The Impact of Short-Sales Constraints on Liquidity and the Liquidity–Return Relations

Pacific-Basin Finance Journal 18 (2010) 521–535

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Pacific-Basin Finance Journal j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p a c f i n

The Impact of Short-Sales Constraints on Liquidity and the Liquidity–Return Relations☆ Wen-I Chuang a, Hsiu-Chuan Lee b,⁎ a b

Department of Finance, National Taiwan University, Taipei, Taiwan, ROC Finance Department, Ming Chuan University, Taipei, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 22 September 2009 Accepted 29 July 2010 Available online 6 August 2010 JEL classification: G10 G12 Keywords: Short-sales constraints Liquidity Sentiment indicator Commonality

a b s t r a c t Baker and Stein's (2004) model predicts that individual stock liquidity, commonality in liquidity across stocks, the contemporaneous correlation between stock returns and liquidity, and the degree of high liquidity associated with low subsequent stock returns decrease in the absence of short-sales constraints relative to in the presence. To test these theoretical predictions, we examine both the component stocks of the Taiwan 50 index and other nonindex stocks for the sample period before and after the removal of short-sales constraints on the former and use trading turnover and Amihud's (2002) illiquidity ratio as the measure of liquidity to proxy for investor sentiment. Overall, our empirical results are consistent with these theoretical predictions and therefore provide evidence in support of Baker and Stein's (2004) model. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction Using liquidity as a sentiment indicator for predicting stock returns has recently gained increasing attention in the literature.1 For example, Baker and Stein (2004) develop a model to explain why increases in liquidity predict lower subsequent stock returns. They show that, in the presence of short-sales constraints, liquidity increases with investor sentiment and high liquidity indicates that the market is

☆ The authors would like to thank an anonymous referee for helpful comments and suggestions that significantly improved this paper. The work of W.-I. Chuang was supported in part by the Center for Research in Econometric Theory and Applications (CRETA), National Taiwan University, Taiwan. All remaining errors are the authors’ own responsibility. ⁎ Corresponding author. 250 Zhong-Shan N. Rd., Sec. 5, Taipei, Taiwan, ROC. Tel.: +886 2 2882 4564x2188; fax: +886 2 2880 9796. E-mail address: [email protected] (H.-C. Lee). 1 Another important role taken by liquidity in the literature is that it is a priced risk factor. For example, the theoretical models of Amihud and Mendelson (1986) and Pastor and Stambaugh (2003) show that liquidity is a priced risk factor, and empirical studies find supporting evidence that expected returns increase in illiquidity (e.g., Amihud and Mendelson, 1986; Haugen and Baker, 1996; Eleswarapu, 1997; Datar et al., 1998; Chordia et al., 2001; Amihud, 2002). 0927-538X/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.pacfin.2010.07.003

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dominated by irrational investors, and thence is overvalued. Consequently, liquidity can be used as a sentiment indicator to predict stock returns. Scheinkman and Xiong (2003), Baker and Wurgler (2007), and Hong and Stein (2007) also provide a complementary argument for using liquidity as a sentiment indicator to predict stock returns. On the empirical side, both trading turnover and Amihud's (2002) illiquidity ratio are commonly used liquidity measures in the literature.2 For example, Baker and Stein (2004) find that high New York Stock Exchange (NYSE) trading turnover predicts low subsequent market returns (MR). Hong and Stein (2007) find that high trading turnover helps explain why the returns to Internet and glamour stocks fall far below non-Internet and value stocks, respectively, when the Internet bubble is collapsing. Avramov et al. (2006) document that stocks with high illiquidity ratio exhibit more price reversal than stocks with low illiquidity ratio. However, these studies do not take into account how short-sales constraints affect the association between high liquidity and low subsequent stock returns. The issue on commonality in liquidity has also been intensively studied in the recent literature. For example, Chordia et al. (2000) find that commonality in liquidity is significant and material even after controlling for well-known individual liquidity determinants such as volatility, volume, and price. Hasbrouck and Seppi (2001) investigate the 30 Dow stocks and find evidence of covariation in liquidity proxies derived from quote data. Coughenour and Saad (2004) examine NYSE specialist firms and find evidence that individual stock liquidity covaries with specialist portfolio liquidity, apart from information reflected by market liquidity variation. Pukthuanthong-Le and Visaltanachoti (2009) find that, in addition to marketwide commonality in liquidity, industrywide commonality in liquidity exists in the Thailand stock market. These studies, however, do not analyze whether commonality in liquidity is affected by short-sales constraints. We characterize Baker and Stein's (2004) model by the following three testable hypotheses. First, liquidity will decrease when short-sales constraints are removed. Second, the contemporaneous correlation between stock returns and liquidity and the degree of high liquidity associated with low subsequent stock returns will decrease when short-sales constraints are removed. Third, commonality in liquidity across stocks will decrease when short-sales constraints are removed.3 Testing these hypotheses sheds important light on the issue of how short-sales constraints affect liquidity, the relation between liquidity and stock returns, and commonality in liquidity across stocks. Note that testing the aforementioned hypotheses requires that short-sales constraints are removed from some stocks or the market. On May 16, 2005, the Taiwan Stock Exchange (TWSE) has removed the short-sales constraint from the component stocks of the Taiwan 50 Index (hereafter, the T50 stocks). This change in the trading mechanism on these stocks provides a good opportunity to examine our hypotheses. Using this unique data set, we can examine the impacts of removing the short-sales constraint on liquidity, on the relation between stock returns and liquidity, and on commonality in liquidity across stocks. As suggested by prior studies, we use trading turnover and illiquidity ratio as liquidity measures to proxy for investor sentiment. Overall, we find empirical evidence in support of our hypotheses. The rest of this paper proceeds as follows. Section 2 describes the Taiwan stock market and data in detail. Section 3 discusses the testable hypotheses of the Baker and Stein (2004) model and introduces our empirical frameworks to test these hypotheses. Section 4 presents and discusses our empirical results. We conclude this paper in Section 5. 2. Background and Data 2.1. Taiwan market rules The TWSE is an order-driven call market where only limit orders are accepted. Unlike the U.S. stock markets, there are no formal designated market makers. All securities listed on the TWSE are traded through the Fully Automated Securities Trading (FAST) system. Orders are executed according to the rule 2 Other liquidity measures were used in the literature. For example, in addition to trading turnover, other liquidity measures used in Korajczyk and Sadka (2008) include quoted and effective spreads, components of price impact (fixed versus variable and temporary versus permanent), and the absolute returns-to-volume ratio. 3 We will discuss Baker and Stein's (2004) model and these three testable hypotheses in detail in Section 3.

