liquidity risk and asset pricing

In a time-series test with a one-factor market model, three-factor excessmarket return, SMB, and HML and four-factor model excess market return, SMB,HML and MOM as well as in a Fama-MacB

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

In this dissertation, I investigate the effect of liquidity risk on asset pricing Inthe first essay, I test the liquidity-adjusted capital asset pricing model (LCAPM) ofAcharya and Pedersen (2005) for 1962-2004 in the US market using various liquidityproxies In a time-series test with a one-factor (market model), three-factor (excessmarket return, SMB, and HML) and four-factor model (excess market return, SMB,HML and MOM) as well as in a Fama-MacBeth regression, I find that test resultsvary according to the liquidity measures used, to the test methodology, to the testassets, and to the weighting scheme Tests based on the liquidity measure of Ami-hud (2002), Pastor and Stambaugh (2003) and zero-return proportion show someevidence that liquidity risks are priced, but in most cases, I could not find evidencethat supports the LCAPM The second essay specifies and tests an equilibrium as-set pricing model with liquidity risk at the global level The analysis encompasses25,000 individual stocks from 48 developed and emerging countries around the worldfrom 1988 to 2004 Though I cannot find evidence that the LCAPM holds in interna-tional financial markets, cross-sectional as well as time-series tests show that liquidityrisks arising from the covariances of individual stocks’ return and liquidity with localand global market factors are priced Furthermore, I show that the US market is

an important driving force of world-market liquidity risk I interpret our evidence asconsistent with an intertemporal capital asset pricing model (Merton (1973)) in which

stochastic shocks to global liquidity serve as a priced state variable The third essayinvestigates how and why liquidity is transmitted across stocks In a vector autore-gressive framework, I uncover a dynamic interaction of liquidity across size portfolios

in that past changes of liquidity of large stocks are positively correlated with currentchanges of liquidity of small stocks Furthermore, liquidity spillovers are not restrictedamong fundamentally-related stocks and are independent of the dynamics in returnand volatility spillovers This finding implies that the process of liquidity generation

is independent of information flows and that portfolio diversification strategies shouldconsider different patterns in return, volatility and liquidity spillovers

to my parents

I don’t know how to thank enough for having such an exceptional doctoral mittee I wish to thank Kewei Hou, G Andrew Karolyi, Ren´e Stulz, and Ingrid M.Werner for their continual support and encouragement

com-I am most grateful to my advisor, G Andrew Karolyi, for his tremendous support,guidance and encouragement Throughout my doctoral work he encouraged me todevelop my analytical thinking and research skills His assistance guided me not only

to a better researcher, but also to a better instructor

I wish to express my deep appreciation to Ren´e Stulz whose consultation, insightfulcomments and encouragement were continual stimulation to my research

I am deeply indebted to Ingrid M Werner whose help, guidance, patience andencouragement tremendously helped me in all my doctoral training process

I would like to thank Kewei Hou for his insightful comments, efforts and guidance

I also thank Karl Diether, Bing Han and Jean Helwege for their encouragementand friendship and thank Bong-Chan Kho for being an excellent role model even from

my school life in Seoul many years ago I thank my brother Tae-Hwy Lee, who is atime-series econometrician, for guiding me in pursuing academic career

I want to share my happiness and thankfulness with my friend, Jungwu Rhie, whopassed away by tragic accident last year and may rest in peace in heaven

