R i,t, R M,t ) V ar (R M,t [C M,t E t 1 (C M,t )]) βi 2 = Cov (C i,t E t 1 (C i,t ),C M,t E t 1 (C M,t )) V ar (R M,t [C M,t E t 1 (C M,t )]) βi 3 = Cov (R i,t, C M,t E t 1 (C M,t )) V ar (R M,t [C M,t E t 1 (C M,t )]) βi 4 = Cov (C i,t E t 1 (C i,t ), R M,t ) V ar (R M,t [C M,t E t 1 (C M,t )]). The ris premium is defined as λ = E (λ t ) = E (R M,t C M,t R f,t ). Additionally, I define: β 5 i β 2 i β3 i β4 i (2.3) β 6 i β 1 i + β 2 i β 3 i β 4 i. β 5 i is defined as a linear combination of the three liquidity betas excluding maret beta, while β 6 i contains all four covariance terms in it. Henceforth, I will call β 5 i the 4 Since liquidity is persistent (Chan (2002), Pastor and Stambaugh (2003), Acharya and Pedersen (2005), Korajczy and Sada (2006)), trading cost terms are denoted in terms of their innovation. 9

22 liquidity net beta and βi 6 the net beta. It is worth noting that the net beta corresponds to the covariance terms in equation (2.2) and the liquidity net beta helps distinguish the pricing effect of liquidity riss from that of maret ris. As shown in Acharya and Pedersen (2005), each component beta has an associated economic interpretation: β 1 i is similar to the traditional maret beta of CAPM except for the terms related to trading cost in the denominator. βi 2 is liquidity ris arising from the comovement of individual stoc liquidity with maret liquidity (Chordia, Roll, and Subrahmanyam (2000), Hasbrouc and Seppi (2001), Huberman and Hala (2001), Coughenour and Saad (2004)). βi 2 is expected to be positively related to asset returns since investors require compensation for a stoc whose liquidity decreases when the maret liquidity goes down. For a similar reason, a stoc whose liquidity negatively comoves with maret liquidity will be traded at a premium since such stoc is easier to sell when the maret is highly illiquid. An unexpected decrease in stoc maret liquidity will bring a potential wealth reduction for investors who hold stocs that are highly sensitive to maretwide liquidity and need to liquidate them immediately since liquidation of such stocs would be costlier under low maret liquidity (Pastor and Stambaugh (2003), Sada (2004)). βi 3 captures this liquidity ris and is negatively related to expected returns since investors are willing to accept low returns on stocs whose expected return is high when the maret is illiquid. The fourth beta, βi 4, is newly proposed by Acharya and Pedersen (2005) and is negatively related to asset returns since stocs that become more liquid in a 10

23 down maret will be preferred by investors, thus will be traded at a premium. The negative sign for βi 4 is due to investors willingness to accept low returns on such stocs. In the next section, I deal with data, its screening and liquidity measures. 2.3 Data and Iliquidity Measures I collect daily return, price and trading volume of common shares listed in AMEX and NYSE from CRSP daily stoc file for July 1, 1962 to December 31, Monthly return and price are collected from CRSP monthly stoc file for the corresponding periods. Stocs are required to have at least 100 positive trading volume days (Chordia, Roll, and Subrahmanyam (2000)). To prevent any disruptive influence from extremely large or small stocs, if any end-month price of stocs in a given year is less than or equal to $2 or great than or equal to $1000, that stoc is dropped from the sample for that year. 5 If a stoc shifts from one trading venue to another in any given year, that stoc is dropped from the sample for that year. As previous studies pointed out, stoc splits affect liquidity (Conroy, Harris, and Benet (1990), Schultz (2000), Dennis and Stricland (2003), Gray, Smith, and Whaley (2003), Goyeno, Holden, and Uhov (2005)), thus I exclude stocs for the year when splits occur. Since the LCAPM is built based on trading cost, illiquidity, rather than on liquidity, the following illiquidity measures are used in this study. First, I use the reversalmeasure of illiquidity based on Pastor and Stambaugh (2003). It is estimated in the following way. r i,d+1,t r M,d+1,t = α i,t + β i,t r i,d,t + γ i,t sign (r i,d,t r M,d,t ) dvol i,d,t + ǫ i,d,t 5 This criterion is also used in Chordia, Roll, and Subrahmanyam (2000) and other papers from the same authors. More recently, Huang (2005) applied the same criterion. 11

