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European Financial Management, Vol. 20, No. 1, 2014, 126151doi: 10.1111/j.1468-036X.2011.00629.x

Liquidity, Liquidity Risk and Stock

Returns: Evidence from JapanBo LiSchool of Management, Xiamen University, Xiamen 361005, China E-mail: [email protected]

Qian Sun Department of Finance, School of Management, Fudan University, Shanghai 200433, China E-mail: [email protected]

Changyun WangSchool of Finance, Renmin University of China, Beijing 100872, China E-mail: [email protected]

Abstract

This paper investigates whether liquidity and liquidity risk are priced in Japan.Using modified Amihud illiquidity measures, we find both cross-sectional and

time series evidence that liquidity is priced in the Japanese stock market during the period 19752006. The evidence is largely consistent with Amihuds (2002) findings in the US market. We further employ the liquidity-adjusted CAPM proposed by Acharya and Pedersen (2005) to examine whether liquidity risk is priced in Japan. Consistent with Acharya and Pedersens findings in the US, we show that liquidity risk is priced in the stock market, in addition to the liquiditylevel. These findings strengthen the confidence that liquidity is a determinant of stock returns.

Keywords: liquidity , Amihud illiquidity measure , liquidity-adjusted CAPM , Japan

JEL classification: G 12

1. Introduction

Liquidity (or illiquidity) and liquidity risk have important practical as well as academicimplications. Several studies have documented that liquidity can explain the difference in

We would like to thank the editor John Doukas and an anonymous referee for their helpfulcomments and suggestions. Qian Sun and Bo Li gratefully acknowledge the research grantsupport from the National Natural Science Foundation of China (No. 70872095) and fromthe Ministry of Education (No. 08JJD630012). Changyun Wang gratefully acknowledges thefinancial support from the China National Science Fund for Distinguished Young Scholars(No.: 70725003). All errors remain ours. Correspondence: Qian Sun.

C 2011 Blackwell Publishing Ltd

China Financial Policy Research Center, Renmin University of China, China

Changyun Wang gratefully acknowledges thenancial support from the National Social Science Foundation of China (No.:11AZD094).All errors remain ours. Correspondence: Qian Sun.

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Liquidity, Liquidity Risk and Stock Returns: Evidence from Japan 127

the cross section of stock returns in the USA. 1 Using the illiquidity measure proposed byAmihud (2002) and the liquidity-adjusted capital asset pricing model (CAPM) proposed by Acharya and Pedersen (2005), we examine whether liquidity and liquidity risk are priced in the Japanese stock market.

Over the sample period analysed in this paper, Japan had the second-largest stock market in the world, next to the USA, in terms of both market capitalisation and number of listed securities. 2 As pointed out by Chan et al. (1991), the study of the Japanese stock market alongside that of the USA is important for the evaluation of empirical models of cross-sectional stock returns. Empirical confirmation of the same determinants in bothcountries would strengthen confidence in the model, while differences between countrieswould induce further exploration of asset pricing theories. In addition, evidence fromthe Japanese market may shed light on the subsumption of explanatory variables and robustness with regard to time period and sample selection.

Chan et al. (1991) relate cross-sectional difference in stock returns in Japan to earningsyield, firm size, book-to-market ratio (BM), and cash flow yield. The authors uncover significant relations between these variables and expected returns in the Japanese market,which is consistent with US findings. Daniel et al. (2001) use Japanese data to test therobustness of Daniel and Titmans (1997) empirical asset pricing model based on USdata. Employing market microstructure data from Japan, Lehmann and Modest (1994)analyse liquidity on the Tokyo Stock Exchange (TSE) and compare their f indings withthose obtained on the New York Stock Exchange (NYSE). Bremer and Hiraki (1999)find evidence linking short-term returns of individual TSE stocks to lagged tradingvolume and compare their results with those found in the US stock market. Usingmarket microstructure data, Ahn et al. (2002) find that stock returns on the TSE are positively related to illiquidity measures.

Few studies have examined the relation between stock returns and liquidity in Japan.An exception is the paper by Chang et al. (2010). In a cross-sectional setup, theseauthors examine the relations between stock returns and six monthly liquidity measures,including such traditional measures as turnover and dollar trading volume, Amihuds(2002) illiquidity measure, the proportion of trading days with zero returns proposed byLesmond et al. (1999), and the liquidity measure proposed by Liu (2006). Chang et al.also analyse the relation between stock returns and liquidity variability (a rough proxy for liquidity risk) measured by the coefficients of variation for turnover, the dollar tradingvolume, and the Amihud illiquidity measure. Chang et al. (2010) obtain mixed results:They show that stock returns are negatively related to four out of six liquidity measures

for the period 19752004, but not consistently so across the subsample periods. Theyalso find that liquidity variability measures are related to stock returns, but with thewrong sign; that is, the more variable the liquidity, the lower the stock return.

1 See Amihud and Mendelson (1986), Glosten and Harris (1988), Hasbrouck (1991), Brennanand Subrahmanyam (1996), Eleswarapu (1997), Chalmers and Kadlec (1998), Easley et al.(2002), andPastor andStambaugh (2003), among others. Using mainly marketmicrostructuredata from the USA and various estimation techniques, these authors report a positive relation between illiquidity and stock returns across companies. Subrahmanyam (2010) provides awhole section to review the literature about liquidity as a cross-sectional predictor of stock

returns. Neumann (2003) documents that liquidity has an impact on price spreads betweendual-class shares.2 China overtook Japan as the worlds second largest stock market in terms of marketcapitalisation in the middle of 2009 .


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Bo Li, Qian Sun and Changyun Wang 128

Our study is different from that of Chang et al. (2010) in the following aspects. First,we focus on the Amihud illiquidity measure. Various proxies for liquidity have been used in previous studies and, as pointed out by Lesmond (2002), some traditional proxies,such as turnover, trading volume, and firm size, may capture the effects of variables notrelated to liquidity. On the other hand, some finer and more accurate measures based onmarket microstructure data, such as bidask spread, amortised effective bidask spread, price response to signed order flow, and the probability of information-based trading, arenot generally available, especially over long periods of time. Amihud (2002) developsa measure that aims to balance the limits of data availability and accuracy: the averageof the daily ratio of the absolute stock return to its dollar trading volume over a given period. This measure is simple, since it only requires the input of daily data to constructand is applicable to all securities and time periods. 3 It is also intuitive, since it can beinterpreted as the daily stock price response to $1 of trading volume, which is consistentwith Kyles (1985) concept of illiquidity, that is, the response of price to order flow,and Silbers (1975) thinness measure, that is, the ratio of the absolute price change tothe absolute excess demand for trading. After comparing a few alternative liquiditymeasures constructed using daily data, Hasbrouck (2005) concludes that the Amihud measure works the best. This study further modifies the Amihud measure based on thesuggestions of Hasbrouck (2005) and Acharya and Pederson (2005), which should makethe Amihud measure better reflect illiquidity in cross-sectional and time series analyses.

Second, we examine the time series relation between liquidity and stock returns, whichis not examined by Chang et al. (2010). In fact, not many studies examine the relation between liquidity and stock returns over time. 4 As pointed out by Amihud (2002), this is probably due to the fact that illiquidity measures based on microstructure data for longtime periods are not available in most markets. Using Amihuds (2002) approach, wetest whether stock returns in Japan are related to the expected and unexpected illiquidityover time. In addition, we examine whether there is the flight to liquidity effect.

Third, we capitalise on Acharya and Pedersens (2005) work to investigate whether liquidity risk is related to stock returns. These authors argue that not only the level of liquidity but also the uncertainty of liquidity (liquidity risk) should be priced. However,using liquidity variability measures, Chordia et al. (2001) and Chang et al. (2010) find a negative and strong relation between liquidity uncertainty and expected stock returns,which is counterintuitive. In contrast, Acharya and Pedersen (2005) propose a liquidity-adjusted CAPM. Using the Amihud illiquidity measure and stock returns to computeliquidity betas, Acharya and Pedersen find some evidence that illiquidity betas are priced

in the USA and that a liquidity-adjusted CAPM is better than the standard CAPM interms of goodness of fit. Our study using Japanese data provides an out-of-sample testof the authors liquidity-adjusted CAPM.

We also take into consideration factors unique to the Japanese market in designing our test and examining alternative model specifications. Using monthly data from 1975 to2006, our empirical findings are largely consistent with those found in Amihud (2002)and Acharya and Pedersen (2005). First, the illiquidity level is positively related to

3 Pastor and Stambaugh (2003) use daily data to construct a liquidity measure based on

signed order flow. Lesmond (2002) develops a liquidity estimate based on the percentage of zero return trading days over a certain period, such as a year.4 Bekaert et al. (2003) use pooled data to study the relation between liquidity and expected returns across firms over time in emerging markets.