November 9, 1970 Born - Taejon, Korea

1989-1996 B.B.A Business Administration,

Seoul National University1997-1999 MBA, International Finance,

Seoul National University1999-2001 M.S Statistics,

University of North Carolina, ChapelHill

2001-present Graduate Teaching and Research

Asso-ciate,The Ohio State University

TABLE OF CONTENTS

Page

Abstract ii

Dedication iv

Acknowledgments v

Vita vi

List of Tables x

List of Figures xii

Chapters: 1 Introduction 1

2 Testing the Liquidity-Adjusted Capital Asset Pricing Model using Differ-ent Measures of Liquidity 4

2.1 Introduction 4

2.2 Liquidity-Adjusted Capital Asset Pricing Model 8

2.3 Data and Iliquidity Measures 11

2.4 Methodology 16

2.4.1 Fama-MacBeth Regression 17

2.4.2 Time-Series Tests 19

2.5 Empirical Results 21

2.5.1 Time-Series Tests 21

2.5.2 Fama-MacBeth Regression 23

2.6 Conclusion 28

3 The World Price of Liquidity Risk 30

3.1 Introduction 30

3.2 Related literature 33

3.3 Liquidity-adjusted capital asset pricing model 36

3.4 Data and liquidity measure 39

3.4.1 Sample screening 39

3.4.2 Summary statistics 43

3.4.3 Is zero-return proportion a good proxy for illiquidity? 45

3.5 Methodology 48

3.5.1 Innovations of return and illiquidity 48

3.5.2 Estimating predicted betas 49

3.6 Empirical results 53

3.6.1 Local and global market betas 53

3.6.2 Fama-MacBeth test results for local liquidity risks 55

3.6.3 Fama-MacBeth test results for global liquidity risks 57

3.6.4 Fama-MacBeth test results for local and world market liq-uidity risks 59

3.6.5 Do US markets drive world market liquidity risks? 63

3.6.6 Time series tests 66

3.6.7 Subperiod analysis 70

3.7 Robustness tests 72

3.7.1 Different innovation 73

3.7.2 Two-way sorts 73

3.8 Conclusion 76

4 Liquidity Spillovers 78

4.1 Introduction 78

4.2 Literature Review 83

4.2.1 Theories 83

4.2.2 Empirical Studies 85

4.3 Hypotheses 88

4.4 Data and Liquidity Measure 90

4.5 Liquidity Spillovers 92

4.5.1 Vector Autoregression 95

4.5.2 VAR Estimation Results 97

4.6 Are Liquidity Spillovers Related to Correlated Fundamentals or In-formation Flow? 99

4.6.1 Intra-Industry Liquidity Spillovers 99

4.6.2 Intra- vs Inter-Industry Liquidity Spillovers 102

4.6.3 Does Information Flow Contribute in Liquidity Spillovers? 105

4.6.4 Does Style Investing Contribute to Liquidity Spillovers? 106

4.7 Robustness Checks 115

4.7.1 Alternative Lags 116

4.7.2 Value-Weighted Average 116

4.8 Discussion 118

4.9 Conclusion 119

5 Conclusion 122

Bibliography 124

Appendices: A Tables 131

B Figures 174

LIST OF TABLES

A.1 Summary Statistics 132

A.2 Betas by Size Group 133

A.3 Intercepts from the Market Model Regression 134

A.4 Intercepts from the Three Factor Model Regression 135

A.5 Intercepts from the Four Factor Model Regression 136

A.6 Fama-French Regression of Size Portfolios with Value-Weighted Market Illiquidity 137

A.7 Fama-French Regression of Size Portfolios with Equal-Weighted Mar-ket Illiquidity 139

A.8 Fama-French Regression of Illiquidity Portfolios with Value-Weighted Market Illiquidity 141

A.9 Fama-French Regression of Illiquidity Portfolios with Equal-Weighted Market Illiquidity 143

A.10 Summary Statistics (Liquidity and Return in World Financial Markets) 145 A.11 Correlation of Liquidity Measures by Size in US Market 147

A.12 Coefficients from the estimation of predicted betas 148

A.13 Mean of Portfolio formed based on Predicted Betas 149

A.14 Fama-French Regression by Predicted Betas (Local Market) 150

A.15 Fama-French Regression by Predicted Betas (World Market) 151

A.16 Fama-French Regression by Predicted Betas (Local and World Market) 152 A.17 Fama-French Regression by Predicted Betas with respect to US market and Non-US World Markets 153

A.18 Time-Series Tests 154

A.19 Fama-French Regression by Global Predicted Betas (Subperiod) 156

A.20 Fama-MacBeth regression with 25 portfolios for US market 158

A.21 Fama-MacBeth regression with post-ranking betas (2-way sorts) 159

A.22 Descriptive Statistics 161

A.23 VAR Estimation Results 162

A.24 Zero-Block Exclusion Tests 163

A.25 Summary Statistics for Industry-Size Portfolios 165

A.26 Within-Industry Liquidity Spillovers 168

A.27 Intra- vs Inter-Industry Liquidity and Volatility Spillovers 170

A.28 Spillovers in Size-B/M Style 172

A.29 Style vs Industry 173

LIST OF FIGURES

B.1 Market Illiquidity and Return 175

B.2 Intercepts from Market Model Regression (Liquidity Net Beta) 178

B.3 Intercepts from Market Model Regression (Net Beta) 181

B.4 Intercepts from Three Factor Model Regression (Liquidity Net Beta) 184 B.5 Intercepts from Three Factor Model Regression (Net Beta) 187

B.6 Intercept from four factor model regression (liquidity net beta) 190

B.7 Intercept from four factor model regression (net beta) 193

B.8 Correlation of Liquidity Measures in US Market 196

B.9 Intercepts from Market Model Regression 197

B.10 Daily Quoted Spread 198

CHAPTER 1

INTRODUCTION

In classical asset pricing models, perfect financial markets without frictions, pecially no trading costs, are assumed and thus the diverse features of liquidity are

affects portfolio investment performance (Holthausen, Leftwich, and Mayers (1991),Keim (2004), Lesmond, Schill, and Zhou (2004), Korajczyk and Sadka (2004)) and

it has a significant implication for portfolio diversification strategies (Domowitz andWang (2002), Harford and Kaul (2005)) In addition, it has been shown that liquidityaffects the cross-sectional differences of asset returns as a characteristic (Amihud andMendelson (1986), Brennan and Subrahmanyam (1996), Amihud (2002)) or as a riskfactor (Pastor and Stambaugh (2003), Sadka (2004), Acharya and Pedersen (2005)).This dissertation consists of three essays devoted to investigating the effect ofliquidity risk on asset pricing In the first essay, I test the liquidity-adjusted capi-tal asset pricing model (LCAPM) of Acharya and Pedersen (2005) for 1962-2004 in1