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of strict price and time priority. Therefore, an order entered into the FAST system at an earlier time should be fully executed before an order at the same price entered at a later time is executed. Daily trading on the TWSE lasts for four and a half hours from 9:00 a.m. to 1:30 p.m., Monday through Friday. Orders can be entered half an hour before the trading session starts at 9:00 a.m. The opening price is determined by selecting the price that maximizes matched trading volume. After the market opens, the periodic call auction method is employed to determine the trading price. Each round of order matching, depending on the trading volume, averages 30 to 90 seconds during the remaining trading session from 9:00 a.m. to 1:30 p.m. This process proceeds until the market closes at 1:30 p.m. On May 16, 2005, the TWSE has removed the up-tick rule on the Taiwan 50 components. Starting from May 16, 2005, the T50 stocks are allowed to be sold below the previous closing price. In other words, short sales by investors were actually allowed before May 16, 2005, as long as transaction prices are higher than previous closing prices. Chang et al. (2007) find evidence that the impact of the tick rule on stock returns is similar to the short-sales constraints and consequently suggest that the up-tick rule can be viewed as another form of short-sales constraints. In addition, Bris et al. (2007) show that the trading costs of short sales are high for Taiwanese investors. Because the up-tick rule is also enforced in Taiwan, Bris et al. (2007) accordingly classify Taiwan as a market in which short-sales are allowed but rarely (or not) practiced. Following the viewpoint of Chang et al. (2007) and Bris et al. (2007), we classify that short-sales are not allowed before the up-tick rule is repealed in Taiwan.4 2.2. Data Our sample period covers almost 5 years (or a total of 1200 trading days) from December 11, 2002 to October 12, 2007. The data are divided into two subperiods: 1) Before the removal of short-sales constraints and 2) After the removal of short-sales constraints. Before, from December 11, 2002 to May 15, 2005 (or a total of 600 trading days), represents the period at which short-sales constraints are imposed on all stocks. After, from May 16, 2005 to October 12, 2007 (or a total of 600 trading days), represents the period at which short-sales constraints are removed from the T50 stocks. Then, we follow Amihud et al. (1997) and Huang and Tsai (2008) to exclude the 20 trading days before and after the event day to avoid selection biases in the event study. Consequently, the trading days for Before and After are -600 to -21 and + 21 to + 600, respectively. Finally, we use 5 trading days to construct a trading period, and hence, there are a total of 232 trading periods (116 for Before and 116 for After). The component stocks of the T50 stocks are quarterly reviewed. Any adjustment of the component stocks will make the pre-event and post-event periods of the added and deleted stocks shorter than 116, and the short pre-event and post-event periods may not be sufficient enough to clearly identify the long patterns of the liquidity and returns of these stocks. Moreover, previous studies have found significant changes in liquidity and stock prices when a stock is added to or deleted from the S&P500 Index (e.g., Harris and Gurel, 1986; Beneish and Whaley, 1996; Hegde and McDermott, 2003). To avoid these potential problems, we only use the 33 stocks that are continually listed on the T50 throughout the sample period as our sample stocks. To be included in our sample, a stock must have available information on daily stock prices and daily trading turnover. These variables are extracted from the Taiwan Economic Journal (TEJ) database. Then, we use the 5-trading-day trading period to calculate weekly stock returns and weekly liquidity measures (trading turnover and illiquidity ratio). As noted by Alexander and Peterson (2008), a comparison of Before with After for the liquidity of the T50 stocks might be due to a systematic change in liquidity for these stocks in these two periods. If so, it is unclear whether the change in the liquidity of the T50 stocks is due to the removal of short-sales constraints on them. To help rule out this possibility, we also employ other noncomponent stocks of the Taiwan 50 index (hereafter, the NT50 stocks) with short-sales constraints as a benchmark for evaluating the change in the liquidity of the T50 stocks. Following Alexander and Peterson (2008), we use a Z-score to select the qualified benchmark stocks from the NT50 stocks. To this end, a Z-score is calculated based on the

4 The authors would like to thank the referee for pointing out that the concept of viewing the up-tick rule as a form of short-sales constraint needs to be clarified.

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Table 1 Matched pair sample description from December 11, 2002 to October 12, 2007. NT50

Z-Score

Panel A: Mean Comparison for the T50 and NT50 Stocks (33 Pairs) Stock Price 51.0193 Market Capitalization 12.1313 Book/Market Ratio 2.1556 Stock Return 0.0004 Trading Volume 8.2315

Variable

T50

40.7739 9.5990 2.2030 0.0004 7.1260

0.0055 0.0040 0.0021 0.0020 0.0022

Panel B: Median Comparison for the T50 and NT50 Stocks (33 Pairs) Stock Price 35.1924 Market Capitalization 12.0845 Book/Market Ratio 1.9475 Stock Return 0.0002 Trading Volume 8.1793

34.0962 9.8576 2.0719 0.0002 7.1753

0.0007 0.0029 0.0006 0.0013 0.0011

This table presents the descriptive statistics on the matched pairs for the T50 and NT50 stocks. The daily average of stock price, market capitalization (measured in natural log), book-to-market ratio, stock return, and trading volume (measured in natural log of the number of trades) from December 11, 2002 to October 12, 2007 are used to compute Z-scores. A Z-score for each pair of stocks ρ is calculated as follows:      2 (1) Zρ;i = FT50;i −FNT50;i = FT50;i + FNT50;i =2 for i = 1; 2; …; 5 where FT50,i and FNT50,i are the financial measure i for the T50 and NT50 stocks, respectively. Then, these five Z-scores are summed up to get an aggregate Z-score for the pair of stocks: (2)

Zρ = Zρ;1 + Zρ;2 + Zρ;3 + Zρ;4 + Zρ;5: The best matches are considered based on aggregate Z-scores.

following five financial measures: 1) stock prices; 2) market capitalization; 3) book-to-market ratio; 4) stock returns; and 5) trading volume. A Z-score for each pair of stocks ρ is calculated as follows5:  h
 io2 n
FT50;i −FNT50;i FT50;i + FNT50;i 2 for i = 1; 2; …; 5 ð1Þ Zρ;i =

=

=

where FT50,i and FNT50,i are the financial measure i for the T50 and NT50 stocks, respectively. Then, these five Z-scores are summed up to get an aggregate Z-score for the pair of stocks, i.e., Zρ = Zρ; 1 + Zρ; 2 + Zρ; 3 + Zρ; 4 + Zρ; 5:

ð2Þ

The best of matches are considered based on aggregate Z-scores. During our sample period, a total of 417 NT50 stocks are not allowed to be sold below the previous closing prices as the candidates. We obtain 33 qualified matched NT50 stocks through aggregate Z-scores. These 33 NT50 stocks do not include the stocks that were removed from the T50 stocks during the sample period. To test our hypotheses, we also form two portfolios based on whether the stocks are T50 stocks, i.e., the T50 and NT50 portfolios. Table 1 presents the characteristics of the sample stocks in this paper. In particular, panels A and B of Table 1 display the average and median values of the five financial measures and Z-scores for 33 pairs of the T50 and NT50 stocks. Because the T50 comprises the 50 largest companies in Taiwan, the average values of financial measures might be affected by outliers. Hence, we focus on the median values of the five financial measures. Panel B of Table 1 shows that the median values of stock prices, market capitalization, and trading volume are 35.19, 12.08, and 8.18, respectively, for the T50 stocks and are 34.10, 9.86, and 7.18, respectively, for the NT50 stocks. Hence, the median values of stock prices, market capitalization, and trading volume are slightly higher for the T50 stocks than for the NT50 stocks. The T50 stocks have a slightly smaller median value of the book-to-market ratio (1.95) than the NT50 stocks (2.07). The T50 and NT50 stocks have an identical median value of stock returns. In sum, these observations indicate that the matched stocks are representative. 5

For each financial measure, the average value of our overall sample period is used to calculate the Z-score.

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3. Methodology and Hypotheses 3.1. Change in liquidity In Baker and Stein's (2004) model, irrationally overconfident investors (or dumb investors) tend to overestimate the relative precision of their own private signals and underreact to the information contained in other investors’ trading. In the presence of short-sales constraints, dumb investors actively participate in the market when they are optimistic, and their trading has a lower price impact, thus boosting liquidity in general. As argued by Baker and Stein (2004), in the absence of short-sales constraints, both dumb and smart investors actively participate in the market.6 Because smart investors are better informed than dumb investors, if dumb investors are more optimistic or pessimistic than smart investors, smart investors will take positions against dumb investors. In this circumstance, some informed trades with higher price impacts will be generated, decreasing liquidity.7 Therefore, the first hypothesis, H1, can be written as follows. H1. Liquidity will decrease when short-sales constraints are removed. As aforementioned, we use both trading turnover and illiquidity ratio as our liquidity measure.8 To measure the change in liquidity before and after short-sales constraints are removed, we start from calculating the weekly average liquidity measure for each stock (Liqi,t) as follows: D

Liqi;t =

1 i;d;t ∑ Liq ; Di;d;t d = 1 i;d;t

ð3Þ

where Liqi,d,t is the liquidity measure (i.e., trading turnover denoted by TORi,d,t and illiquidity ratio denoted by ILLQi,d,t) for stock i on day d of week t, and Di,d,t is the number of days for stock i on day d of week t. Then, the time-series mean of the weekly average liquidity measure for each stock (i.e., trading turnover denoted by TORi and illiquidity ratio denoted by ILLQi) is calculated for both the T50 and NT50 stocks as follows: ALiqi;j =

1 T ∑ Liqi;j;t T t =1

ð4Þ

for i = 1; 2;…; 33; j = Before and After; and t = 1; 2;…; 116 where Liqi,j,t is the weekly average liquidity measure for stock i on week t during the period j, and T is the number of weeks (i.e., 116) at each subperiod. To examine the impact of short-sales constraints on liquidity, we follow Alexander and Peterson (2008) to calculate the difference of difference in percentage, DIFODIF(%), with regard to ALiq as follows:
 DIFODIFALiq ð%Þ = ALiqT50;A –ALiqT50;B ALiqT50;B
 – ALiqNT50;A –ALiqNT50;B ALiqNT50;B

=

=

ð5Þ

where ALiq is the time-series mean of the weekly average liquidity measure for each stock as described in (4) (ATOR and AILLQ), T50 and NT50 are the stocks of the T50 and NT50 portfolios, respectively, and A and B refer to After and Before, respectively. If DIFODIFATOR (DIFODIFAILLQ) in percentage is negatively (positively) significant, it provides evidence in favor of the first hypothesis, H1. 3.2. Relation between stock returns and liquidity Baker and Stein (2004) show that, in the presence of short-sales constraints, dumb investors actively participate in the market only when they are optimistic. When dumb investors are pessimistic, they are 6

Baker and Stein (2004) argue that if the short-sales constraint is absent, it is similar to Region 2 in their model. Diamond and Verrecchia (1987) take an opposite view that liquidity will increase when short sales are possible, and Biais et al. (1999), Jones (2003), and Charoenrook and Daouk (2009) find evidence in support of this view. 8 The construction of our liquidity measures of illiquidity ratio is the same as that of Amihud's (2002) illiquidity ratio. 7

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kept out of the market altogether by short-sales constraints. Consequently, in the presence of short-sales constraints, high liquidity is a sign that the market is dominated by dumb investors, and as a result, the market is overvalued.9 Their model therefore implies that the contemporaneous correlation between liquidity and stock returns is positive, because liquidity increases with investor sentiment, and an increase in sentiment increases stock prices. Their model also implies that high liquidity is associated with a reduction in subsequent expected returns, because stocks are overpriced. Baker and Stein (2004) argue that, in the absence of short-sales constraints, both dumb and smart investors actively participate in the market. In this circumstance, the interaction of their sentiment keeps liquidity from always increasing with dumb investors’ sentiment, and stocks are less overpriced. This condition implies that the positive contemporaneous correlation between liquidity and stock returns and the degree of the association between high liquidity and low subsequent stock returns will decrease. We therefore formally state the second hypothesis, H2, as follows. H2. The contemporaneous positive correlation between stock returns and liquidity and the degree of high liquidity associated with low subsequent stock returns will decrease when short-sales constraints are removed. To test our second hypothesis, the following regression model is estimated for each T50 and NT50 stock: Ri;j;t = αi;j + βi;j DLiqi;j;t + γi;j DLiqi;j;t−1 + λi;j Ri;j;t−1 + ui;j;t ; for i = 1; 2; …; 33; j = Before and After; and t = 1; 2; …; 116;