24 where r i,d,t is a return of stoc i on day d in month t, r M,d,t is a maret return (CRSP value-weighted return) on a day d in a month t, and dvol i,d,t is a dollar trading volume (in million dollar unit). The coefficient of signed dollar trading volume (γ i,t ), the liquidity measure, is expected to be negative reflecting price reversals due to large trading volume. To give precision, I require stocs to have at least 15 days with valid observations within a month. 6 To convert the liquidity measure to an illiquidity measure, I multiply it by -1. Our illiquidity measure, PS, is: PS i,t γ i,t ( 1). (2.4) Our next illiquidity measure is a price impact measure by Amihud (2002). RV i,d,t r i,d,t P i,d,t V O i,d,t 10 6 where, P i,d,t and V O i,d,t are a price and a daily share trading volume (in one share unit) of stoc i on day d in month t, respectively. Note that this measure is defined only for positive volume days. Monthly illiquidity measure is constructed as an equallyweighted average of daily RV s. RV i,t = 1 T i,t T i,t RV i,d,t (2.5) i=1 where T i,t is a number of daily observations of stoc i in month t. I also restrict the stoc to have at least 15 days with valid observations within a month as in PS. Turnover has been a popular liquidity measure in the previous literature (e.g. Rouwenhorst (1999), Chordia and Swaminathan (2000), Dennis and Stricland (2003)). We may attribute the reason for using turnover as a liquidity measure to Demsetz 6 Due to 9/11 terrorist attac, the number of total available trading days in September 2001 is 15. Thus, I require stocs to have at least 14 days only in September

25 (1968), Glosten and Milgrom (1985) and Constantinides (1986) among others. Demsetz (1968) shows that the price of immediacy would be smaller for stocs with high trading frequency since frequent trading reduces the cost of inventory controlling. Glosten and Milgrom (1985) shows that stocs with high trading volume would have lower level of information asymmetry to the extent that information is revealed by prices. 7 Constantinides (1986) shows that investors would increase their holding periods (thus, reduce turnover) when a stoc is highly illiquid. To be consistent with other measures, I convert turnover into an illiquidity measure by multiplying it by -1: TV i,d,t = V O i,d,t NSH i,d,t ( 1) where NSH i,d,t is a number of shares outstanding (in one share unit) of stoc i on day d of month t. Monthly turnover is constructed as an equally-weighted average of daily TV s. TV i,t = 1 T i,t T i,t TV i,d,t (2.6) i=1 I also restrict stocs to have at least 15 days with valid observations in a given month. A relatively recent and popular measure of illiquidity is the zero-return proportion measure proposed by Lesmond, Ogden, and Trzcina (1999). ZR i,t N i,t T t (2.7) where T t is a number of trading days in month t and N i,t is the number of zero-return days of stoc i in month t. The economic intuition is as follows: when the trading cost is too high to cover the benefit from informed trading, informed investors would 7 Consistent with this argument, Hasbrouc (1991) found that the information asymmetries are more significant for small stocs. 13

26 choose not to trade and this non-trading would lead to an observed zero return for that day. The zero return measure has been used to evaluate the impact of trading costs in a momentum strategy (Lesmond, Schill, and Zhou (2004)), the relation between maret liquidity and political riss in emerging marets (Lesmond (2005)), liquidity contagion across international financial marets (Stahel (2004a)), and the implication of liquidity on asset pricing in emerging marets (Beaert, Harvey, and Lundblad (2003)). Importantly, ZR is defined over zero-volume days as well as positive volume days since this measure assumes that a zero-return day with positive volume is a day when noise trading induces trading volume. Our last illiquidity measure is from Roll (1984). Roll proposed a proxy for effective spread based on bid-as bounce: 2 Cov (r i,d 1,t, r i,d,t ). However, the measure cannot be defined if the covariance term is positive. In that case, I force covariance terms to have negative values by taing absolute values with a negative sign added (Harris (1989), Lesmond (2005)). Thus, Roll s measure is defined as: RO i,t = 2 Cov (r i,d 1,t, r i,d,t ). (2.8) Figure B.1 shows maret return and maret illiquidity, which is formed as an equally-weighted average of individual stocs illiquidity. Following Pastor and Stambaugh (2003), Porter (2003) and Acharya and Pedersen (2005), P S and RV are multiplied by the scaling factor, which is computed as a ratio of total maret value at the end of month t divided by that in August This is to adjust the time-trend of the measures due to different values of currency over time. As manifested in Pastor and Stambaugh (2003), the time-series of maret illiquidity based on P S adequately captures anecdotal events in liquidity. It shows peas on November 1973 (Oil shoc), October 1987 (stoc maret crash) and September 14