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.

the US market using various liquidity proxies The LCAPM is attractive in that itcovers various channels through which liquidity may affect asset prices in one modelwhile incorporating traditional market risk as well Liquidity risk that arises fromthe covariance of individual stock return with market liquidity, which is investigated

by Pastor and Stambaugh (2003), is present in the LCAPM as one source of riskthrough which liquidity affects asset prices Commonality in liquidity, which de-notes the comovement of individual stock liquidity with market liquidity (Chordia,Roll, and Subrahmanyam (2000), Hasbrouck and Seppi (2001), Huberman and Halka(2001)), is also captured in the LCAPM In addition, the LCAPM proposed a newsource of liquidity risk, which arises from the covariance of individual stock liquid-ity with market returns While the LCAPM covers liquidity as a risk factor, it alsoencompasses 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 variouschannels In a time-series test with a one-factor (market model), three-factor (excessmarket return, SMB, and HML) and four-factor model (excess market return, SMB,HML and MOM) as well as in a Fama-MacBeth regression, I find that test results varyaccording 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 thatliquidity risks are priced, but in most cases, I could not find evidence that supportsthe LCAPM

The second essay extends the study of liquidity risk and asset pricing to tional financial markets by testing the LCAPM at the global level The analysis en-compasses 25,000 individual stocks from 48 developed and emerging countries around

interna-the world from 1988 to 2004 Though I cannot find evidence that interna-the LCAPM holds

in international financial markets, cross-sectional as well as time-series tests showthat liquidity risks arising from the covariances of individual stocks’ returns and liq-uidity with local and global market factors are priced Furthermore, I show that the

US market is an important driving force of world-market liquidity risk I interpretour evidence as consistent with an intertemporal capital asset pricing model (Merton(1973)) in which stochastic shocks to global liquidity serve as a priced state variable.The third essay investigates how and why liquidity is transmitted across stocks

In a vector autoregressive framework, I uncover a dynamic interaction of liquidityacross size portfolios in that past changes of liquidity of large stocks are positivelycorrelated with current changes of liquidity of small stocks Furthermore, liquidityspillovers are not restricted among fundamentally-related stocks and are independent

of the dynamics in return and volatility spillovers This finding implies that theprocess of liquidity generation is independent of information flows and that portfoliodiversification strategies should consider different patterns in return, volatility andliquidity spillovers

commis-a theoreticcommis-al model, the liquidity-commis-adjusted ccommis-apitcommis-al commis-asset pricing model (the LCAPM,henceforth), that encompasses liquidity as a stock characteristic as well as a source ofvarious undiversifiable risks However, they tested the model using a specific proxyand a particular test methodology In this paper, I test the LCAPM for 1962-2004

in the US market and investigate the robustness of their conclusion using variousliquidity proxies and test methodologies

While explicit trading costs are easy to measure, this is not so for implicit tradingcosts For example, it is hard to measure price impact cost, which is defined as the

difference in price when the trading occurs and that when the trading does not occur,since it requires a benchmark 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 validmeasures of such trading costs

Liquidity proxies based on high frequency data have received a lot of attention asdesirable measures (Amihud and Mendelson (1986), Huang and Stoll (1997), Chordia,Sarkar, and Subrahmanyam (2005), among others) However, high frequency data isavailable only for a relatively short period of time as data from the Institute for theStudy and Securities Markets (ISSM) starts in 1983

Hence, many researchers have suggested proxies of liquidity based on daily returnand trading volume since they give longer time-series of liquidity Roll (1984), forexample, 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 oftotal shares outstanding, has also been a popular measure of liquidity The theoreticalmotivation for using turnover as a liquidity proxy goes back to Demsetz (1968) andGlosten and Milgrom (1985) Demsetz (1968) shows that the price of immediacywould be smaller for stocks with high trading frequency since frequent trading reducesthe cost of inventory controlling On the other hand, Glosten and Milgrom (1985)shows that stocks with high trading volume would have lower level of informationasymmetry to the extent that information is revealed by prices Amihud (2002)proposed a simple and intuitive liquidity measure, which is defined as the absolutedaily return divided by daily trading volume Pastor and Stambaugh (2003) proposed

a liquidity measure based on return reversal More recently, Lesmond, Ogden, and

Trzcinka (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 stock is highlyilliquid.2

While these measures have many benefits in that they provide relatively long series of liquidity for researchers and more importantly, in that they are simple, therehave been arguments questioning the reliability of these liquidity measures (Hasbrouck(2005), Goyenko, Holden, Lundblad, and Trzcinka (2005)) Given the limitations ofvarious liquidity measures, I construct each of these measures using daily returns andtrading volume data from CRSP for 1962 to 2004 Acharya and Pedersen (2005)used the liquidity proxy of Amihud (2002) and found evidence validating the model

time-in the US market for 1962-1999 This paper examtime-ines whether this empirical result

is unique to the specific measure used For comprehensive tests of the model, weemploy two different test methodologies of Fama-MacBeth cross-sectional regressionand time-series test