ð6Þ

where Ri,j,t is the stock return for stock i on day t during the period j. DLiqi,j,t is the detrended liquidity measure for stock i on day t during the period j. Before represents the period at which short sales are constrained for all stocks. After represents the period at which short sales are allowed for the T50 stocks. For each stock, the detrended liquidity measure is estimated as follows:
 2 log Liqi;j;t = ai;j + bi;j t + ci;j t + νi;j;t ;

ð7Þ

where Liqi,j,t is the liquidity measure for stock i on day t during the period j, t and t2 are the linear and quadratic time trends, respectively, and νi,j,t is the residual term that is used as the detrended liquidity measure (i.e., DLiqi,j,t) in (6). In (6), the βi,j and γi,j coefficients measure the contemporaneous relation between stock returns and liquidity and the lead–lag relation between current stock returns and lagged liquidity, respectively. Based on Baker and Stein's (2004) model, the βi,j coefficient should significantly be positive (negative), whereas the γi,j coefficient should significantly be negative (positive), when trading turnover (illiquidity ratio) is used as a liquidity measure. However, the extensive regression output for each T50 and NT50 stock is difficult to report on a stock-by-stock basis. For brevity, we report the average coefficient estimates of βi,j and γi,j across stocks (i.e., βj and γj) for each subperiod. Using trading turnover (illiquidity ratio) as the proxy of liquidity, our second hypothesis predicts that βj will decrease (increase) and γj will increase (decrease) when short-sales constraints are removed from the T50 stocks. 3.3. Commonality in liquidity Baker and Stein's (2004) model also provides a behavioral explanation for commonality in liquidity across stocks.10 As indicated by Baker and Stein (2004), among others, common marketwide factors drive firm-level liquidity, leading to common liquidity movements. They suggest that one of such common marketwide factors is investor sentiment. In particular, in the Baker and Stein (2004) model, dumb investors’ sentiment is reflected in market liquidity and is affected by short-sales constraints. When short 9 Miller (1977) and Figlewski (1981) also show that, in the presence of short-sales constraints, stocks can be overpriced if some investors are very optimistic, with pessimistic investors sitting on the sidelines. Hong and Stein (2003) develop a theory of market crashes based on differences of opinion among investors. Their model predicts that short-sales constraints lead to a higher frequency of extreme negative stock returns or market crashes. 10 Brockman and Chung (2002), Fabre and Frino (2004), and Pukthuanthong-Le and Visaltanachoti (2009) find that the market structures have significant impacts on the commonality in liquidity.

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sales are restricted, dumb investors with positive sentiments will dominate the market, and smart investors sit on the sidelines. If dumb investors’ optimistic sentiments make them trade in the same direction, their collective trading will generate a common variation in liquidity.11 On the other hand, when short sales are allowed, both dumb and smart investors actively participate in the market. When informed smart investors trade against uninformed dumb investors, market liquidity and liquidity covariation across stocks will decrease. Our third hypothesis based on these implications is therefore formalized as follows. H3. Commonality in liquidity across stocks will decrease when short-sales constraints are removed. We employ Korajczyk and Sadka's (2008) approach to examine commonality liquidity across stocks for the two subperiods.12 In particular, at each time period, the standardized liquidity measure is calculated as follows:
  ˆ j;t−1 ; Liqi;j;t = Li;j;t − μˆ j;t−1 σ ð8Þ for i = 1; 2; …; 33; j = Before and After; and t = 1; 2; …; 116;

=

where L*i, j, t is the liquidity measure (trading turnover or illiquidity ratio) for stock i on day t during the period j, and Li,* j, t is an n × T matrix. μˆ j;t−1 and σˆ j;t−1 are the time-series mean and standard deviation of the cross-sectional average of liquidity measure. Then, the latent factors, CLiqj, t, k, are obtained by calculating the eigenvectors that correspond to the k largest eigenvalues of Ωj = Liqi,' j, tLiqi, j, t / n, where n is the number of stocks, and Ωj is a T × T matrix. As suggested by Korajczyk and Sadka (2008), if there are missing data for the liquidity measure, the missing observation is replaced by zero, and then, Ω*j = Liq'i, j, tLiqi, j, t / N'N, where N = 1 if Liqi,j,t is available and N = 0 if Liqi,j,t is missing, and N is an n × T matrix. Then, the commonality in liquidity for the T50 and NT50 stocks before and after the removal of short-sales constraints from the T50 stocks is estimated as follows (see also Chordia et al., 2000; Korajczyk and Sadka, 2008; Hameed et al., 2010): 3

StdLiqOWN;j;t = αOWN; j + ∑ βOWN;k CLiqOTHER;k;j;t k=1

4

+ ∑ γp;j MRj;t−p + λ1 ΔStdj;t + λ2 ΔStdj;t−1 + uOwn;j;t

ð9Þ

p=1

for j = Before and After and t = 1; 2; …; 116; where StdLiqj,t is the standardized liquidity measure of the sample stock on day t during the period j for each T50 stock, CLiqj,t,k is the kth common factor of liquidity measure of the sample stock on day t during the period j, which is estimated by Asymptotic Principal Components (APC). The subscript OWN represents the T50 stocks, the subscript OTHER represents the matched NT50 stocks, and vice versa. In particular, the dependent variable StdLiq and the independent variable CLiq are the standardized trading turnover (illiquidity ratio), denoted by StdTOR (StdILLQ), and the common factor, denoted by CTOR (CILLQ), respectively, when trading turnover (illiquidity ratio) is used as a liquidity proxy. We follow Korajczyk and Sadka (2008) in using the first three common factors as the independent variables in (9). Motivated by the findings of Hameed et al. (2010) that MR and market volatility have significant effects on marketwide commonality in liquidity, weekly MR and the change in weekly market volatility (ΔStd) are included in (9) as control variables.13 Following Hameed et al. 11 This line of reasoning is consistent with Coughenour and Saad's (2004) argument that systematic liquidity variation could arise, because variation in a common factor stimulates systematic variation in the desire to trade. 12 The following issues should be noted when commonality in liquidity across stocks is examined. First, Kamara, Lou, and Sadka (2008) show that commonality of liquidity across stocks has a time trend and is therefore not a stationary time series. Second, choosing any weighting schemes for constructing portfolio liquidity to examine commonality in liquidity across stocks might be arbitrary to some extent. Last, the missing data might occur for the liquidity measures. Korajczyk and Sadka (2008) suggest using the Asymptotic Principal Components (APC) to reduce the aforementioned potential problems. 13 In our empirical tests, we estimate (9), including both market returns and market volatility as control variables as in Hammed et al. (2010) and excluding them as in Korajczyk and Sadka (2008). Both results show that the adjusted R2 of (9) significantly decreases after removing short-sales constraints. We also find similar results, irrespective of whether market returns and market volatility are used as control variables. The only exception is that, when the first common factor of liquidity measure is used as the dependent variable in (9), the difference in the adjusted R2 becomes insignificant after control variables are included in (9). Due to the space limitations, the estimation results of (9), excluding control variables, are not presented here but are available upon request from the authors.