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stock returns across firms for the whole sample period. Second, the expected liquidity is positively related to stock returns while the unexpected liquidity is negatively related tostock returns over time. We also find some evidence in support of the flight to liquidityhypothesis proposed by Amihud (2002). Finally, liquidity risk is priced, in the sensethat the liquidity-adjusted CAPM fits data better than the standard CAPM. However, a puzzling finding is that liquidity seems unrelated to stock returns across firms for the sub-sample period 19902006. A similar finding is also documented by Chang et al. (2010).

The rest of the paper is organised as follows. Section 2 describes the data and theilliquidity measure. Section 3 examines the cross-sectional relation between illiquidityand stock returns, while the time series relation between illiquidity and stock returns isstudied in Section 4. Section 5 further examines whether illiquidity risk is priced in theliquidity-adjusted CAPM setting, and Section 6 concludes.

2. Data and the Illiquidity Measure

All the data used in this study, unless otherwise stated, are from the Pacific-Basin CapitalMarkets Database (PACAP) Japan Database, which covers the period from January 1975to December 2006. 5 According to Amihud (2002), daily stock illiquidity is computed as the ratio of absolute daily returns to the daily trading value. However, we followHasbrouck (2005) by further taking the square root of this ratio to filter out the impactof outliers:

ILLid = | Rid | / VALid (1)where Rid is the return for stock i on day d , VAL

id is the trading value for stock i on

day d in millions of yen, and ILLid represents the absolute percentage price change per 1 million of trading value with the square root transformation.

Following Lehmann and Modest (1994) and Bremer and Hiraki (1999), we includeonly stocks listed on the first section of the TSE, because the stocks in different sectionssatisfy different listing criteria and are likely to have very different trading and liquiditycharacteristics. For example, stocks listed on the first section are much larger and muchmore actively traded than those in the second section. We use daily stock returns and trading values in each month to construct our monthly illiquidity series. Our sample period starts July 1975 and ends in December 2006 (378 monthly observations). Itstarts in July 1975 instead of January 1975 for the following three reasons: First, most

Japanese firms use March as their fiscal year-end, and financial reports may not beavailable until June, and we need some of the annual report data to construct proxies for firm characteristics, such as the BM and cash flow-to-price ratio (CP). Second, we use previous 150 daily return data to compute the monthly beta. Third, we use the averagemonthly returns for the previous two quarters to control for a possible momentum or reversal effect.

The monthly illiquidity for stock i is

ILLim = (1/ Dim ) Dim

d = 1 | Rimd | / VALimd (2)

where Dim is the number of trading days for stock i in month m.

5 As of the end of 2010 , the PACAP Japan Database has not generated data beyond 2006 .


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All stocks in our sample must meet the following two criteria: 1) It must have valid observations of daily returns and trading values for more than 200 days in a year and more than 15 days in a month so that the illiquidity estimate is more reliable. 2) Themonth-end stock price must be greater than 100 so that stock returns are not affected too much by the minimum tick size of 1.6 Our final sample, ranging from 656 firmsin 1975 to 1693 firms in 2006, is described in Table 1.

The monthly market illiquidity is the average illiquidity across stocks in the market portfolio M in month m:

ILL M m = (1/ M ) M

ILLim (3)

Figure 1a presents the monthly market illiquidity over 19752006. It shows that marketilliquidity trended down from 1975 to 1990 but increased and then oscillated after that.Correspondingly, as shown in Figure 1b, the Nikkei 225 experienced an upward trend

from 1975 to 1989, but declined and oscillated thereafter. According to Securities Market in Japan (2001), a publication of the Japan Securities Research Institute, the developmentof the Japanese securities market from 1975 to 1999 can be divided into several stages:(1) 19751984 was the period of coping with the oil crisis; (2) 19851989 was the period of the economic bubble; (3) 19901999 was the period of financial reform involvingdebate on and enforcement of Japans Financial System Reform Law. Roughly, the firsttwo periods coincide with the rapid development of the stock market and a decliningtrend in illiquidity, while the last period is associated with a market slowdown and an increasing illiquidity trend. Therefore, we divide the whole sample period into twosubsample periods in subsequent tests: the first one from 1975 to 1989 and the second one from 1990 to 2006. This also coincides with the sample division of Chang et al.(2010), whose further division of the sample period into four stages based on businesscycles does not reveal any qualitative difference.

3. The Cross-Sectional Relation between Illiquidity and Stock Returns

In the spirit of Amihud (2002), we specify the following cross-sectional regressionmodel:

Rim = k 0m + k 1m ILLM im 1 + k 2m

im 1 + k 3m R

i Q1

+ k 4m Ri Q2 + k 5m BM

im 1 + k 6m ln CAP

im 1

+ k 7mSTDim 1 + k 8mCP im 1 +

im (4)

where the monthly individual stock return R im is a function of illiquidity and a setof control variables. Since the monthly stock illiquidity varies dramatically over time,illiquidity for stock i is further scaled by market illiquidity in month m to obtain the

6 In addition to tick size, the TSE also has price limit rules for both the maximum daily price changes and maximum price changes between trades. However, the limit betweentrades is irrelevant, because our illiquidity measure uses daily data. The daily price limitsare quite large, ranging from 10% to 30%, and are rarely hit in practice. Therefore, wedo not particularly consider them in our sample selection process. Information on tick sizeschedules and price limit rules for TSE stocks as of 2006 is available from the authors.


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Table 1Sample selection

This table reports the sample selection. The sample period is from July 1975 to December 2006. Thestocks included in the sample must have valid observations of daily returns and trading values for more

than 200 days in a year and more than 15 days in a month, as well as month-end prices greater than100.

Original stocks Stocks with Stocks with Stocks withFiscal Trading in the month-end monthly trading annual trading Finalyear days f irst section price > 100 days > 15 days > 200 sample

1975 286 832 822 740 665 6561976 286 840 819 771 724 7041977 285 846 836 791 743 7361978 285 856 855 771 777 7761979 286 865 861 756 747 7431980 285 872 859 761 758 7451981 285 884 873 769 718 7091982 286 898 890 795 758 7541983 287 915 911 806 789 7871984 284 928 928 859 814 8141985 285 953 953 908 865 8651986 274 980 980 957 880 8801987 274 998 998 970 943 9431988 261 1023 1023 983 944 9441989 247 1041 1041 1014 994 9941990 245 1054 1054 992 967 9671991 247 1065 1065 962 941 9411992 247 1077 1077 1026 943 9431993 247 1094 1094 1063 1013 10131994 248 1111 1111 1058 1024 10241995 247 1127 1127 1088 1070 10701996 247 1171 1171 1132 1083 10831997 246 1211 1198 1146 1102 10891998 246 1252 1246 1232 1160 11541999 247 1321 1287 1303 1238 12042000 246 1416 1389 1389 1297 12702001 245 1472 1391 1441 1386 13062002 247 1524 1500 1517 1453 14302003 246 1616 1611 1612 1530 15252004 245 1669 1663 1664 1615 16092005 247 1696 1689 1695 1667 16602006 125 1715 1700 1708 1701 1693

mean-adjusted illiquidity

ILLM im = ILLim / ILL

M m (5)

Other stock characteristics or control variables included in equation (4) are (1) themonthly firm beta, im 1 , which is the market beta; (2) the returns of stock i for the pasttwo quarters Ri Q1 and R

i Q2; (3) the BM, B M

im 1, which is the most recent yearly book

value of equity at the end of year y 1 (June) divided by the market value of equity


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Fig. 1. Time series pattern of monthly market illiquidity and the Nikkei 225

Figures 1a and 1b show the time series pattern of the monthly market illiquidity and the level of the Nikkei 225 during the sample period, respectively, where is calculated as the cross-sectional averageof monthly stock illiquidity for all the sample stocks during 19752006. The stocks included in thesample must have valid return and trading value data observations for more than 200 days a year and more than 15 days a month. The month-end prices are greater than 100. The Nikkei 225 is the indexvalue at the end of each month.

for stock i at the end of the previous month; (4) firm size, ln CAP im 1, which is thelogarithm of market capitalisation for stock i at the end of month m 1; (5) total risk,

STDim 1, which is the standard deviation of the daily return on stock i in month m 1(multiplied by 10 2); and (6) cash flow yield ( CP im 1), which is the ratio of earnings plusdepreciation per share in year y 1 divided by the share price for stock i at the end of month m 17 .