27 1998 (LTCM). The same is true for RV and RO. However, TV and ZR show that the stoc maret was highly liquid on October 1987, when the stoc maret crash occurred. Table A.1 shows summary statistics of daily percentage returns and our illiquidity proxies by 25 size groupings. Each size group is formed based on the total maret value of each stoc at the end of previous year. Average and standard deviations are obtained as time-series average or standard deviation of medians in each size group. We see some interesting patterns in the table. Most importantly, we find that illiquidity is higher for small stocs than for large stocs. This is consistent with the previous literature (Amihud and Mendelson (1986), Amihud (2002)) and fits well with our intuition. Except for turnover, all illiquidity proxies show a monotonic relation between illiquidity and size. For example, P S is for the smallest size group, while it is almost zero for the largest size group. A similar pattern is shown for RV, RO and ZR. RV is 6.55 for the smallest size group and it is for the largest size group. RO (ZR) is (0.28) for the smallest size group and it is (0.07) for largest size group. However, T V does not show a clear monotonic pattern. Though the smallest size group has a turnover of , which is larger than for the largest size group, there is increasing pattern of TV from the 23rd largest size group to the largest. Turning to standard deviation, small stocs have higher volatility of returns and illiquidity across all illiquidity proxies except T V. Standard deviation of returns for the smallest stocs is 7.77% while it is 4.17% for the largest stocs. Standard deviation of PS is 0.41 for the smallest size group while it is for the largest 15

28 size group. In sum, Table A.1 shows that the returns and illiquidity and their volatility are negatively correlated with size, which is consistent with the previous literature. 2.4 Methodology This paper employs two different test methods in this paper. One is the traditional Fama-MacBeth regression using size and illiquidity portfolios as test assets. The other is a time-series test, where each beta in the LCAPM is computed for individual stocs. Using these two different methods provides opportunity to examine the robustness of the test results. The tests use portfolios as well as individual stocs as test assets. Choosing test assets at individual stoc level or at portfolio levels has benefits and costs. First, individual stocs preserve information that might be removed by forming portfolios. Second, using individual stocs may prevent controversy when the test results vary according to test assets used. Third, using individual stocs gives more power to the tests due to the large number of observations. However, estimated betas at the individual stoc level may be noisy. Considering these benefits and costs, we use both individual stoc and portfolios as test assets. Since traditional Fama-MacBeth regression is portfolio-level test, I use size and illiquidity portfolios in Fama-MacBeth regressions. However, I assign betas which are estimated at the portfolio level to individual stocs based on stoc characteristics such as maret capitalization or illiquidity. This way, we can reduce the noise which could be present when the betas are estimated at the individual stoc level (Fama and French (1992)). CRSP value-weighted index return is used as our maret return. However, in all tests, I construct maret illiquidity as both a value-weighted average and an 16

29 equally-weighted average of individual stocs illiquidity. The value-weighting scheme is motivated by Chordia, Shivaumar, and Subrahmanyam (2004) who find that the aggregate maret liquidity is more strongly reflected in large firms than in small firms in US marets, while the equal-weighting scheme has the benefit of preventing over-representation of large stoc liquidity in maret liquidity Fama-MacBeth Regression For the Fama-MacBeth regressions, 25 size portfolios and illiquidity portfolios were formed based on maret capitalization at the end of previous year and based on average illiquidity over the previous year, respectively. For each portfolio, maret ris as well as three liquidity riss in the LCAPM ( post-raning betas) are estimated using monthly return and illiquidity over the whole sample period. These post-raning betas are assigned to member stocs over the remaining sample period. At the final step, I run cross-sectional regressions using individual stocs monthly returns and estimated betas each month. Illiquidity is highly persistent. The first order autocorrelation of equally-weighted maret illiquidity is for PS, for RV, for TV, for ZR and for RO. Thus, I wor with the innovations in illiquidity rather than with the level of illiquidity. Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) employ residuals obtained from an AR(2) model fitted over the entire sample period. Since time-series fitting is made ex-post, AR(2) fitting does have a loo-ahead bias. However, I employ this for two reasons. First, a liquidity event is more explicitly shown by an AR(2) fitting. Second, since Acharya and Pedersen (2005) used the same approach 17