The LCAPM is attractive in that it covers various channels through which liquiditymay affect asset prices in one model while incorporating traditional market risk aswell Liquidity risk that arises from the covariance of individual stock return withmarket liquidity, which is investigated by Pastor and Stambaugh (2003), is present

in the LCAPM as one source of risk through which liquidity affects asset prices.Commonality in liquidity, which denotes the comovement of individual stock liquiditywith market liquidity (Chordia, Roll, and Subrahmanyam (2000), Hasbrouck andSeppi (2001), Huberman and Halka (2001)), is also captured in the LCAPM Inaddition, the LCAPM proposed a new source of liquidity risk, which arises from the2

All of these measures will be introduced in detail in section 2.3.

covariance of individual stock liquidity with market returns While the LCAPM coversliquidity as a risk factor, it also encompasses liquidity level in the model Hence, thetest of the LCAPM gives us an opportunity to investigate the effect of liquidity onasset prices through various channels.

In time-series tests with one-factor (market model), three-factor (excess marketreturn, SMB, and HML) and four-factor models (excess market return, SMB, HMLand MOM) as well as in Fama-MacBeth cross-sectional regression tests, we find thatthe results are sensitive to the liquidity measures, to the test assets used, to theweighting scheme and to the test methodologies Tests based on liquidity measure ofAmihud (2002), Pastor and Stambaugh (2003) and zero-return proportion suggestedthat liquidity risks are priced, but in most cases, we could not find evidence supportingthe 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 eachmeasure proxies different aspect of liquidity? I think both can be at least the part

of the answer First, proxies of trading costs used in this paper are, as manifested inthe previous studies (Goyenko, Holden, Lundblad, and Trzcinka (2005), Hasbrouck(2005), Lesmond (2005)), noisy measures In a recent paper of Korajczyk and Sadka

strongly priced This result may come from reducing noise of each liquidity measure

by principal component analysis as well as from capturing common systematic pects of liquidity that each liquidity measure jointly proxies for Second, and more3

as-Those measures are Amihud (2002), turnover, quoted spread, effective spread, and four measures from Sadka (2004).

importantly, I did not consider the impact of different holding periods on liquidity

in the empirical tests (Amihud and Mendelson (1986), Constantinides (1986), Atkinsand 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)’sLCAPM is introduced Data and liquidity proxies are illustrated in section 2.3 andthe test methodology is shown in section 2.4 Empirical results are summarized insection 2.5 separately by different methodologies I conclude in section 2.6

It has been empirically shown that liquidity is a priced factor both as a istic and as a systematic risk factor However, a theoretical asset pricing model thatincludes both of these aspects of liquidity was proposed only recently The liquidity-adjusted capital asset pricing model of Acharya and Pedersen (2005) is derived from aframework similar to the CAPM in that risk-averse investors maximize their expected

absolute amount, in an overlapping-generations economy The LCAPM is presentedas,

Et(Ri,t+1− Ci,t+1) = Rf + λt

Covt(Ri,t+1− Ci,t+1, RM,t+1− CM,t+1)

V art(RM,t+1− CM,t+1) . (2.1)

variance denotes that these operators are conditional on the information set available

up to time t Subscript M denotes that the variable is defined in terms of the marketportfolio.

As a result of the study of the liquidity-adjusted price, LCAPM has three tional covariance terms related to stochastic trading costs other than the traditional

the LCAPM in (2.1) is equivalent to the traditional CAPM

By assuming constant conditional variance or constant premia, the unconditionalversion of the model is derived as:

Since liquidity is persistent (Chan (2002), Pastor and Stambaugh (2003), Acharya and Pedersen (2005), Korajczyk and Sadka (2006)), trading cost terms are denoted in terms of their innovation.

liquidity net beta and β6

to the covariance terms in equation (2.2) and the liquidity net beta helps distinguishthe pricing effect of liquidity risks from that of market risk As shown in Acharya andPedersen (2005), each component beta has an associated economic interpretation:

related to trading cost in the denominator

with market liquidity (Chordia, Roll, and Subrahmanyam (2000), Hasbrouckand Seppi (2001), Huberman and Halka (2001), Coughenour and Saad (2004))

β2

compensation for a stock whose liquidity decreases when the market liquiditygoes down For a similar reason, a stock whose liquidity negatively comoveswith market liquidity will be traded at a premium since such stock is easier tosell when the market is highly illiquid

• An unexpected decrease in stock market liquidity will bring a potential wealthreduction for investors who hold stocks that are highly sensitive to market-wide liquidity and need to liquidate them immediately since liquidation of suchstocks would be costlier under low market liquidity (Pastor and Stambaugh

to expected returns since investors are willing to accept low returns on stockswhose expected return is high when the market is illiquid

is negatively related to asset returns since stocks that become more liquid in a

down market will be preferred by investors, thus will be traded at a premium.