Beta is included in equation (4) to control for systematic risk. It is estimated usingthe FamaFrench (1992) methodology. However, stocks are ranked by their marketcapitalisation each month, instead of each year, and sorted into 25 portfolios. Themarket model is estimated using daily data for the previous 150 trading days of each portfolio, with the ScholesWilliams (1977) adjustment to obtain the portfolio beta.This portfolio beta is then assigned to each individual stock in the portfolio as its beta

7 Using annual BM and CP data for each month in a year does not qualitatively affect our results.


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risk for that month. The variable STDim 1 is also included, since investors portfoliosmay not be well diversified. Since expected stock returns may be affected by their pastreturns 8 , we include Ri Q1 and R

i Q2to control for a possible momentum or reversal

effect.We use ln CAP i

m 1 as a control for the well-known size effect. However, as documented

in the literature, size itself is often used as a proxy for liquidity. In our case, the Pearson(Spearman) correlation coefficient between our illiquidity measure and size measureis 0.635 ( 0.754) for the whole sample period (see Table 2). To avoid multicollinearity,we first make ln CAP im 1 orthogonal to illiquidity before including it in our cross-sectional regressions.

Chan et al. (1991) document BM i and CP i but not dividend yield as major determinantsof Japanese stock returns. Hence, our model includes BM i and CP i as control variables.

Panel A of Table 2 presents the summary statistics for all the variables described above and the correlation matrix between them. In each month, the cross-sectionalmean, standard deviation, skewness, median, minimum, and maximum are calculated for the sample stocks and then averaged over 378 months. The correlations between thevariables are presented in panel B of Table 2. Notice that the correlations are generallylow except for that between illiquidity and size, as mentioned earlier.

The regression results for equation (4) are reported in Table 3. The first to fourthcolumns show the results with only four independent variables, namely, illiquidity, firm beta, and two lagged quarterly return terms, in the regression, while the fifth througheighth columns show the results with all eight independent variables included. FollowingFama and MacBeth (1973), we estimate equation (4) for each month during our sample period from July 1975 to December 2006 (the first to fifth columns). The mean of theestimated coefficients is calculated for each independent variable, followed by a t-testconducted on the hypothesis that the mean of the coefficients is equal to zero. To controlfor the famous January effect 9 and to verify whether the cross-sectional relation is stableover time, tests are also performed for the sample excluding January (the second and sixth columns), and for the subsamples 19751989 (the third and seventh columns) and 19902006 (the fourth and eighth columns).

Fromthe first four columns, we see that the mean of the estimated illiquidity coefficientfor all months is 0.0014 and significant at the 5% level. When January is excluded, thecoefficient is 0.0013 and also significant at the 5% level. These results are consistentwith Amihuds (2002) and suggest the existence of a positive cross-sectional relation between illiquidity and stock returns in general. However, the relation appears unstableover the two subperiods. The mean illiquidity coefficient in the first subsample period is 0.0025, much larger compared to the whole sample result and highly significantat the 1% level, while it is less than 0.0004 for the second subsample period and not significant at all. In contrast, the results reported in Amihud (2002) show that theilliquidity is significant in both subsampleperiods. 10 Ourestimated meanbeta coefficientis negative, though not statistically significant, in all four-variable regression samples.However, the insignificant beta coefficient estimates in Japan are consistent with the

8 Bremer and Hiraki (1999) document that TSE stocks exhibit short-term price reversals.9

Hamori (2001) documents the January effect in Japan for the entire period between 1971and 1997 , although it tends to disappear later in the sample period.10 We also tried subsample periods 1975 1990 versus 1991 2006 and 1975 1988 versus1989 2006 . The results are similar.


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Table 2Summary statistics and correlation of stock characteristics

This table presents the summary statistics and correlation matrix for variables used in the cross-sectional regression. In Panel B, the upper triangular matrix reports the Spearman correlation and the

lower triangular matrix reports the Pearson correlation. Rim is the market return of stock i in monthm. The illiquidity measure, ILLim , is the average for month m of the daily ratio of absolute returns tothe trading value of stock i in month m. The variable im is the market beta for stock i in month m asestimated using the FamaFrench (1992) method with the ScholesWilliams (1977) adjustment; B M imis the most recent yearly book value of equity at the end of year y 1 (June) divided by the marketvalue of equity for stock i at the end of month m; CAP im is the market capitalisation of stock i at theend of month m; S TD im is the standard deviation of the return for stock i across days in month m; CP

im

is the ratio of earnings plus depreciation per share in year y 1 divided by the share price for stock iat the end of month m; Ri Q1 is stock returns over the last three months, and R

i Q 2 is the return from

month m 4 to month m 6. The period covers 19752006. The stocks included in the sample musthave valid observations of daily returns and trading values for more than 200 days in a year and more

than 15 days in a month, and month-end prices greater than 100. We multiply most variables by 100so that we can present the values with only three decimal places.

Panel A: Summary statistics

Mean of Median of Minimum of Maximum of Mean of Mean of monthly monthly monthly monthly monthly monthly

Variable means means means means St.dev. skewness

Rim (%) 1.143 1.291 20.726 23 .271 9.431 1.827 ILLim (%) 2.444 2.398 0.817 4.980 2.117 1.878 im 1.058 1.057 0.973 1.172 0.114 0.031 B M im 0.638 0.554 0.244 1.414 0.333 0.006CAP im (million ) 190,881 206,030 39,419 420,745 584960 10.610STD im (%) 2.417 2.312 1.735 3.531 0.730 0.874CP im (%) 6.992 6.142 3.128 11 .182 17 .865 7.349 Ri Q 1 (%) 3.192 4.116 32.968 39 .233 16 .484 2.156 Ri Q 2(%) 3 .151 4.092 33.605 39 .149 16 .434 2.151

Panel B: Correlations

Variable ILLim ln CAP im

im ST D

im CP

im B M

im R

i Q1 R

i Q2

ILLim 0.754 0.111 0.175 0.055 0.242 0.096 0.063

ln CAP im 0.635 0.166 0.246 0.175 0.337 0.059 0.060 im 0.011 0.057 0.130 0.044 0.004 0.025 0.022STD im 0.194 0.252 0.072 0.174 0.075 0.020 0.028CP im 0.019 0.015 0.015 0.064 0.290 0.042 0.024 B M im 0.235 0.342 0.015 0.069 0.035 0.155 0.151 Ri Q 1 0.082 0.040 0.004 0.065 0.000 0.138 0.019 Ri Q 2 0.053 0.039 0.001 0.066 0.004 0.132 0.019

finding of Hodoshima et al. (2000). On the other hand, Ri Q1 is negative and highlysignificant while Ri Q2is not, in all four samples, suggesting short-term price reversals

for Japanese stocks. This is inconsistent with Amihuds (2002) finding, that there has been a strong momentum effect for the past 100 days and even the past year. However,


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T a b l e 3

C r o s s - s e c t i o n a l i l l i q u i d i t y e f f e c t s o n s t o c k r e t u r n s

T h i s t a b l e p r e s e n t s t h e m e a n s o f t h e e s t i m a t e d c o e f f i c i e n t s a n d t h e c o r r e s p o n d i n g t - v a l u e s ( i n p a r e n t h e s e s ) f r o m t h e f o l l o w i n g m o n t h l y c r o s s - s e c t i o n a l r e g r e s s i o n

o f s t o c k r e t u r n s o n t h e r e s p e c t i v e v a r i a b l e s f o r v a r i o u s s a m p l e s :

R i m =

k 0 m

+ k 1

m I L L M i m

1 + k 2

m i m

1

+ k 3

m R i

Q 1

+ k 4

m R i

Q 2

+ k 5

m B M i m

1

+ k 6

m l n C A P i m

1 +

k 7 m

S T D i m

1

+ k 8

m C P i m

1

+ i m

w h e r e I L L M

i m

1 i s t h e m e a n - a d j u s t e d i l l i q u i d i t y f o r s t o c k i a c r o s s t h e d a y s i n m

o n t h m

1 ; i m

1 i

s t h e m a r k e t b e t a f o r s t o c k i i n m o n t h m

1 , w h i c h i s e s t i m a t e d

u s i n g t h e F a m a F r e n c h ( 1 9 9 2 ) m e t h o d w i t h t h e S c h o l e s W i l l i a m s ( 1 9 7 7 ) a d j u s t m e n t ; R i

Q 1

i s t h e s t o c k r e t u r n o v e r t h e l a s t t h r e e m o n t h s a n d R i