30 to obtain illiquidity innovation, I closely follow their method so that we have better opportunity to examine whether their empirical results can be generalized. Since we do not want an AR(2) fitting to unduly impact the construction of the innovations, following Pastor and Stambaugh (2003) and Acharya and Pedersen (2005), I use the following AR(2) fitting for PS and RV : RV i,t scl t = arv i,t 1 scl t + brv i,t 2 scl t + ε i,t where scl t is a scaling factor at month t which is a ratio of total maret value at the end of month t 1 to that on August, Note that the scaling factors at month t are uniformly used for RV s at month t, t 1 and t 2 in the above regression. A similar AR(2) fitting will be used for PS. Table A.2 summarizes estimated betas of 25 size portfolios. The numbers in the table are multiplied by 100 for expositional purposes. β 2 and β 3 estimated by PS decrease in absolute terms as size increases. This monotonic trend is also shown for RV, consistent with Acharya and Pedersen (2005). However, no monotonic relation is shown for these betas for other measures. Other betas, β 1 and β 4, do not show monotonicity for any measures. At the last step of the Fama-MacBeth procedure, the following cross-sectional regression is performed every month using the individual stoc returns and estimated betas. E (R i,t R f,t ) = a + be (C i,t ) + λ j β1 i,t + λ j β2 i,t λ j β3 i,t λ j β4 i,t (2.9) I use average monthly illiquidity obtained from the previous 12 months (and at least 6 months) as a proxy for expected illiquidity at time t, E (C i,t ). If the LCAPM holds, 18

31 the intercept will not be significantly different from zero (a = 0) and the coefficient on the expected illiquidity will be one (b = 1) in equation (2.9) Time-Series Tests A popular method for showing the importance of liquidity riss in asset pricing is a time-series test used in the prior studies (e.g. Pastor and Stambaugh (2003), Sada (2004) and Liang and Wei (2005)). This test gives an easy interpretation of economic magnitude of liquidity riss. In this test, I use a different method for getting innovations in liquidity since it is possible that individual stocs have discontinuous time-series due to the screening procedure described in the earlier section or due to missing data during the sample period. Thus, instead of time-series fitting, I use the change in illiquidity, defined as first difference of illiquidity, as its innovation. 8 This way, we also have the benefit of removing the loo-ahead bias present in fitting an AR(2) model over the entire sample period. The test procedure is as follows. For each individual stoc, maret ris as well as three liquidity riss in the LCAPM are estimated using the previous 5 years of monthly returns and illiquidity. That is, for each individual stoc i, betas in year t, β i,t ( = 1, 2, 3, 4), are calculated by the definitions in equations (2.3) and (2.3) using the innovations in illiquidity from year t 4 to t. The five-year window starts from July 1962 or from the first month when the stocs are present in the sample and is rolled forward at yearly intervals. Stocs should have at least 36 monthly returns and innovations in illiquidity within the given window to have betas in year t. Every year, 8 Changes in liquidity have been used as a liquidity innovation in previous studies. See Chordia, Roll, and Subrahmanyam (2000), for example. 19

32 I sort sample stocs into decile portfolios based on the liquidity net beta (β 5 ) or on net beta (β 6 ) obtained this way. Portfolios are formed both as equally weighted and maret-value weighted averages. I regress each portfolio return in a maret model, three factor model (Fama and French (1993)) and four factor model (Carhart (1997)) adding momentum factors, MOM, to the three factor model. That is, r p,t r f,t = α p + δ p (r M,t r f,t ) + ξ p,t (2.10) r p,t r f,t = α p + δ p (r M,t r f,t ) + ϕ 1 SMB t + ϕ 2 HML t + ξ p,t (2.11) r p,t r f,t = α p + δ p (r M,t r f,t ) + ϕ 1 SMB t + ϕ 2 HML t + ϕ 3 MOM t + ξ p,t (2.12) where p = 1, 2,, 10 denoting ten portfolios (low numbered portfolio is formed based on small beta). r p,t is an equally-weighted or value-weighted return of portfolio p at month t, r f,t is a three-month US Treasury rate, and r M,t is a maret return. The three- and four factors are obtained from Ken French s website. 9 Intercept α p from each regression is the excess return earned by trading based on liquidity riss or based on the LCAPM net beta that is not explained by commonly used one-, three- and four-factor models. The profit from a zero-investment cost trading strategy, is obtained by examining the difference between the intercepts of the highest and lowest decile portfolios (henceforth 10-1 spread). Significant 10-1 spread implies that the liquidity ris is priced. Our empirical results based on this time-series method with equal- and value-weighted portfolios are shown in the next section. 9 I than Ken French for maing the data available from his website. 20