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Table 2 Trading turnover before and after the removal of short-sales constraints. Panel A: Descriptive Statistics for ATORT50 and ATORNT50 ATORT50

Mean Median Max Min Number of Stocks

ATORNT50

Before (1)

After (2)

Before (3)

After (4)

0.6071 0.5442 1.9847 0.0766 33

0.3836 0.3525 0.8924 0.1036 33

1.2687 0.8966 3.4771 0.3385 33

1.2874 1.2157 2.8229 0.1964 33

Panel B: DIFATOR and DIFODIFATOR in Level

Mean Median Max Min Number of Stocks

DIFATOR for T50

DIFATOR for NT50

Wilcoxon test (t-test)

[(5) = ((2) - (1))]

[(6) = ((4) - (3))]

[(7) = ((5) - (6))]

-0.2235 -0.1736 0.1831 -1.2565 33

0.0187 -0.0939 1.6016 -1.3849 33

-1.6928⁎ (-1.7383⁎) — — — —

DIFATOR (%) for T50

DIFATOR (%) for NT50

Wilcoxon test (t-test)

[(8) = ((2) - (1)) / (1)]

[(9) = ((4) - (3)) / (3)]

[(10) = ((8) - (9))]

-0.2610 -0.3568 0.6323 -0.7571 33

0.2423 -0.0653 3.9007 -0.6758 33

-2.8938⁎⁎⁎ (-3.0038⁎⁎⁎) — — — —

Panel C: DIFATOR and DIFODIFATOR in Percentage

Mean Median Max Min Number of Stocks

ATORT50 and ATORNT50 are the weekly average of trading turnover for the T50 and NT50 portfolios, respectively, for the two subperiods. Before represents the period at which short sales are constrained for all stocks. After represents the period at which short sales are allowed for the T50 stocks. The means for DIFATOR in level, for example, are calculated as follows. First, for the difference in level, DIFATOR in level, each stock is computed as the difference between the weekly averages trading turnover after and before the removal of short-sales constraints. Then, we calculate the cross-sectional mean of DIFATOR in level. The statistics of median, maximum, and minimum values of DIFATOR in level are analogously calculated. For the means of the difference in percentage, DIFATOR in percentage, each stock, for example, is computed as the difference between the weekly averages trading turnover after and before the removal of short-sales constraints divided by the weekly average trading turnover before the removal of short-sales constraints. Then, we calculate the cross-sectional mean of DIFATOR in percentage. The statistics of median, maximum, and minimum values of DIFATOR in level and percentage are analogously calculated. The Wilcoxon test and t-test statistics are used to test the equality of DIFATOR in level and percentage for the T50 and NT50 portfolios. Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

(2010), weekly market volatility is estimated from the daily MR using the method described in French et al. (1987).14 Following Korajczyk and Sadka (2008), we use the adjusted R2 to investigate whether the degree of commonality across stocks decreases when short-sales constraints are removed from the T50 stocks. Korajczyk and Sadka (2008) use the adjusted R2 of (9) to examine whether commonality in liquidity across stocks exists. Korajczyk and Sadka (2008) find that their results are consistent with the observation of Chordia et al. (2000) that commonality in liquidity can be observed in different liquidity measures. Motivated by Korajczyk and Sadka (2008), Pu (2009) also computes the adjusted R2 to measure commonality in liquidity across bond and CDS markets. If commonality in liquidity across stocks decreases 14 Furthermore, for a robustness check, we also use the Garman–Klass volatility (GKV) as the proxy of market volatility in (9) (see Garman and Klass, 1980). The results using the GKV proxy are qualitatively identical to the results reported in the paper. The results of robustness check are not reported here but are available upon request from the authors.

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Table 3 Illiquidity ratio before and after the removal of short-sales constraints. Panel A: Descriptive Statistics for ILLQT50 and AILLQNT50 AILLQT50

Mean Median Max Min Number of Stocks

AILLQNT50

Before (1)

After (2)

Before (3)

After (4)

0.0375 0.0304 0.1398 0.0072 33

0.0284 0.0241 0.0743 0.0048 33

0.4333 0.2195 1.8733 0.0604 33

0.3891 0.1202 4.4603 0.0302 33

Panel B: DIFAILLQ and DIFODIFAILLQ in Level

Mean Median Max Min Number of Stocks

DIFAILLQ for T50

DIFAILLQ for NT50

Wilcoxon test (t-test)

[(5) = ((2) - (1))]

[(6) = ((4) - (3))]

[(7) = ((5) - (6))]

-0.0091 -0.0038 0.0407 -0.1125 33

-0.0442 -0.1002 2.5871 -1.2620 33

3.0779⁎⁎⁎ (0.3237) — — — —

DIFAILLQ (%) for T50

DIFAILLQ (%) for NT50

Wilcoxon test (t-test)

[(8) = ((2) - (1)) / (1)]

[(9) = ((4) - (3)) / (3)]

[(10) = ((8) - (9))]

-0.1370 -0.2019 1.3688 -0.8050 33

-0.2382 -0.4668 1.3810 -0.8877 33

1.8724⁎ (0.7023) — — — —

Panel C: DIFAILLQ and DIFODIFAILLQ in Percentage

Mean Median Max Min Number of Stocks

AILLQT50 and AILLQNT50 are the weekly average of illiquidity ratio for the T50 and NT50 portfolios, respectively, for the two subperiods. Before represents the period at which short sales are constrained for all stocks. After represents the period at which short sales are allowed for the T50 stocks. The means for DIFAILLQ in level, for example, are calculated as follows. First, for the difference in level, DIFAILLQ in level, each stock is computed as the difference between the weekly averages illiquidity ratio after and before the removal of short-sales constraints. Then, we calculate the cross-sectional mean of DIFAILLQ in level. The statistics of median, maximum, and minimum values of DIFAILLQ in level are analogously calculated. For the means of the difference in percentage, DIFAILLQ in percentage, each stock, for example, is computed as the difference between the weekly averages illiquidity ratio after and before the removal of short-sales constraints divided by the weekly average illiquidity ratio before the removal of short-sales constraints. Then, we calculate the cross-sectional mean of DIFAILLQ in percentage. The statistics of median, maximum, and minimum values of DIFAILLQ in level and percentage are analogously calculated. The Wilcoxon test and t-test statistics are used to test the equality of DIFAILLQ in level and percentage for the T50 and NT50 portfolios. Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

after short-sales constraints on the T50 stocks are removed, we expect to observe that the adjusted R2 of (9) will decrease. We use both the Wilcoxon test and t-test to test the equality of the variables through H1–H3 before and after the short-sales constraints are removed from the T50 stocks. Our sample only includes 33 pairs of the T50 and NT50 stocks; therefore, the results of the t-test might not be very robust. As such, we interpret our empirical results primarily based on the Wilcoxon tests, and the t-tests are reported for complements.