on such stocks

In the next section, I deal with data, its screening and liquidity measures

I collect daily return, price and trading volume of common shares listed in AMEXand NYSE from CRSP daily stock file for July 1, 1962 to December 31, 2004 Monthlyreturn and price are collected from CRSP monthly stock file for the correspondingperiods Stocks are required to have at least 100 positive trading volume days (Chor-dia, Roll, and Subrahmanyam (2000)) To prevent any disruptive influence fromextremely large or small stocks, if any end-month price of stocks in a given year isless than or equal to $2 or great than or equal to $1000, that stock is dropped from

given year, that stock is dropped from the sample for that year As previous studiespointed out, stock splits affect liquidity (Conroy, Harris, and Benet (1990), Schultz(2000), Dennis and Strickland (2003), Gray, Smith, and Whaley (2003), Goyenko,Holden, and Ukhov (2005)), thus I exclude stocks for the year when splits occur.Since the LCAPM is built based on trading cost, illiquidity, rather than on liquid-ity, the following illiquidity measures are used in this study First, I use the reversal-measure of illiquidity based on Pastor and Stambaugh (2003) It is estimated in thefollowing way

ri,d+1,t− rM,d+1,t = αi,t+ βi,tri,d,t+ γi,tsign (ri,d,t− rM,d,t) · dvoli,d,t+ ǫi,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.

where ri,d,tis a return of stock i on day d in month t, rM,d,t is a market return (CRSP

the liquidity measure, is expected to be negative reflecting price reversals due tolarge trading volume To give precision, I require stocks to have at least 15 days with

measure, I multiply it by -1 Our illiquidity measure, P S, is:

of stock i on day d in month t, respectively Note that this measure is defined onlyfor positive volume days Monthly illiquidity measure is constructed as an equally-weighted average of daily RV s

stock to have at least 15 days with valid observations within a month as in P S.Turnover has been a popular liquidity measure in the previous literature (e.g.Rouwenhorst (1999), Chordia and Swaminathan (2000), Dennis and Strickland (2003))

We may attribute the reason for using turnover as a liquidity measure to Demsetz6

Due to 9/11 terrorist attack, the number of total available trading days in September 2001 is

15 Thus, I require stocks to have at least 14 days only in September 2001.

(1968), Glosten and Milgrom (1985) and Constantinides (1986) among others setz (1968) shows that the price of immediacy would be smaller for stocks with hightrading frequency since frequent trading reduces the cost of inventory controlling.Glosten and Milgrom (1985) shows that stocks with high trading volume would havelower level of information asymmetry to the extent that information is revealed by

pe-riods (thus, reduce turnover) when a stock is highly illiquid To be consistent withother measures, I convert turnover into an illiquidity measure by multiplying it by -1:

T Vi,d,t = V Oi,d,t

NSHi,d,t

× (−1)

day d of month t Monthly turnover is constructed as an equally-weighted average ofdaily T V s

I also restrict stocks 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 proportionmeasure proposed by Lesmond, Ogden, and Trzcinka (1999)

Tt

(2.7)

days of stock i in month t The economic intuition is as follows: when the tradingcost is too high to cover the benefit from informed trading, informed investors would7

Consistent with this argument, Hasbrouck (1991) found that the information asymmetries are more significant for small stocks.

choose not to trade and this non-trading would lead to an observed zero return for thatday 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 betweenmarket liquidity and political risks in emerging markets (Lesmond (2005)), liquiditycontagion across international financial markets (Stahel (2004a)), and the implication

of liquidity on asset pricing in emerging markets (Bekaert, Harvey, and Lundblad(2003)) Importantly, ZR is defined over zero-volume days as well as positive volumedays since this measure assumes that a zero-return day with positive volume is a daywhen noise trading induces trading volume

Our last illiquidity measure is from Roll (1984) Roll proposed a proxy for

cannot be defined if the covariance term is positive In that case, I force covarianceterms to have negative values by taking absolute values with a negative sign added(Harris (1989), Lesmond (2005)) Thus, Roll’s measure is defined as:

q

Figure B.1 shows market return and market illiquidity, which is formed as anequally-weighted average of individual stocks’ illiquidity Following Pastor and Stam-baugh (2003), Porter (2003) and Acharya and Pedersen (2005), P S and RV aremultiplied by the scaling factor, which is computed as a ratio of total market value atthe end of month t divided by that in August 1962 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 market uidity based on P S adequately captures anecdotal events in liquidity It shows peaks

illiq-on November 1973 (Oil shock), October 1987 (stock market crash) and September

1998 (LTCM) The same is true for RV and RO However, T V and ZR show thatthe stock market was highly liquid on October 1987, when the stock market crashoccurred.