Q 2

i s t h e r e t u r n

f r o m m o n t h m

4 t o m o n t h m

6 ; B M i m

1 i s

t h e m o s t r e c e n t y e a r l y b o o k v a l u e o f e q u i t y a t t h e e n d o f y e a r y 1 d i v i d e d b y t h e m a r k e t v a l u e o f e q u i t y f o r s t o c k i

a t t h e e n d o f m o n t h m

1 ; l n C A P i m

1 i

s t h e l o g a r i t h m o f t h e m a r k e t c a p i t a l i s a t i o n f o r s t o c k i a t t h e e n d o f m o n t h m

1 a f t e r b e i n g m a d e o r t h o g o n a l t o I L L M i m

1 ;

S T D i m

1 i s

t h e s t a n d a r d d e v i a t i o n o f r e t u r n s f o r s t o c k i a c r o s s t h e d a y s o f m o n t h m

1 ( m u l t i p l i e d b y 1 0 2 ) ; a n d C P i m

1 i

s t h e r a t i o o f e a r n i n g s p l u s d e p r e c i a t i o n

p e r s h a r e i n y e a r y

1 d i v i d e d b y t h e s h a r e p r i c e f o r s t o c k i a t t h e e n d o f m o n t h m

1 . T h e m o n t h l y r e t u r n s a r e f r o m J u l y 1 9 7 5 t o D e c e m b e r 2 0 0 6 , a n d t h e s t o c k

c h a r a c t e r i s t i c s a r e f r o m J u n e 1 9 7 5 t o N o v e m b e r 2 0 0 6 . , a

n d d e n o t e s i g n i f i c a n c e a t t h e 1 % a n d 5 % l e v e l s , r e s p e c t i v e l y .

V a r i a b l e

A l l m o n t h s

E x c l . J a n

u a r y

1 9 7 5 1

9 8 9

1 9 9 0 2 0 0 6

A l l m o n t h s

E x c l . J

a n u a r y

1 9 7 5 1

9 8 9

1 9 9 0 2

0 0 6

C o n s t a n t

0 . 0 1 0 5

0 . 0 1 2 4

0 . 0 2 3 1

0 . 0

0 1 0

0 . 0 1 4 2

0 . 0 1 8 4

0 . 0 3 1 0

0 . 0 0 1 3

( 1 . 6

5 2 )

( 1 . 8 7 9

)

( 2 . 8

2 7 )

( 0 . 1

0 4 )

( 2 . 2

1 5 )

( 2 . 7

6 4 )

( 3 . 8

1 7 )

( 0 . 1 3 7 )

I L L M i m

1

0 . 0 0 1 4

0 . 0 0 1 3

0 . 0 0 2 5

0 . 0

0 0 4

0 . 0 0 1 9

0 . 0 0 1 6

0 . 0 0 2 6

0 . 0 0 0 6

( 2 . 3

1 1 )

( 2 . 1 6 2

)

( 2 . 6

7 8 )

( 0 . 5

0 4 )

( 2 . 8

5 5 )

( 2 . 5

0 9 )

( 2 . 8

3 4 )

( 0 . 7

4 1 )

i m

1

0 . 0 0 5 1

0 . 0 0 8 4

0 . 0 0 8 7

0 . 0

0 1 9

0 . 0 0 3 4

0 . 0 0 6 0

0 . 0 0 9 7

0 . 0 0 2 4

( 0 . 7 9 1 )

( 1 . 2 4 2 )

( 1 . 2 5 8 )

( 0 . 1

7 9 )

( 0 . 6 0 4 )

( 1 . 0 1 0 )

( 1 . 4 8 8 )

( 0 . 2

7 0 )

R i

Q 1

0 . 0 2 5 9

0 . 0 1 9 6

0 . 0 2 3 7

0 . 0

2 7 8

0 . 0 2 7 6

0 . 0 2 1 2

0 . 0 2 6 9

0 . 0 2 8 3

( 4 . 4 7 9 )

( 3 . 4 1 4 )

( 3 . 7 1 5 )

( 2 . 9

6 3 )

( 4 . 9 0 9 )

( 3 . 7 5 6 )

( 4 . 0 1 0 )

( 3 . 1 8 0 )

R i

Q 2

0 . 0 0 0 8

0 . 0 0 3 8

0 . 0 0 2 6

0 . 0

0 3 8

0 . 0 0 0 1

0 . 0 0 5 4

0 . 0 0 3 4

0 . 0 0 3 2

( 0 . 1 8 9 )

( 0 . 9 3 0

)

( 0 . 4

7 0 )

( 0 . 6

7 8 )

( 0 . 0 1 6 )

( 1 . 3

1 3 )

( 0 . 5

5 3 )

( 0 . 6 0 1 )

B M i m

1

0 . 0 1 8 1

0 . 0 1 7 9

0 . 0 2 5 4

0 . 0 1 1 3

( 6 . 4

1 5 )

( 5 . 9

4 6 )

( 4 . 2

9 4 )

( 3 . 7

3 7 )

l n C A P i m

1

0 . 0 0 1 3

0 . 0 0 0 6

0 . 0 0 2 2

0 . 0 0 0 4

( 1 . 3 9 2 )

( 0 . 8 8 7 )

( 1 . 5 2 2 )

( 0 . 5 3 1 )

S T D i m

1

0 . 0 0 1 8

0 . 0 0 3 3

0 . 0 0 1 5

0 . 0 0 2 0

( 1 . 5 3 0 )

( 2 . 8 7 9 )

( 1 . 0 3 2 )

( 1 . 1 3 8 )

C P i m

1

0 . 0 1 3 8

0 . 0 1 2 3

0 . 0 3 3 2

0 . 0 0 4 1

( 5 . 4 1 9 )

( 4 . 6 2 4 )

( 7 . 5 8 5 )

( 1 . 9

4 2 )


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it is consistent with Bremer and Hiraki (1999) that TSE stocks exhibit short-term pricereversals 11 .

When all eight independent variables are included, the results are largely the same,in the sense that the illiquidity coefficient is still positively and significantly related tothe stock returns in the whole sample, the sample with January excluded, and the firstsubsample period, but it is close to zero and insignificant in the second subsample period.The estimated beta coefficient is insignificant and mostly negative, and the lagged stock return Ri Q1 has a negative and significant impact on the current stock return in allsamples, while Ri Q2 does not.

For additional control variables, we find that coefficient estimates for ln CAP im 1 areconsistently insignificant and mostly negative in the fifth to eighth columns of Table 3.This may be due to the fact that the ln CAP im 1 included in the regression is only theresidual part that is orthogonal to our illiquidity measure. The estimated coefficient for STDim 1 is negative but mostly insignificant. The variable B M

im 1 has a positive and

significant impact on stock returns in all four samples, which is consistent with Chanet al. (1991). In addition, CP im 1 has a significant impact on stock returns; however, itssign is not consistent across samples: It is negative for the whole sample, the sampleexcluding January, and the first subsample period, but it is positive in the second subsampleperiod, again indicatingsomethinguniqueabout thesecond subsampleperiod.

On the whole, our results suggest that illiquidity is priced in the Japanese market, butnot in the second subsample period. This pattern is robust across different specifications.In fact, Chang et al. (2010) also find that the Amihud measure is unrelated to stock returns during the period 19902004. From Figure 1, we see that the first subsample period corresponds to a booming market trend with declining illiquidity, while thesecond subsample period coincides with a down and oscillating market and a trend of increasing and fluctuating illiquidity. Further examination of the monthly market excessreturns shows that, of the 180 months in the first subsample period, 115 are associated with positive market excess returns and 65 with negative market excess returns. Of the198 months in the second subsample period, only 97 are associated with positive marketexcess returns, and 101 with negative market excess returns. Therefore, the ratio of negative excess market return months to positive ones is much higher in the second subsample period (101/97) than in the f irst period (65/115).

Using Japanese stock return data from 1956 to 1995, Hodoshima et al. (2000) find thatregressing returns on beta without differentiating between positive and negative marketexcess returns leads to a flat relation between beta and returns. However, significantconditional positive or negative relations between beta and returns are found oncethe observations are separated into positive and negative market premium groups,where the positive and negative market premiums refer to Rm R f > 0 and Rm R f < 0, respectively. 12 The authors explain that the expected market excess return should

11 We also follow Amihud (2002) to include past 100-day returns and the returns of the pastyear minus the past 100-day returns in the regression. The results are largely the same; that is,we f ind negative and significant coefficients for the past 100-day returns, but insignificantcoefficients for further past returns.12 Chan and Lakonishok (1993), Grundy and Malkiel (1996), and Pettengill et al. (1995)investigate the relation between returns and beta by considering whether the market excessreturn is positive or negative in the US market. These authors find that beta and stock returnsare significantly related.