4. Empirical Results 4.1. Change in liquidity Table 2 reports the empirical results of (5) using trading turnover as a liquidity proxy. In particular, panel A of Table 2 reports the descriptive statistics on ATORT50 and ATORNT50, panel B of Table 2 reports the

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results of the difference and difference of difference in level for ATORT50 and ATORNT50, and panel C of Table 2 reports the results of the difference and difference of difference in percentage for ATORT50 and ATORNT50. Panel A of Table 2 shows that, in both Before and After periods, the means of ATORT50 are lower than the means of ATORNT50, which implies that the liquidity of the T50 portfolio tends to be lower than the NT50 portfolio. Moreover, panel A of Table 2 shows that the T50 (NT50) portfolio has a smaller (larger) mean of trading turnover in the After period than in the Before period. Panel B of Table 2 shows that the Wilcoxon test statistic (and the t-test statistic) for the DIFODIFATOR in level is negative at the 10% significance level. Moreover, panel C of Table 2 shows that the Wilcoxon test statistic (and the t-test statistic) is negative and rejects the null hypothesis of the equality of DIFODIFATOR in percentage at the 1% significance level. Put together, these results suggest that the trading turnover of the T50 stocks significantly decreases after the short-sales constraints are removed. The results using illiquidity ratio as a liquidity proxy yield similar observations and are reported in Table 3. In particular, panel A of Table 3 presents that the means of illiquidity ratio of AILLQT50 in both the Before and After periods are lower than those of AILLQNT50, suggesting that the T50 portfolio tends to be less illiquid than the NT50 portfolio. Panel C of Table 3 shows that the differences in percentage for the T50 and NT50 portfolios are -0.1370 and -0.2382, respectively. Furthermore, the Wilcoxon test statistic is positive and rejects the null hypothesis of the equality of DIFODIFAILLQ in percentage at the 10% significance level. These observations indicate that the degree of illiquidity of the T50 stocks significantly increases after the short-sales constraints are removed. Overall, the results of Tables 2 and 3 show that liquidity for the T50 stocks decreases subsequent to the removal of short-sales constraints, regardless of which liquidity proxy is used. These results provide evidence in favor of our first hypothesis.

Table 4 Impact of trading turnover on stock returns before and after the removal of short-sales constraints. T50

NT50

Before

After

Wilcoxon test (t-test)

Before

After

Wilcoxon test (t-test)

(1)

(2)

[(3) = ((2)-(1))]

(4)

(5)

[(6) = ((5)-(4))]

Panel A: Impact of Contemporaneous Trading Turnover on Stock Returns (β) Mean 0.0406 0.0175 -4.4244⁎⁎⁎ (-5.2486⁎⁎⁎) Median 0.0384 0.0175 — Max 0.0878 0.0532 — Min 0.0051 -0.0130 — Number of Stocks 33 33 —

0.0430 0.0431 0.0948 0.0121 33

0.0424 0.0399 0.0956 0.0120 33

-0.2052 (-0.1200) — — — —

Panel B: Impact of Lagged Trading Turnover on Stock Returns (γ) Mean -0.0302 -0.0139 3.6806⁎⁎⁎ (3.9605⁎⁎⁎) Median -0.0299 -0.0155 — Max 0.0012 0.0117 — Min -0.0735 -0.0642 — Number of Stocks 33 33 —

-0.0268 -0.0233 0.0083 -0.0719 33

-0.0255 -0.0251 0.0019 -0.0559 33

0.0898 (0.3835) — — — —

Panel C: Adjusted R2 for the Regression Model Mean 0.1209 0.0371 Median 0.0993 0.0295 Max 0.3092 0.1229 Min -0.0073 -0.0266 Number of Stocks 33 33

0.1589 0.1660 0.3750 0.0268 33

0.1250 0.1221 0.2497 -0.0067 33

-1.5646 (-1.8281⁎) — — — —

-4.2064⁎⁎⁎ (-5.0633⁎⁎⁎) — — — —

For each stock, the following regression model is run to test the impact of short-sales constraints on the relation between stock returns and liquidity for the T50 and NT50 stocks across the two subperiods: Ri;j;t = αi;j + βi;j DTORi;j;t + γi;j DTORi;j;t−1 + λi;j Ri;j;t−1 + ui;j;t ; for i = 1; 2; …; 33; j = Before and After; and t = 1; 2; …; 116;

(6)

where Ri,j,t is the stock return for stock i on day t during the period j, and DTORi,j,t is the detrended trading turnover for stock i on day t during the period j. Before represents the period at which short sales are constrained for all stocks. After represents the period at which short sales are allowed for the T50 stocks. Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

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4.2. Relation between stock returns and liquidity Panels A and B of Table 4 report the estimated results of (6), which is devised to investigate the contemporaneous correlation between stock returns and trading turnover, and the degree of high trading turnover associated with low subsequent stock returns when short-sales constraints are removed from the T50 stocks for the T50 and NT50 stocks. In addition, panel C of Table 4 reports the adjusted R2 of (6) before and after the removal of short-sales constraints from the T50 stocks for the T50 and NT50 stocks. In particular, panel A of Table 4 shows that the impact of contemporaneous trading turnover on stock returns significantly decreases from 0.0406 to 0.0175 for the T50 stocks. This impact, however, is not statistically significant in the case of the NT50 stocks. Panel B of Table 4 displays that the impact of lagged trading turnover on stock returns for the T50 significantly decreases from -0.0302 to -0.0139, whereas this is not the case for the NT50 stocks. Finally, panel C of Table 4 shows that the adjusted R2 for the T50 stocks experiences a significant decrease from 0.1209 to 0.0371 and that there is no significant difference in the adjusted R2 between the two subperiods for the NT50 stocks. Similar estimated results of (6) using illiquidity ratio as a liquidity proxy can be observed in Table 5. Panel A of Table 5 shows that the negative contemporaneous relation between illiquidity ratio and stock returns significantly decreases from -0.0283 to -0.0135 for the T50 stocks, whereas this negative contemporaneous relation significantly increases from -0.0309 to -0.0381 for the NT50 stocks. Panel B of Table 5 shows that the positive causal relation between lagged illiquidity ratio and current stock returns significantly decreases from 0.0188 to 0.0070 for the T50 stocks and that the change in this positive causal relation is not statistically significant for the NT50 stocks. Finally, panel C of Table 5 shows that the adjusted R2 of (6) significantly decreases after the removal of short-sales constraints for the T50 stocks, but there is no significant change in the adjusted R2 for the NT50 stocks.