Table A.1 shows summary statistics of daily percentage returns and our illiquidityproxies by 25 size groupings Each size group is formed based on the total marketvalue of each stock at the end of previous year Average and standard deviations areobtained 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 thatilliquidity is higher for small stocks than for large stocks This is consistent with theprevious literature (Amihud and Mendelson (1986), Amihud (2002)) and fits well withour intuition Except for turnover, all illiquidity proxies show a monotonic relationbetween illiquidity and size For example, P S is 0.067 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 0.005 for the largest sizegroup RO (ZR) is 0.028 (0.28) for the smallest size group and it is 0.011 (0.07) forlargest size group However, T V does not show a clear monotonic pattern Thoughthe smallest size group has a turnover of -0.0015, which is larger than -0.0016 for thelargest size group, there is increasing pattern of T V from the 23rd largest size group

to the largest

Turning to standard deviation, small stocks have higher volatility of returns andilliquidity across all illiquidity proxies except T V Standard deviation of returnsfor the smallest stocks is 7.77% while it is 4.17% for the largest stocks Standarddeviation of P S is 0.41 for the smallest size group while it is 0.0003 for the largest

size group In sum, Table A.1 shows that the returns and illiquidity and their volatilityare negatively correlated with size, which is consistent with the previous literature.

The tests use portfolios as well as individual stocks as test assets Choosing testassets at individual stock level or at portfolio levels has benefits and costs First,individual stocks preserve information that might be removed by forming portfolios.Second, using individual stocks may prevent controversy when the test results varyaccording to test assets used Third, using individual stocks gives more power tothe tests due to the large number of observations However, estimated betas at theindividual stock level may be noisy Considering these benefits and costs, we useboth individual stock and portfolios as test assets Since traditional Fama-MacBethregression is portfolio-level test, I use size and illiquidity portfolios in Fama-MacBethregressions However, I assign betas which are estimated at the portfolio level toindividual stocks based on stock characteristics such as market capitalization or illiq-uidity This way, we can reduce the noise which could be present when the betas areestimated at the individual stock level (Fama and French (1992))

CRSP value-weighted index return is used as our market return However, inall tests, I construct market illiquidity as both a value-weighted average and an

equally-weighted average of individual stocks’ illiquidity The value-weighting scheme

is motivated by Chordia, Shivakumar, and Subrahmanyam (2004) who find that theaggregate market liquidity is more strongly reflected in large firms than in smallfirms in US markets, while the equal-weighting scheme has the benefit of preventingover-representation of large stock liquidity in market liquidity

For the Fama-MacBeth regressions, 25 size portfolios and illiquidity portfolioswere formed based on market capitalization at the end of previous year and based onaverage illiquidity over the previous year, respectively For each portfolio, market risk

as well as three liquidity risks in the LCAPM (“post-ranking” betas) are estimatedusing monthly return and illiquidity over the whole sample period These post-rankingbetas are assigned to member stocks over the remaining sample period At the finalstep, I run cross-sectional regressions using individual stocks’ monthly returns andestimated betas each month

Illiquidity is highly persistent The first order autocorrelation of equally-weightedmarket illiquidity is 0.357 for P S, 0.941 for RV , 0.963 for T V , 0.971 for ZR and 0.685for RO Thus, I work with the innovations in illiquidity rather than with the level ofilliquidity Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) employresiduals obtained from an AR(2) model fitted over the entire sample period Sincetime-series fitting is made ex-post, AR(2) fitting does have a look-ahead bias However,

I employ this for two reasons First, a liquidity event is more explicitly shown by anAR(2) fitting Second, since Acharya and Pedersen (2005) used the same approach

to obtain illiquidity innovation, I closely follow their method so that we have betteropportunity to examine whether their empirical results can be generalized.

Since we do not want an AR(2) fitting to unduly impact the construction ofthe innovations, following Pastor and Stambaugh (2003) and Acharya and Pedersen(2005), I use the following AR(2) fitting for P S and RV :

RVi,t· sclt= aRVi,t−1· sclt+ bRVi,t−2· sclt+ εi,t

end of month t − 1 to that on August, 1967 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 Asimilar AR(2) fitting will be used for P S

Table A.2 summarizes estimated betas of 25 size portfolios The numbers in the

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

monotonicity for any measures

At the last step of the Fama-MacBeth procedure, the following cross-sectionalregression is performed every month using the individual stock returns and estimatedbetas

I use average monthly illiquidity obtained from the previous 12 months (and at least

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)

A popular method for showing the importance of liquidity risks in asset pricing is

a time-series test used in the prior studies (e.g Pastor and Stambaugh (2003), Sadka(2004) and Liang and Wei (2005)) This test gives an easy interpretation of economicmagnitude of liquidity risks

In this test, I use a different method for getting innovations in liquidity since it

is possible that individual stocks have discontinuous time-series due to the screeningprocedure described in the earlier section or due to missing data during the sampleperiod Thus, instead of time-series fitting, I use the change in illiquidity, defined as

of removing the look-ahead bias present in fitting an AR(2) model over the entiresample period

The test procedure is as follows For each individual stock, market risk as well

as three liquidity risks in the LCAPM are estimated using the previous 5 years ofmonthly returns and illiquidity That is, for each individual stock i, betas in year t,

βk

the innovations in illiquidity from year t − 4 to t The five-year window starts fromJuly 1962 or from the first month when the stocks are present in the sample and isrolled forward at yearly intervals Stocks should have at least 36 monthly returns andinnovations 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.