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never be negative, but actual observations used in the regression often are. Similarly,one can argue that the expected illiquidity premium should never be negative, butthe realised premium may well be so. If the realised illiquidity premium is positivelycorrelated with excess market returns, then the estimated relation between the Amihud measure and stock returns may be distorted. Therefore, we repeat the cross-sectionalregressions by discarding all months associated with the negative market premiumobservations to see if illiquidity and beta are priced, especially in the second subsample period.

Table 4 presents the estimation results. Consistent with Hodoshima et al. (2000), betais mostly positive and significant. However, estimated coefficients for illiquidity arestill qualitatively the same as those reported in Table 3. The coefficient of illiquidityremains insignificant in the second subsample period, whether for four- or eight-variable regressions. This suggests that the insignificant mean estimate for the illiquiditycoefficient in the second subsample period is not due to the concentration of morenegative excess market returns in the period.

The second subsample period may be special because it coincided with many changesin the Japanese financial system. Hamao et al. (2003) document that idiosyncraticvolatility in Japanese stocks has fallen, coinciding with a slowdown in the capitalallocation process within the Japanese economy. The authors opine that Japanesecorporate managers may have chosen to bail out large companies in their respectivekeiretsu rather than allocate capital to young companies, which caused the stock pricesof Japanese stocks in the 1990s to be more correlated than those of the 1980s. It is possible that corporate behaviour as well as investor risk tolerance may have undergonesome big changes in the 1990s, such that illiquidity risk was not captured by the Japanesedata during this period.

We also repeat the regressions for the months when the market premium is negative. Asexpected, beta is mostly negative and significant, but the estimated illiquidity coefficientremains insignificant in the second subsample period. We further perform a few morerobustness checks: (1) We sort the portfolios annually rather than monthly for betaestimation and use daily returns in the previous year to estimate the beta; (2) we useannual data to compute BM and CP, as in Chan et al. (1991); and (3) we use anindividual firm illiquidity measure without scaling with market illiquidity. All thesefactors do not qualitatively affect our results, which are not reported here to savespace.

4. Time Series Relation between Illiquidity and Stock Returns

Amihud (2002) argues that stocks are not only riskier but also less liquid than short-term treasury securities. Hence, stock returns in excess of the T-bill rate (risk premium)include a premium for illiquidity. It follows that if investors anticipate higher marketilliquidity, they will expect higher returns. More specifically, expected stock returnsshould be positively related to expected illiquidity, while unexpected illiquidity should be negatively related to contemporaneous stock returns.

We use the following AR(1) model to generate the expected and unexpected marketilliquidity:

ILL M m P M m 1 = c0 + c1 ILL

M m 1 P

M m 1 + vm (6)


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T a b l e 4

C r o s s - s e c t i o n a l i l l i q u i d i t y e f f e c t s o n s t o c k r e t u r n s f o r m o n t h s w i t h p o s i t i v e m a r k e t p r e m i u m

T h i s t a b l e p r e s e n t s t h e m e a n s o f t h e e s t i m a t e d c o e f f i c i e n t s a n d c o r r e s p o n d i n g t - v a l u e s ( i n p a r e n t h e s e s ) f r o m t h e f o l l o w i n g m o n t h l y c r o s s - s e c t i o n a l r e g r e s s i o n o f

s t o c k r e t u r n s o n t h e r e s p e c t i v e v a r i a b l e s f o r v a r i o u s s a m p l e s :

R i m =

k 0 m

+ k 1

m I L L M i m

1 + k 2

m i m

1

+ k 3

m R i

1 Q

+ k 4

m R i

Q 2

+ k 5

m B M i m

1

+ k 6

m l n C A P i m

1 +

k 7 m

S T D i m

1

+ k 8

m C P i m

1

+ i m

O n l y m o n t h s w i t h a p o s i t i v e m a r k e t p r e m i u m

a r e i n c l u d e d i n t h e r e g r e s s i o n . H e r e , I L L M i m

1 i

s t h e m e a n - a d j u s t e d i l l i q u i d i t y f o r s t o c k i a c r o s s t h e d a y s i n m o n t h

m

1 ; i m

1 i s t h e m a r k e t b e t a f o r s t o c k i i n m o n t h m

1 a s e s t i m a t e d u s i n g t h e F a m a F r e n c h ( 1 9 9 2 ) m e t h o d w i t h t h e S c h o l e s W

i l l i a m s ( 1 9 7 7 ) a d j u s t m e n t ; R i

Q 1

i s s t o c k r e t u r n s o v e r t h e l a s t t h r e e m o n t h s a n d R i

Q 2

i s t h e r e t u r n f r o m m o n t h s m

4 t o m

6 ; B M i m

1

i s t h e m o s t r e c e n t y e a r l y b o o k v a l u e o f e q u i t y a t t h e e n d

o f y e a r y 1 ( J u n e ) d i v i d e d b y t h e m a r k e t v a l u e o f e q u i t y f o r s t o c k i a t t h e e n d o f m o n t h m

1 ; l n C A P i m

1

i s t h e l o g a r i t h m o f t h e m a r k e t c a p i t a l i s a t i o n f o r s t o c k

i a t t h e e n d o f m o n t h m

1 a f t e r m a d e o r t h o g o n a l t o I L L M i m

1 ;

S T D i m

1

i s t h e s t a n d a r d d e v i a t i o n o f r e t u r n s f o r s t o c k i a c r o s s t h e d a y s o f m o n t h m

1 ( m u l t i p l i e d

b y 1 0 2 ) ; a n d C P i m

1

i s t h e r a t i o o f e a r n i n g s p l u s d e p r e c i a t i o n p e r s h a r e i n y e a r y

1 d i v i d e d b y t h e s h a r e p r i c e f o r s t o c k i a t t h e e n d o f m o n t h m 1 . T h e m o n t h l y

r e t u r n s a r e f r o m J u l y 1 9 7 5 t o D e c e m b e r 2 0 0 6 , a n d t h e s t o c k c h a r a c t e r i s t i c s a r e f r o m J u n e 1 9 7 5 t o N o v e m b e r 2 0 0 6

. , a

n d d e n o t e s i g n i f i c a n c e a t t h e 1 % a n d 5 %

l e v e l s , r e s p e c t i v e l y .

V a r i a b l e

A l l m o n t h s

E x c l . J a n

u a r y

1 9 7 5 1

9 8 9

1 9 9 0 2 0 0 6

A l l m o n t h s

E x c l . J

a n u a r y

1 9 7 5 1

9 8 9

1 9 9 0 2

0 0 6

C o n s t a n t

0 . 0 1 5 9

0 . 0 1 7 8

0 . 0 4 2 6

0 . 0

1 3 8

0 . 0 0 6 8

0 . 0 1 0 6

0 . 0 3 3 5

0 . 0 2 1 0

( 1 . 8

1 7 )

( 1 . 9 0 9

)

( 4 . 8

4 3 )

( 0 . 9

1 0 )

( 0 . 7

9 7 )

( 1 . 1

8 6 )

( 3 . 5

0 5 )

( 1 . 5 1 6 )

I L L M i m

1

0 . 0 0 3 7

0 . 0 0 3 4

0 . 0 0 6 1

0 . 0

0 1 2

0 . 0 0 2 7

0 . 0 0 2 8

0 . 0 0 5 3

0 . 0 0 0 1

( 3 . 9

1 7 )

( 3 . 3 0 7

)

( 4 . 5

3 0 )

( 0 . 8

7 4 )

( 2 . 7

3 8 )

( 2 . 6

7 7 )

( 3 . 9

6 0 )

( 0 . 0 7 6 )

i m

1

0 . 0 2 1 7

0 . 0 1 9 2

0 . 0 0 9 4

0 . 0

5 6 4

0 . 0 1 7 5

0 . 0 1 5 9

0 . 0 0 6 0

0 . 0 2 9 5

( 2 . 5

9 4 )

( 2 . 1 7 6

)

( 1 . 3 2 6 )

( 3 . 7

2 7 )

( 3 . 0

9 6 )

( 2 . 5

8 5 )

( 1 . 0

2 0 )

( 3 . 0

5 0 )

R i

Q 1

0 . 0 1 9 0

0 . 0 1 9 0

0 . 0 0 4 5

0 . 0

3 5 2

0 . 0 1 8 8

0 . 0 1 8 2

0 . 0 0 6 3

0 . 0 3 1 7

( 4 . 4 5 7 )

( 4 . 6 6 9 )

( 1 . 0 4 3 )

( 4 . 8

1 9 )

( 4 . 8 3 4 )

( 4 . 7 4 3 )

( 1 . 4 1 9 )