Table 5 Impact of illiquidity ratio on stock returns before and after the removal of short-sales constraints. T50

NT50

Before

After

Wilcoxon test (t-test)

Before

After

Wilcoxon test (t-test)

(1)

(2)

[(3) = ((2)-(1))]

(4)

(5)

[(6) = ((5)-(4))]

Panel A: Impact of Contemporaneous Illiquidity Ratio on Stock Returns (β) Mean -0.0283 -0.0135 4.7579⁎⁎⁎ (5.7975⁎⁎⁎) Median -0.0284 -0.0149 — Max -0.0082 0.0012 — Min -0.0589 -0.0263 — Number of Stocks 33 33 —

-0.0309 -0.0274 -0.0033 -0.0639 33

-0.0381 -0.0359 -0.0159 -0.0636 33

-2.2058⁎⁎ (-2.2067⁎⁎) — — — —

Panel B: Impact of Lagged Illiquidity Ratio on Stock Returns (γ) Mean 0.0188 0.0070 -4.2705⁎⁎⁎ (-4.7481⁎⁎⁎) Median 0.0159 0.0089 — Max 0.0514 0.0278 — Min 0.0034 -0.0069 — Number of Stocks 33 33 —

0.0184 0.0175 0.0493 -0.0034 33

0.0226 0.0225 0.0485 0.0023 33

1.4363 (1.4918) — — — —

Panel C: Adjusted R2 for the Regression Model Mean 0.0828 0.0244 Median 0.0914 0.0161 Max 0.1933 0.1326 Min 0.0015 -0.0262 Number of Stocks 33 33

0.1252 0.1299 0.2592 0.0025 33

0.1275 0.1259 0.2465 0.0204 33

-0.0385 (0.1491) — — — —

-4.7579⁎⁎⁎ (-5.6917⁎⁎⁎) — — — —

For each stock, the following regression model is run to test the impact of short-sales constraints on the relation between stock returns and liquidity for the T50 and NT50 stocks across the two subperiods: Ri;j;t = αi;j + βi;j DILLQi;j;t + γi;j DILLQi;j;t−1 + λi;j Ri;j;t−1 + ui;j;t ; for i = 1; 2; …; 33; j = Before and After; and t = 1; 2; …; 116; (6) where Ri,j,t is the stock return for stock i on day t during the period j, and DILLQi,j,t is the detrended illiquidity ratio for stock i on day t during the period j. Before represents the period at which short sales are constrained for all stocks. After represents the period at which short sales are allowed for the T50 stocks. Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

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In sum, the results of Tables 4 and 5 are consistent with the theoretical prediction of Baker and Stein's (2004) model that an increase in liquidity increases stock prices and high liquidity is associated with a reduction in subsequent stock returns when there are short-sales constraints for both the T50 and NT50 stocks. More importantly, consistent with our second hypothesis, we find that the contemporaneous positive (negative) correlation between stock returns and trading turnover (illiquidity ratio) and the degree to which high (low) trading turnover (illiquidity ratio) makes stock returns reversal in subsequent periods become significantly weaker after short-sales constraints on the T50 stocks are removed. Because short-sales constraints remain unchanged for the NT50 stocks, as expected, the impacts of the contemporaneous and lagged liquidity on stock returns exhibit no significant difference across the two subperiods, which is also consistent with our second hypothesis.

4.3. Commonality in liquidity Table 6 presents the estimation results of the adjusted R2 of (9), which is devised to investigate concurrent commonality in liquidity across stocks before and after the removal of short-sales constraints from the T50 stocks when trading turnover is used as a liquidity measure. In particular, panels A–C of Table 6 present the results when the first one, first two, and first three common factors are used as the independent variables, respectively. Because the results of panels A–C are similar to one another, our interpretations focus on the results of panel C. It shows that, based on the Wilcoxon test statistic (and t-test statistic), the adjusted R2 significantly decreases from the Before to After periods, irrespective that the

Table 6 Commonality in liquidity for trading turnover before and after the removal of short-sales constraints. T50

NT50

Before

After

Wilcoxon test (t-test)

Before

After

Wilcoxon test (t-test)

(1)

(2)

[(3) = ((2)-(1))]

(4)

(5)

[(6) = ((5)-(4))]

Panel A: Adjusted R2 for the First Factor Mean 0.0638 0.0486 Median 0.0457 0.0373 Max 0.2190 0.2502 Min -0.0495 -0.0572 Number of Stocks 33 33

-0.8079 (-0.8427) — — — —

0.0770 0.0525 0.2648 -0.0386 33

0.0209 0.0050 0.1387 -0.0521 33

-3.2446⁎⁎⁎ (-3.5654⁎⁎⁎) — — — —

Panel B: Adjusted R2 for the First Two Factors Mean 0.1400 0.0824 Median 0.1285 0.0817 Max 0.3866 0.3084 Min -0.0324 -0.0566 Number of Stocks 33 33

-2.2186⁎⁎ (-2.4635⁎⁎) — — — —

0.1441 0.1362 0.3751 0.0075 33

0.0867 0.0753 0.3089 -0.0234 33

-2.5649⁎⁎⁎ (-2.6650⁎⁎) — — — —

Panel C: Adjusted R2 for the First Three Factors Mean 0.1699 0.0938 Median 0.1590 0.1039 Max 0.4294 0.3317 Min -0.0143 -0.0590 Number of Stocks 33 33

-2.7444⁎⁎⁎ (-2.9673⁎⁎⁎) — — — —

0.2011 0.1715 0.4166 0.0226 33

0.0954 0.0923 0.3121 -0.0334 33

-3.7704⁎⁎⁎ (-4.4666⁎⁎⁎) — — — —

The following regression model is estimated to investigate commonality in liquidity across the T50 and NT50 stocks before and after the removal of short-sales constraints from the T50 stock: 3