I sort sample stocks into decile portfolios based on the liquidity net beta (β5) or on

market-value weighted averages I regress each portfolio return in a market 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,

where p = 1, 2, · · ·, 10 denoting ten portfolios (low numbered portfolio is formed based

liquidity risks or based on the LCAPM net beta that is not explained by commonlyused one-, three- and four-factor models The profit from a zero-investment costtrading strategy, is obtained by examining the difference between the intercepts ofthe highest and lowest decile portfolios (henceforth ‘10-1’ spread) Significant ‘10-1’spread implies that the liquidity risk is priced Our empirical results based on thistime-series method with equal- and value-weighted portfolios are shown in the nextsection

9

I thank Ken French for making the data available from his website.

2.5 Empirical Results

Table A.3 summarizes the time-series test results based on a one-factor, marketmodel of (2.10) To save space, I report only intercepts with t-values in parenthesis

of each panel Intercepts from market model regressions are shown according to theportfolio group in each row The intercept is interpreted as the monthly percentagereturn In the last row, the ‘10-1’ spread is shown also with t-values Test results arereported separately for the equally-weighted portfolio (labelled with ‘EW’) and the

Figures B.2 and B.3 are visual representation of each column of both panels inTable A.3 The bar graph shows the size of intercepts (corresponding axis is on theleft side) while bullet lines denote corresponding t-values Dark-shaded bars are usedfor intercepts from equally-weighted portfolios and light-shaded bars are for value-weight 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) ofthe same table

In panel A of Table A.3 and Figure B.2, we see that test results are differentaccording to illiquidity measures and portfolio weighting schemes Tests based onAmihud’s measure, RV , and Roll’s measure, RO, show evidence that the liquid-ity risks are priced when the portfolios are formed as a value-weighted basis: ‘10-1’10

Tables A.4 and A.5 also have the same format.

spreads of 0.74% and 0.30% for RV and RO, respectively, are significant with responding t-values of 3.25 and 1.89 A monthly return of 0.74% is economicallysignificant in that its annual excess (in the sense that it is not explained by marketrisk) return is 9.3% However, results based on other illiquidity measures are different.For example, time-series tests with P S and ZR show that the intercept is higher forportfolios with lower liquidity risk than for portfolios with higher liquidity risk, whichproduces negative and insignificant ‘10-1’ spreads in both equally-weighted and value-weighted cases T V also shows negative ‘10-1’ spreads in equally-weighted portfolios.

cor-In both equally-weighted and value-weighted cases, intercepts are not monotonicallyincreasing according to liquidity net beta for T V

Panel B and Figure B.3 show the test results based on net beta Consistent withthe 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 3.80when the portfolio is value-weighted However, this is the only case that supports theLCAPM All other cases where different measures and weighting schemes are usedshow negative or positive but always insignificant ‘10-1’ spreads Intercepts are notmonotonic according to net betas in all cases In sum, we cannot find supportingevidence for LCAPM beyond the RV measure

Table A.4 shows the test results based on the three factor model of (2.11) Thetable format is the same as that of Table A.3 Figures 4 and 5 are graphical represen-tation of each panel of Table A.4 Panel A and Figure B.4 show similar test results

as the market model-based test The ‘10-1’ spread based on RV and value-weighted

portfolios show monthly returns of 0.51%, which is an annualized 6.3% This is tically significant with t-value of 2.76 However, other measures and other weightingschemes do not show such evidence that the liquidity risks are priced.

statis-Table A.5 and Figures B.6 and B.7 show intercepts from a four factor modelspecified in (2.12) In panel A, which shows the test result based on liquidity netbeta, 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 1.95 Monthly excess return

of 0.46% is economically significant (annual excess return is 6%) In panel B, wesee that RV with value-weighted test assets produces a ‘10-1’ monthly spread of0.97%, which is highly significant both statistically (t-value of 4.76) and economically(annual 12.34%) We also find some weak evidence from RO with equally-weightedportfolios in that ‘10-1’ spread is 0.23% with t-value of 1.76 However, most cases donot support LCAPM

Empirical results from Fama-MacBeth regression are reported in this section Inthe first subsection, results from size portfolios as test assets will be reported sepa-rately for value-weighted market factors and equally-weighted market factors In asubsequent subsection, I use illiquidity portfolios as test assets

Size Portfolios

Tables A.6 and B.7 summarize the Fama-MacBeth regression results when testassets are size portfolios Table A.6 is for results when the market illiquidity isformed as market-value weighted average of individual stocks’ illiquidity while TableA.7 is for equally-weighted market illiquidity

In Table A.6, P S shows some supporting evidence of the LCAPM β6 is significantwith a premium of 0.0012 (t-value is 6.90) Liquidity-related risks are all highly

is significant with a premium of 0.03 and with a negative sign (absolute t-value is

which is contrary to what the model suggests However, the illiquidity level, ‘liq’, isnot priced in all specifications for P S