( 5 . 1 4 5 )

R i

Q 2

0 . 0 0 2 8

0 . 0 0 4 4

0 . 0 1 2 7

0 . 0

2 0 1

0 . 0 0 5 3

0 . 0 0 5 4

0 . 0 0 8 3

0 . 0 1 9 5

( 0

. 5 3 3 )

( 0 . 7 9 4 )

( 1 . 7

6 4 )

( 2 . 6

9 6 )

( 1 . 0 2 7 )

( 0 . 9 9 6 )

( 1 . 1

0 2 )

( 2 . 8 8 0 )

B M i m

1

0 . 0 0 3 8

0 . 0 0 3 7

0 . 0 0 4 5

0 . 0 0 3 0

( 1 . 1

9 5 )

( 1 . 0

7 3 )

( 0 . 8

9 3 )

( 0 . 8

0 4 )

l n C A P i m

1

0 . 0 0 3 1

0 . 0 0 2 7

0 . 0 0 3 4

0 . 0 0 2 7

( 3 . 4 4 2 )

( 2 . 7 9 7 )

( 2 . 3 8 4 )

( 2 . 5 6 5 )

S T D i m

1

0 . 0 0 8 4

0 . 0 0 6 8

0 . 0 0 4 0

0 . 0 1 3 0

( 6 . 2

6 0 )

( 5 . 1

5 7 )

( 2 . 4

9 3 )

( 6 . 2

5 5 )

C P i m

1

0 . 0 0 1 3

0 . 0 0 0 3

0 . 0 0 1 3

0 . 0 0 4 0

( 0 . 3 5 8 )

( 0 . 0 6 4 )

( 0 . 1

9 1 )

( 1 . 2 1 3 )


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where ILL M m is the monthly market illiquidity and vm is the residual representing theunexpected market illiquidity ILLU M m . We do not use logarithmic transformations for illiquidity, because its square root is already transformed, as described in the previoussection. The variable P M m 1 is the ratio of the capitalisation of the market portfolio at theend of month t 1 to that at the end of June 1975. A potential problem with using theAmihud illiquidity measure in the time series regression is that it is measured in percent per 1 million. As pointed out by Acharya and Pedersen (2005), the Amihud measuremay be non-stationary ( e.g. , inflation is ignored); however, we want to relate it to stock returns, which are stationary. This is not an issue in cross-sectional regressions, but it isin time series regressions. Multiplying ILL M m with P

M m 1 can make the illiquidity measure

relatively stationary. Following Acharya and Pederson (2005), we use the same monthof the market index ( P M m 1) to adjust for the illiquidity measure in months m and m 1.This is to ensure that we are measuring expected and unexpected illiquidity rather thanthe change in market index.

Let us define adjusted illiquidity in month m as AILL M m = ILL M m P

M t 1 , and that in month

m 1 as AILL M m 1 = ILL M m 1 P M t 1 . The expected illiquidity after adjustment AILLE M m inmonth m is determined by

AILLE M m = c0 + c1 AILL M m 1 (7)

Then the expected market excess return is generated by

R M m R f m = f 0 + f 1 AILLE

M m + um = g 0 + g 1 AILL

M m 1 + um (8)

where g 0 = f 0 + f 1c0, g 1 = f 1c1 , R M m is the return of the market portfolio M (all stocksin our sample) in month m,13 and R f m is the monthly call money rate, or one-monthGensaki rate, for month m, as in Chan et al. (1991), which can be retrieved from themonthly key economic file in the PACAP Database. The term um can be decomposed intothe unexpected illiquidity ILLU M m (or AILLU

M m ) and an error term wm. After controlling

for the January effect, the time series regression of excess market returns on marketilliquidity is 14

R M m R f m = g 0 + g 1 AILL

M m 1 + g 2 AILLU

M m + g 3 JAN m + wm (9)

The two testable hypotheses are as follows.

Hypothesis 1: Expected market illiquidity is positively related to expected market excessreturn, that is, g 1 > 0. Hypothesis 2: Unexpected market illiquidity is negatively related to contemporaneousmarket excess returns, that is, g 2 < 0.

Amihud (2002) further proposes and tests the flight to liquidity hypothesis. Increasesin expected market illiquidity have two effects on expected stock returns: On the onehand, the stock price declines and expected returns rise for all stocks; on the other hand,capital flies from less liquid to more liquid stocks. These two effects reinforce each other

13 It is calculated as the log difference of two consecutive month-end daily closing prices.14 A similar specification has been used by French et al. (1987) in testing the effect of risk on excess stock returns.


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for illiquid stocks, but offset each other for liquid ones. Increasing market illiquiditynot only negatively affects prices for illiquid stocks but also induces investors to switchto more liquid stocks, which further depresses the price for illiquid stocks. However,increasing market illiquidity leads to an increase in demand for liquid stocks, whichmitigates their price decline. Therefore, the illiquidity effect should be stronger for small stocks and weaker for large stocks because firm size is negatively correlated withilliquidity. Replacing market portfolio return series with size portfolio return series, 15

we can rewrite equation (9) as

R P m R f m = g

P 0

+ g P 1 AILL P m 1 + g

P 2 AILLU P m + g

P 3 JAN m + w

P m

(10)

where p denotes one of the 10 size-based portfolios (portfolio 10 contains the largeststocks) and R pm is the average return across stocks in portfolio p for month m. Thetestable hypotheses are as follows.

Hypothesis 3: The expected illiquidity effect g p1

should be positive but decrease as portfolio size increases, that is, g 21 > g

41 > g

61 > g

81 > g

101 > 0 .

Hypothesis 4: The unexpected illiquidity effect g p2 should be negative but increase as portfolio size increases, that is, g 22 < g

42 < g

62 < g

82 < g

102 < 0 .

Table 5 presents the estimation results for the whole sample period from July 1975to December 2006 (378 months). Several observations are evident. First, expected illiquidity AILL pm 1 has a positive and significant impact on the expected return for thewhole market, as well as for all portfolios; however, there is no monotonically decreasing pattern for the estimated coefficients across size portfolios. This is consistent with H1,that expected illiquidity should be positively and significantly related to expected stock returns, but inconsistent with H3, that expected illiquidity effect should decrease withfirm size. Second, unexpected illiquidity AILLU pm is negatively associated with expected stock returns, and the estimated coefficient is significant and monotonically increasingwith firm size. This finding is consistent with both H2, that contemporaneous stock returns are negatively associated with unexpected illiquidity, and H4, that the unexpected illiquidity effect is negative and increases with firm size. Finally, we find that the Januaryeffect is more significant for smaller stock portfolios but insignificant for the portfoliowith the largest firms. These results are consistent with the findings in Amihud (2002),except we do not find a monotonically decreasing coefficient for expected illiquiditywith increasing firm size.

Table 6 further presents the results for the two subsample periods. These results areconsistent across the two subsample periods and also consistent with the results inTable 5. However, it is worth mentioning that the estimated coefficient for expected illiquidity is much larger in the first subsample period than in the second subsample period, whereas for unexpected illiquidity, it is much smaller in the first subsample period (more negative). This suggests that expected illiquidity is priced less whileunexpected illiquidity is priced more in the Japanese stock market in the second subsample period than in the first subsample period. This finding may be related with that in Section 3, that illiquidity levels are priced in the first subsample period, but not in the second. The illiquidity measure used in the cross-sectional regressionsis the lagged level of illiquidity, which is similar to the expected illiquidity used in

15 The 10 size portfolios are the same as those formed in Section 3.


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Table 5Time series illiquidity effects on stock returns

This table presents time series regression results for the market, as well as size-sorted portfolios. Theregression equation is

R P m R f m = g

P 0


P 2 AILLU P m + g

P 3 JAN m + w

P m

where R pm is the monthly equally weighted size portfolio return and p = 2, 4, 6, 8, and 10. Of course,when p = M , it is the equally weighted market return. Here, R f m is the one-month Gensaki monthly rate, AILL pm 1 is the expected monthly portfolio illiquidity, AILLU

pm is the unexpected monthly portfolio

illiquidity, and JAN m is a January dummy that equals one in January and zero otherwise. The sample period is from July 1975 to December 2006. , and denote significance at the 1% and 5% levels,respectively.