4

k=1

p=1

StdTOROWN;j;t = αOWN;j + ∑ βOWN;k CTOROTHER;k;j;t + ∑ γp;j MRj;t−p + λ1 ΔStdj;t + λ2 ΔStdj;t−1 + uOwn;j;t ; for j = Before and After and t = 1; 2; …; 116;

(9)

where StdTORj,t is the standardized trading turnover of the sample stock on day t during the period j for each T50 stock, and CTORj,t,k is the kth common factor of trading turnover of the sample stock on day t during the period j, which is estimated by APC. The subscript OWN represents the T50 stocks, the subscript OTHER represents the matched NT50 stocks, and vice versa. MRj,t and Stdj,t are the MR and market volatility on day t during the period j, respectively. Stdj,t is calculated as described in the work of French et al. (1987). Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

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Table 7 Commonality in liquidity for illiquidity ratio before and after the removal of short-sales constraints. T50

NT50

Before

After

Wilcoxon test (t-test)

Before

After

Wilcoxon test (t-test)

(1)

(2)

[(3) = ((2)-(1))]

(4)

(5)

[(6) = ((5)-(4))]

Panel A: Adjusted R2 for the First Factor Mean 0.2204 0.0633 Median 0.1669 0.0584 Max 0.6899 0.1825 Min -0.0581 -0.0329 Number of Stocks 33 33

-1.5261 (-3.6499⁎⁎⁎) — — — —

0.4672 0.5881 0.7971 -0.0514 33

0.0297 0.0228 0.1224 -0.0327 33

-5.4760⁎⁎⁎ (-9.0418⁎⁎⁎) — — — —

Panel B: Adjusted R2 for the First Two Factors Mean 0.2415 0.0838 Median 0.1866 0.0765 Max 0.7232 0.2361 Min -0.0648 -0.0120 Number of Stocks 33 33

-2.0776⁎⁎ (-3.6706⁎⁎⁎) — — — —

0.5212 0.5882 0.8072 0.0075 33

0.1122 0.1016 0.3116 -0.0347 33

-6.0660⁎⁎⁎ (-9.4006⁎⁎⁎) — — — —

Panel C: Adjusted R2 for the First Three Factors Mean 0.2520 0.1020 Median 0.1787 0.1045 Max 0.7260 0.2350 Min -0.0530 -0.0160 Number of Stocks 33 33

-2.0134⁎⁎ (-3.5222⁎⁎⁎) — — — —

0.5334 0.6031 0.8169 0.0023 33

0.1384 0.1170 0.3433 0.0012 33

-5.9121⁎⁎⁎ (-9.0108⁎⁎⁎) — — — —

The following regression model is estimated to investigate commonality in liquidity across the T50 and NT50 stocks before and after the removal of short-sales constraints from the T50 stock: 3

4

k=1

p=1

StdILLQ OWN;j;t = αOWN;j + ∑ βOWN;k CILLQOTHER;k;j;t + ∑ γp;j MRj;t−p + λ1 ΔStdj;t + λ2 ΔStdj;t−1 + uOwn;j;t ; for j = Before and After and t = 1; 2; …; 116;

(9)

where StdILLQ j,t is the standardized illiquidity ratio of the sample stock on day t during the period j for each T50 stock, and CILLQ j,t,k is the kth common factor of illiquidity ratio of the sample stock on day t during the period j which is estimated by APC. The subscript OWN represents the T50 stocks, the subscript OTHER represents the matched NT50 stocks, and vice versa. MRj,t and Stdj,t are the MR and market volatility on day t during the period j, respectively. Stdj,t is calculated as described in the work of French et al. (1987). Note: ⁎⁎⁎, ⁎⁎, ⁎ denote significant at the 1%, 5%, and 10% levels, respectively.

standardized trading turnover of the T50 stocks or that of the NT50 stocks are used as an independent variable. Table 7 reports the estimation results of the adjusted R2 of (9) using illiquidity ratio as a liquidity measure. Similar to what we observed in panel C of Table 6, panel C of Table 7 shows that, as indicated by the Wilcoxon test statistic (and t-test statistic), there is a significant decrease in the adjusted R2 across the two subperiods, regardless that the standardized illiquidity ratio of the T50 stocks or that of the NT50 stocks are used as an independent variable. Moreover, consistent with the findings of Korajczyk and Sadka (2008), the results of panel C of Tables 6 and 7 show that commonality in illiquidity is stronger than in trading turnover in three out of four cases. For example, in the Before (After) period, the adjusted R2s are 0.2011 and 0.5334 (0.0954 and 0.1384) when the standardized trading turnover and standardized illiquidity ratio of the NT50 stocks are used as the dependent variables, respectively. In sum, the results in Tables 6 and 7 suggest that commonality in liquidity between the T50 and NT50 stocks decreases after short-sales constraints are removed from the T50 stocks. These findings provide empirical support for our third hypothesis. 5. Concluding Remarks In this paper, we have derived three testable hypotheses from Baker and Stein's (2004) model, and these hypotheses describe how short-sales constraints affect liquidity, the relations between stock returns and liquidity, and commonality in liquidity across stocks. Testing these hypotheses requires that short-

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sales constraints are removed from some stocks or the market. The short-sales constraint on the T50 stocks has been removed on May 16, 2005, and this change offers a good platform for testing our hypotheses. We then devised several empirical frameworks in an attempt to provide an evaluation of the empirical validity of these three hypotheses using trading turnover and illiquidity ratio as a liquidity measure. Some important findings are noted as follows. First, the liquidity of the T50 stocks significantly decreases after the short-sales constraints are removed. Second, the positive contemporaneous correlation between stock returns and liquidity, and the degree of high liquidity associated with low subsequent stock returns decrease after short-sales constraints on the T50 stocks are removed. Third, commonality in liquidity between the T50 and NT50 stocks significantly decreases after short-sales constraints are repealed from the T50 stocks. Moreover, these results are robust to using trading turnover or illiquidity ratio as a liquidity measure. Overall, these findings provide evidence in support of our hypotheses. Baker and Stein's (2004) model implies that dumb investors tend to buy and hold overpriced stocks when they are more optimistic than smart investors in the presence of short-sales constraints. Consequently, dumb investors are more likely to lose in the market than smart investors. Individual investors are the main market participants in the Taiwanese stock market. Barber et al. (2009) find that Taiwanese individual investors are dumb investors, because they, as a group, lose money from their trades, whereas Taiwanese institutional investors are smart investors, because they, as a group, profit from their trades. 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