Consistent with Acharya and Pedersen (2005), net beta and liquidity net beta arehighly significant with correct signs, consistent with the LCAPM Liquidity net beta,

Level of illiquidity, which is a proxy for expected illiquidity, is highly significant in

as market capitalization and book-to-market The commonality beta is priced with

a correct sign in all reported specifications When the stock characteristics such as

and Stambaugh (2003) It has a premium of 0.02 with a t-value of 2.79 Generally,the results based on RV are consistent with the results in Pastor and Stambaugh(2003) and Acharya and Pedersen (2005)

are priced with flipped signs, that are inconsistent with the LCAPM However, the

significant β3 coefficient drives the liquidity net beta, β5, to be priced In some cases,

we see that the expected level of illiquidity is priced for T V

In the case of ZR, the expected level of illiquidity is priced in all reported tions with t-values varying from 2.16 to 5.99 Consistent with Pastor and Stambaugh

sign but market beta and commonality beta are priced with wrong signs Thoughexpected level of illiquidity is highly significant with correct signs in many reportedspecifications, RO shows strong evidence against the LCAPM

Table A.7 is reports regression results when the market illiquidity is formed as anequally-weighted average of individual stocks’ illiquidity Equally-weighted marketilliquidity has a benefit in that it prevents over-representation of large stock illiquidity

in the market-wide illiquidity measure Results based on P S and RV are, however,generally similar to those in the value-weighted market illiquidity case reported in

priced in ZR case In the case of RO, because of priced commonality beta with awrong sign, liquidity net beta is no more priced Results for other cases are similar

to the previous table

Illiquidity Portfolios

Table A.8 presents the Fama-MacBeth regression results for 25 equally-weightedilliquidity portfolios formed based on the average illiquidity over the previous year.Market illiquidity is formed as the market value-weighted average of individual stocks’illiquidity

Regression results based on P S show that the liquidity risks are priced

the premium of market beta is negative and significant Netting out market beta,

and t-value of 5.91 Consistent with Pastor and Stambaugh (2003), the sensitivity

LCAPM proposes Also consistent with Acharya and Pedersen (2005), who showthat the liquidity risk arising from the covariance of individual stock liquidity with

with a premium of 0.001 and t-value of 6.06

Tests based on RV show evidence that liquidity risks are priced Generally, resultsare stronger than in the case of size portfolios as test assets All liquidity-related risksare priced with correct signs and their absolute t-values varying from 2.16 to 7.83.These liquidity risks are priced even after controlling for size and book-to-market.The illiquidity level is priced in some cases

In T V , we see that all risks are priced but with flipped signs that are inconsistent

now has a positive premium, which is the opposite to what the LCAPM suggests(premium is 0.23 with a t-value of 4.46) The level of illiquidity is not priced correctly

in any reported specifications

not priced or priced with a wrong sign when the test assets are size portfolios Its

com-monality beta loses its significance when the size and book-to-market are controlled

priced with t-values varying from 1.95 to 5.83

RO-based tests do not show that liquidity risks are priced However, the illiquiditylevel is significant in all reported specifications

Table A.9 shows the results for illiquidity portfolios but with equally-weightedmarket illiquidity Results are virtually the same as with the previous value-weighted

signifi-cant

priced when the stock characteristics are controlled for Consistent with Acharyaand Pedersen (2005), we find that the liquidity net beta is priced with a premium

consistent with Pastor and Stambaugh (2003) Tests with other measures show similarresults

2.6 Conclusion

I test the liquidity-adjusted capital asset pricing model of Acharya and sen (2005) for 1962-2004 in the US market using various liquidity measures Intime-series tests with a one-factor (market model), three-factor (excess market re-turn, SMB, and HML) and four-factor model (excess market return, SMB, HML andMOM), and in Fama-MacBeth cross-sectional regression tests, we find that the testresults vary according to the liquidity measures used in the test, to the weightingscheme (equally-weighted vs value-weighted), to the test methodologies and to thetest assets Consistent with Acharya and Pedersen (2005), tests based on liquiditymeasure of Amihud (2002) show supporting evidence that liquidity risks are priced.Tests based on Pastor and Stambaugh (2003) and zero-return proportion also providesome supporting evidence However, in most cases, we could not find evidence thatsupports the LCAPM

Peder-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 eachmeasure proxies different aspect of liquidity? I think both can be at least the part

of the answer First, proxies of trading costs used in this paper are, as manifested inthe previous studies (Goyenko, Holden, Lundblad, and Trzcinka (2005), Hasbrouck(2005), Lesmond (2005)), noisy measures In a recent paper of Korajczyk and Sadka(2006), common factors across eight different liquidity measures are shown to bestrongly priced This result may come from reducing noise of each liquidity measure

by principal component analysis as well as from capturing common systematic pects of liquidity that each liquidity measure jointly proxies for Second, and more