Portfolio Constant AILLm 1 AILLU m JAN m R 2

Market 0 .075 0.022 0.084 0.026 0.161(3.767) (5 .275) ( 5.935) (2 .340) (0 .154)

Portfolio 2 0 .060 0.020 0.132 0.048 0.197(2.477) (3 .908) ( 7.677) (3 .512) (0 .190)

Portfolio 4 0 .072 0.022 0.107 0.038 0.175(3.207) (4 .636) ( 6.687) (2 .996) (0 .168)

Portfolio 6 0 .074 0.021 0.091 0.031 0.157(3.450) (4 .867) ( 5.987) (2 .606) (0 .150)

Portfolio 8 0 .082 0.023 0.071 0.018 0.142(4.153) (5 .639) ( 5.025) (1 .586) (0 .135)

Portfolio 10 0 .081 0.022 0.052 0.013 0.118(4.271) (5 .677) ( 3.837) (1 .207) (0 .111)

this section, albeit the former is for individual stocks while the latter is for the wholemarket or size portfolios. However, we are unable to fully explain why liquidity is priced less in the second subsample period, which deserves further exploration in futureresearch.

We also perform the following robustness checks. First, Kendall (1954) points outthat the estimated coefficient c1 from the finite samples is biased downward in AR(1)models such as equation (7). The author proposes a simple but accurate bias correctionapproximation procedure:Augment the estimated coefficient c1 by the term (1 + 3c1)/ T ,where T is the sample size. We apply Kendalls bias correction in the computation of unexpected illiquidity. Second, we include the term yield premium in the estimation. 16

Third, we repeat the same tests using portfolios formed on the BM rather than marketcapitalisation. None of these checks qualitatively change the results reported in Tables 5and 6. The results are available upon request.

16 The term yield premium TM m = YLm RG 3m is computed as the difference between theyield to maturity of 10-year government bonds ( YLm) and the three-month Gensaki rate inmonth m ( RG 3m ). The default yield premium is not included in the regression because we donot have the data for Japan.


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Table 6Time series illiquidity effects on stock returns for the two subsample periods

This table presents time series regression results for the market, as well as size-sorted portfolios. Theregression equation is

R P m R f m = g

P 0


P 2 AILLU P m + g

P 3 JAN m + w

P m

where R pm is the monthly equally weighted size portfolio return and p = 2, 4, 6, 8, and 10. Of course,when p = M , it is the equally weighted market return. Here, R f m is the one-month Gensaki monthly rate, AILL pm 1 is the expected monthly portfolio illiquidity, AILLU

pm is the unexpected monthly portfolio

illiquidity, and JAN m is a January dummy that equals one in January and zero otherwise. Panel Areports the results for the first subsample period, July 1975 to December 1989, and Panel B presents theresults for the second subsample period, January 1990 to December 2006. , and denote significanceat the 1% and 5% levels, respectively.

Panel A: 19751989

Portfolio Constant AILLm 1 AILLU m JAN m R 2

Market 0 .086 0.026 0.064 0.035 0.168(1.562) (2 .424) ( 3.616) (3 .045) (0 .154)

Portfolio 2 0 .070 0.023 0.108 0.058 0.245(1.050) (1 .794) ( 5.097) (4 .248) (0 .233)

Portfolio 4 0 .085 0.026 0.084 0.045 0.192(1.340) (2 .112) ( 4.155) (3 .465) (0 .178)

Portfolio 6 0 .094 0.027 0.071 0.041 0.182(1.581) (2 .398) ( 3.738) (3 .409) (0 .168)

Portfolio 8 0 .113 0.031 0.053 0.027 0.129(1.914) (2 .738) ( 2.809) (2 .249) (0 .115)

Portfolio 10 0 .095 0.027 0.032 0.018 0.074(1.625) (2 .397) ( 1.712) (1 .542) (0 .058)

Panel B: 19902006

Market 0 .033 0.010 0.101 0.020 0.130(1.148) (1 .535) ( 4.831) (1 .092) (0 .116)

Portfolio 2 0 .029 0.011 0.149 0.040 0.175(0.804) (1 .325) ( 5.774) (1 .739) (0 .161)

Portfolio 4 0 .033 0.011 0.124 0.033 0.152(1.027) (1 .459) ( 5.262) (1 .572) (0 .139)

Portfolio 6 0 .032 0.009 0.095 0.019 0.115

(1.080) (1 .436) ( 4.502) (1 .005) (0 .101)Portfolio 8 0 .034 0.010 0.086 0.011 0.105

(1.227) (1 .553) ( 4.290) (0 .601) (0 .091)Portfolio 10 0 .036 0.010 0.069 0.010 0.082

(1.371) (1 .647) ( 3.615) (0 .575) (0 .068)

5. Liquidity Risk and Stock Returns

Following Acharya and Pedersen (2005), this section tests if liquidity risk is priced over and above the illiquidity level and the market risk in Japan. We define a one-beta CAPM

for net returns as

E t Rit + 1 C it + 1 = R

f + t cov t Rit + 1 C

it + 1 , R

M t + 1 C

M t + 1

var t R M t + 1 C M t + 1

(11)


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where Rit = d it + p

it

pit 1is the expected gross return of an asset; C it =

cit pit 1

is the relative

illiquidity cost; R M t =i s

i (d it + pit )

i s i pit 1

is the market return; C M t =i s

i c it i s i p

it 1

is the relativemarket illiquidity; d it and c

it refer to the dividend paid and illiquidity cost (the cost of

selling the asset) incurred for security i during each time t , respectively; pit denotes the

price for security i at the end of time t; s i denotes the number of shares for security i; and = E ( R M t C

M t R

f ) is the risk premium after the illiquidity cost. Further expandingand rewriting equation (11), we obtain the following liquidity-adjusted CAPM: 17

E t Rit + 1 = R f + E t C it + 1 + t

cov t Rit + 1 , R M t + 1


+ t covt C it + 1 , C

M t + 1


t covt Rit + 1 , C

M t + 1


t covt C it + 1, R

M t + 1


(12)

Assuming constant conditional covariances of innovations in illiquidity and returns,we can express equation (12) as

E Rit R f t = E C

it +

1i + 2i 3i 4i (13)

This simple theoretical framework suggests that (1) the liquidity risk affects asset pricesthrough the last three terms in the equation and (2) the effects of the liquidity level E t (C it + 1) and the liquidity risk are separate. The market risk is captured by

1 p. Thethree liquidity risk factors are commonality in liquidity, 2 p, individual stock returnsensitivity to market illiquidity, 3 p, and individual stock illiquidity sensitivity to marketreturn, 4 p.

Commonality in liquidity,cov t 1(C it , C M

t ), should be positively associated with ex-

pected returns because investors need to be compensated for the risk that their assetsmay become illiquid when the market as a whole is illiquid. Individual return sensitivityto market illiquidity, cov t 1( Rit , C

M t ), should have a negative impact on expected returns

because investors are willing to accept lower returns on assets normally associated withhigh returns in times of market illiquidity. Individual illiquidity sensitivity to marketreturns,cov t 1(C it , R

M t ), should also have a negative impact on expected returns because

investors are willing to accept lower returns on assets with higher liquidity when marketreturns are low.

Using Center for Research in Security Prices (CRSP) data from 1962 to 1999, Acharyaand Pedersen (2005) show that the required return of a security i does increase in thecovariance between its illiquidity and market illiquidity,cov t 1(C it , C M t ), and decreasesin the covariance between the securitys return and market illiquidity, cov t 1( Rit , C

M t ), as

well as its illiquidity and market return, cov t 1(C it , R M t ). In addition, the authors show

that the liquidity-adjusted CAPM explains the data better than the standard CAPM.Furthermore, they present evidence that liquidity risk is important over and above theeffects of market risk and the level of liquidity.

To estimate illiquidity costs and various betas, we first compute the return and normalised illiquidity cost for each firm each month. The normalised illiquidity cost of selling over the ex-dividend price ( cit / p

it 1) is proxied by the transformation of Amihuds

measure, as suggested by Acharya and Pedersen (2005). Second, we form a market portfolio and 25 test portfolios sorted on the basis of illiquidity or BM and compute their

17 For the models assumptions and derivation details, see Acharya and Pedersen (2005) .


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monthly returns and normalised illiquidity. Third, we estimate illiquidity innovations,and thus liquidity betas, for each portfolio. We then test the liquidity-adjusted CAPM by applying the generalised method of moments (GMM) to estimate equation (13) and its variations. 18

Table 7 reports the estimated betas and other properties for odd-numbered illiquidity-sorted portfolios: Panel A presents the results for the whole sample period 19752006, 19while panels B and C present the results for the first (19751989) and second (19902006) subsample periods, respectively.