33 2.5 Empirical Results Time-Series Tests Table A.3 summarizes the time-series test results based on a one-factor, maret model of (2.10). To save space, I report only intercepts with t-values in parenthesis. Panel A shows the test for portfolios sorted by liquidity net beta (β 5 ) while panel B is for net beta (β 6 ). The illiquidity measures used in the test are shown below the legend of each panel. Intercepts from maret model regressions are shown according to the portfolio group in each row. The intercept is interpreted as the monthly percentage return. In the last row, the 10-1 spread is shown also with t-values. Test results are reported separately for the equally-weighted portfolio (labelled with EW ) and the value-weighted portfolio ( VW ). 10 Figures B.2 and B.3 are visual representation of each column of both panels in Table A.3. The bar graph shows the size of intercepts (corresponding axis is on the left side) while bullet lines denote corresponding t-values. Dar-shaded bars are used for intercepts from equally-weighted portfolios and light-shaded bars are for valueweight portfolios. Figure B.2 is for panel A of Table A.2 (thus, for portfolios sorted by liquidity net beta) while Figure B.3 is for panel B (portfolio based on net beta) of the same table. In panel A of Table A.3 and Figure B.2, we see that test results are different according to illiquidity measures and portfolio weighting schemes. Tests based on Amihud s measure, RV, and Roll s measure, RO, show evidence that the liquidity riss are priced when the portfolios are formed as a value-weighted basis: Tables A.4 and A.5 also have the same format. 21

34 spreads of 0.74% and 0.30% for RV and RO, respectively, are significant with corresponding t-values of 3.25 and A monthly return of 0.74% is economically significant in that its annual excess (in the sense that it is not explained by maret ris) return is 9.3%. However, results based on other illiquidity measures are different. For example, time-series tests with PS and ZR show that the intercept is higher for portfolios with lower liquidity ris than for portfolios with higher liquidity ris, which produces negative and insignificant 10-1 spreads in both equally-weighted and valueweighted cases. T V also shows negative 10-1 spreads in equally-weighted portfolios. In both equally-weighted and value-weighted cases, intercepts are not monotonically increasing according to liquidity net beta for TV. Panel B and Figure B.3 show the test results based on net beta. Consistent with the result in Acharya and Pedersen (2005), RV shows that the 10-1 spread is 0.92% monthly, which is economically significant (annually 11.67%), with a t-value of 3.80 when the portfolio is value-weighted. However, this is the only case that supports the LCAPM. All other cases where different measures and weighting schemes are used show negative or positive but always insignificant 10-1 spreads. Intercepts are not monotonic according to net betas in all cases. In sum, we cannot find supporting evidence for LCAPM beyond the RV measure. Table A.4 shows the test results based on the three factor model of (2.11). The table format is the same as that of Table A.3. Figures 4 and 5 are graphical representation of each panel of Table A.4. Panel A and Figure B.4 show similar test results as the maret model-based test. The 10-1 spread based on RV and value-weighted 22

35 portfolios show monthly returns of 0.51%, which is an annualized 6.3%. This is statistically significant with t-value of However, other measures and other weighting schemes do not show such evidence that the liquidity riss are priced. Table A.5 and Figures B.6 and B.7 show intercepts from a four factor model specified in (2.12). In panel A, which shows the test result based on liquidity net beta, we see that the 10-1 spreads of 0.46% and 0.32% for RV and RO, respectively, are significant with corresponding t-values of 2.41 and Monthly excess return of 0.46% is economically significant (annual excess return is 6%). In panel B, we see that RV with value-weighted test assets produces a 10-1 monthly spread of 0.97%, which is highly significant both statistically (t-value of 4.76) and economically (annual 12.34%). We also find some wea evidence from RO with equally-weighted portfolios in that 10-1 spread is 0.23% with t-value of However, most cases do not support LCAPM Fama-MacBeth Regression Empirical results from Fama-MacBeth regression are reported in this section. In the first subsection, results from size portfolios as test assets will be reported separately for value-weighted maret factors and equally-weighted maret factors. In a subsequent subsection, I use illiquidity portfolios as test assets. Size Portfolios Tables A.6 and B.7 summarize the Fama-MacBeth regression results when test assets are size portfolios. Table A.6 is for results when the maret illiquidity is formed as maret-value weighted average of individual stocs illiquidity while Table A.7 is for equally-weighted maret illiquidity. 23