We see in panel A of Table 7 that a sort on past illiquidity produces portfolios withmonotonically increasing average illiquidity ( E (C p)) and the commonality in illiquidity beta ( 2p ) from portfolios 1 through 25 20 but with a largely decreasing portfolio returnsensitivity to market illiquidity ( 3p ) and illiquidity sensitivity to market returns ( 4p )from portfolios 1 through 25. All portfolio betas have predicted signs with significantt-values. According to Acharya and Pedersen (2005), such an association between theilliquidity level and the liquidity betas supports the flight to liquidity hypothesis. Thatis, the higher the illiquidity level, the higher the illiquidity risk.

In addition, we see that stocks with higher average illiquidity tend to have a higher market beta ( 1 p), a higher volatility of illiquidity innovation ( ( c p)), higher BM,a higher volatility of portfolio returns ( ( R p)), smaller market capitalisation ( CAP ),and lower trading turnover. More importantly, we find that the portfolio excess return E ( R p R f ) exhibits an increasing, though not monotonically, trend with the illiquidity-sorted portfolios. All these findings are very consistent with theoretical predictions, aswell as the empirical findings in Acharya and Pedersen (2005).

The subsample results reported in panels B and C of Table 7 are qualitatively thesame, except that portfolio excess returns in the second subsample period do not show aclear trend with illiquidity-sorted portfolios. This echoes the finding in previous sectionsthat the liquidity effect in the second subsample period is weaker in the Japanese stock market.

We also compute similar statistics for odd-numbered portfolios sorted by a standard deviation of the illiquidity. The results are generally the same as those presented inTable 7. We further compute the betas for portfolios sorted by BM . Again the results arelargely the same. These results are available upon request.

The correlation matrices for the betas of illiquidity-sorted portfolios in the wholesample period as well as subsample periods are shown in Table 8. We find high and significant correlation coefficients between these betas, as shown in Table 8. This is not

surprising, given the results in Table 7, but it does suggest that we face a multicollinearity problem when estimating equation (13). 21

Table 9 presents the GMM estimates of equation (13) and its variations. Panel A of Table 9 reports the regressions for illiquidity-sorted portfolios for the whole sample

18 The GMM point estimates are the same as those derived using ordinary least squares, either in a pooled regression or using the FamaMacBeth (1973) method. However, the GMM ismore efficient because it takes into account possible heteroskedasticity and serial correlation.19 We use the entire time series to compute the four betas, as Black et al. (1990) and Pastor and Stambaugh (2003) do. Therefore, they are not directly comparable to the yearly betascomputed in Section 3.20 Portfolio 1 is the least illiquid, while portfolio 25 is the most illiquid.21 Acharya and Pedersen (2005) find even higher correlation coefficients between these four betas.


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T a b l e 7

P o r t f o l i o p r o p e r t i e s

T h i s t a b l e r e p o r t s t h e p r o p e r t i e s o f t h e o d d - n u m b e r e d i l l i q u i d i t y - s o r t e d p o r t f o l i o s f o r m e d e a c h y e a r d u r i n g 1 9 7 5 2

0 0 6 . T h e m a r k e t b e t a ( 1 p ) a n d t h e l i q u i d i t y

b e t a s (

2 p ,

3 p , a

n d

4 p ) a r e c o m p u t e d u s i n g t h e m o n t h l y r e t u r n s a n d i l l i q u i d i t y o b s e r v a t i o n s o f e a c h t e s t p o r t f o l i o a n d t h e e q u a l l y w e i g h t e d m a r k e t p o r t f o l i o f o r

t h e w h o l e p e r i o d a s w e l l a s f o r t h e t w o s u b p e r i o d s

. T h e s t a n d a r d d e v i a t i o n o f i l l i q u i d i t y i n n o v a t i o n s i s r e p o r t e d i n t h e c o l u m n f o r ( c p ) . T h e a v e r a g e i l l i q u i d i t y

E ( C p ) , t h e a v e r a g e e x c e s s r e t u r n E ( R p

R f )

, t h e a v e r a g e t u r n o v e r ( T R N ) , t h e a v e r a g e m a r k e t c a p i t a l i s a t i o n ( C A P ) , a n d t h e a v e r a g e b o o k - t o - m a r k e t r a t i o ( B M )

a r e a l s o c o m p u t e d f o r e a c h p o r t f o l i o a s t i m e s e r i e s a v e r a g e s o f t h e r e s p e c t i v e m o n t h l y c h a r a c t e r i s t i c s . H e r e

( R p ) i s t h e a v e r a g e o f t h e s t a n d a r d d e v i a t i o n o f d a i l y

r e t u r n s f o r t h e p o r t f o l i o s c o n s t i t u e n t s t o c k s c o m p u t e d e a c h m o n t h . T

h e t - s t a t i s t i c s a r e r e p o r t e d i n p a r e n t h e s e s . S i n c e t h e m a g n i t u d e s o f t h e e s t i m a t e d

2 p ,

3 p , a

n d

4 p a r e s m a l l , w e m u l t i p l y a l l e s t i m a t e d b e t a s b y 1 0 0 .

P a n e l A :

1 9 7 5 2

0 0 6

1 p

2 p

3 p

4 p

E ( C p )

( c p )

E ( R p

R f )

( R p )

T R N

C A P

P o r t f o l i o

( 1 0 0 )

( 1 0 0 )

( 1 0 0 )

( 1 0 0 )

( % )

( % )

( % )

( % )

( % )

( b i l l i o n )

B M

1

5 9 . 3

8 ( 1 4 . 2 5 )

0 . 0 0 0 0 ( 6

. 8 4 )

0 . 4 4 ( 5 . 2 9 )

0 . 0 0 ( 9

. 3 9 )

0 . 2 5

0 . 0 0

0 . 5 4

1 . 9 4

6 . 3 3

2 0 5 1

. 3 9

0 . 4 1

3

7 9 . 5

0 ( 2 7 . 1 6 )

0 . 0 0 0 3 ( 1 0 . 2 5 )

0 . 4 9 ( 6 . 1 2 )

0 . 0 2 ( 1 0

. 2 9 )

0 . 2 6

0 . 0 0

0 . 5 3

2 . 0 7

6 . 7 4

4 4 7 . 5 3

0 . 4 7

5

8 7 . 3

9 ( 3 6 . 3 3 )

0 . 0 0 0 7 ( 1 4 . 1 1 )

0 . 6 0 ( 7 . 4 6 )

0 . 0 4 ( 1 0

. 6 4 )

0 . 2 6

0 . 0 0

0 . 4 6

2 . 1 6

6 . 4 7

2 3 6 . 8 6

0 . 5 0

7

9 1 . 8

5 ( 4 1 . 9 3 )

0 . 0 0 1 4 ( 1 6 . 2 6 )

0 . 5 9 ( 7 . 1 8 )

0 . 0 7 ( 1 1

. 4 3 )

0 . 2 7

0 . 0 1

0 . 4 9

2 . 2 0

5 . 7 9

1 6 4 . 3 4

0 . 5 7

9

9 9 . 3

3 ( 4 7 . 1 0 )

0 . 0 0 2 6 ( 2 0 . 3 1 )

0 . 6 5 ( 7 . 4 0 )

0 . 1 1 ( 1 1

. 8 9 )

0 . 2 9

0 . 0 1

0 . 6 7

2 . 2 6

6 . 0 2

1 2 4 . 9 0

0 . 5 9

1 1

1 0 2 . 0 0 ( 5 3 . 9 5 )

0 . 0 0 4 3 ( 2 0 . 2 4 )

0 . 6 8 ( 7 . 7 9 )

0 . 1 6 ( 9 . 8 2 )

0 . 3 1

0 . 0 2

0 . 3 7

2 . 2 5

5 . 4 4

8 9 . 5

1

0 . 6 2

1 3

1 0 5 . 6 3 ( 5 2 . 7 6 )

0 . 0 0 7 5 ( 2 5 . 4 6 )

0 . 7 7 ( 8 . 6 1 )

0 . 2 8 ( 1 0

. 6 2 )

0 . 3 4

0 . 0 3

0 . 5 9

2 . 2 8

5 . 4 5

7 2 . 6

4

0 . 6 7

1 5

1 0 2 . 6 7 ( 5 3 . 7 5 )

0 . 0 1 1 3 ( 2 4 . 4 3 )

0 . 7 7 ( 8 . 9 4 )

0 . 3 7 ( 9 . 0 5 )

0 . 3 9

0 . 0 5

0 . 7 2

2 . 3 0

5 . 0 3

6 2 . 9

2

0 . 6 9

1 7

1 0 1 . 9 5 ( 5 4 . 1 1 )

0 . 0 1 7 9 ( 2 8 . 8 7 )

0 . 7 4 ( 8 . 5 6 )

0 . 5 2 ( 8 . 3 5 )

0 . 4 6

0 . 0 7

0 . 5 6

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