Uncertainty elasticity of liquidity and expected stock returns in China

Transcription

1 Uncertainty elasticity of liquidity and expected stock returns in China Ping-Wen Sun International Institute for Financial Studies Jiangxi University of Finance and Economics Bin Yu International Institute for Financial Studies Jiangxi University of Finance and Economics Abstract We examine the uncertainty elasticity of liquidity (UEL: percentage change in the individual stock s liquidity given percentage change in the market volatility) and its influences on expected stock returns in the Chinese stock market from 2002 to We find that stocks of firms with lower share price, smaller market capitalization, higher book to market ratio, higher past year return, higher illiquidity ratio, higher non-tradable percentage, and fewer analysts following have higher UEL. The factor model analysis shows that the highest UEL decile portfolio monthly earns 0.36% more than the lowest UEL decile portfolio and have higher factor loadings on SMB, RMW, and CMA of the Fama and French five factor model. Furthermore, firm-level analysis shows that UEL does not have additional explanation power on expected stock returns after controlling for the liquidity risk. Finally, on average, stocks UEL is higher when the stock market return is lower. JEL classification: G12, G14 Keywords: uncertainty, liquidity, liquidity risk, stock returns, volatility, China Preliminary Comments are welcome January 10, 2015 All errors are ours. Ping-Wen Sun gratefully acknowledges the financial support from the National Natural Science Foundation of China (No ). 1

2 1. Introduction Do investors care about the stock market volatility when they trade stocks? If the stock market uncertainty proxied by the stock market volatility can influence a stock s liquidity, how does the uncertainty elasticity of liquidity (the percentage change in the stock s liquidity given the percentage change in the stock market volatility) of the stock vary with the stock s expected return? Our study investigates these two research questions in the Chinese stock market from April 2002 to October Chung and Chuwonganant (2014) find that uncertainty exerts a greater impact on stock liquidity in the U.S. market when public traders play a greater role and market makers play a reduced role in liquidity provision. Because individual investors play an important role in the Chinese stock market and the Chinese stock market is an order-driven market without market makers, the Chinese stock market becomes a good candidate for us to examine whether findings of Chung and Chuwonganant (2014) still apply. Furthermore, Chung and Chuwonganant (2014) suggest a fruitful area of future research is to find out whether stock returns are related to UEL. We investigate this question in the Chinese stock market and provide evidence to show that there is a positive relationship between a stock s uncertainty elasticity of liquidity (UEL) and its expected return. Our study is related to the liquidity commonality literature. Previous studies have shown that the individual stock s liquidity commoves with the market liquidity. Chordia, Roll, and Subrahmanyam (2000) first document the individual stock liquidity co-move with market- and industry-wide liquidity. Acharya and Pedersen 2

3 (2005) derive a liquidity-adjusted capital asset pricing model and show that the commonality between the individual stock s liquidity and the stock market liquidity positively correlates with the expected stock returns. Lee (2011) further shows that commonality in liquidity is priced on a global level. Karolyi, Lee, and Van Dijk (2012) find commonality in liquidity is greater in countries with and during high market volatility, greater presence of international investors, and more correlated trading activity. Karolyi et al. (2012) further argue that demand-side explanation which contends liquidity commonality arises from the behavior of investors and traders is more consistent with their findings than the supply-side explanation which asserts liquidity commonality arises from liquidity providers information sharing and capital constraints as argued by Coughenour and Saad (2004). Nevertheless, several studies also provide evidence for the supply-side explanation of liquidity commonality. Chordia, Sarkar, and Subrahmanyam (2005) examine stock and bond market liquidity and find monetary expansions during crisis periods are associated with increased liquidity. Brunnermeier and Pedersen (2009) provide a model that links an asset s market liquidity and traders funding liquidity and show that market liquidity and funding liquidity may mutually reinforce to lead to liquidity downward spirals when margins are destabilizing. Hu, Pan, and Wang (2013) use U.S. Treasuries price deviations from asset fundamentals as a measure of market illiquidity and document their illiquidity measure captures episodes of liquidity crisis of different origins across the financial market. Hu et al. (2013) suggest their illiquidity measure is closely connected to the amount of arbitrage capital available in 3

4 the aggregate financial market. Nyborg and Ostberg (2014) contend there is a connection between the interbank market for liquidity and the broader financial markets. They find tighter interbank markets are associated with more volume in more liquid stocks, selling pressure in more liquid stocks, and transitory negative returns. The event in the Chinese market, from June 17 to June 24 in 2013, the Shanghai stock exchange index fell 9% during the week while the short-term interest rate increased from 3.33% to the highest 11.96% and closed at 5.01%, provides vivid supporting evidence for their findings to support the supply-side explanation for liquidity commonality. In addition to liquidity commonality, the individual stock s liquidity is also correlated with the stock market return. Acharya and Pedersen (2005) argue that this correlation stems from the willingness of investors to accept a lower expected return on a security that is liquid in a down market. They further show that the covariation of a security s illiquidity to market returns also has a significant impact on expected returns. Lee (2011) also shows that a security s required rate of return depends on the covariance of its own liquidity with local and global market returns. Hameed, Kang, and Viswanathan (2010) find that negative market returns decrease stock liquidity, especially during times of tightness in the funding market. Instead of examining the comovement between the individual stock s liquidity and the market liquidity or return, our study investigates how the stock market volatility affects the stock liquidity. Chordia, Sarkar, and Subrahmanyam (2005) find that innovations to stock and bond market liquidity and volatility are significantly 4

5 correlated and suggest that common factors drive liquidity and volatility in both markets. Chung and Chuwonganant (2014) show the influence of market uncertainty measured by VIX on stock liquidity is greater than the combined effects of all other common determinants of stock liquidity. To examine whether the stock market uncertainty can influence investors trading behavior is interesting because the sensitivity of stock liquidity to the stock market volatility may provide another channel for us to better understand the equity risk premium. Bansal, Kiku, Shaliastovich, and Yaron (2014) find an increase in macroeconomic volatility is associated with an increase in discount rates and a decline in consumption. Hence, investors may hesitate to trade a stock until the stock s price provides enough expected return to cover its transaction costs when the stock market is volatile. Under this circumstance, investors may also require additional risk premium for holding stocks with higher uncertainty elasticity of liquidity. We find there is a significant difference in characteristics between stocks with high UEL and low UEL in the Chinese stock market. Stocks with higher UEL have lower share price, smaller firm size, higher book to market ratio, better past year stock return performance, higher Amihud (2002) illiquidity ratio and non-tradable percentage, and less analyst coverage. The highest UEL decile portfolio monthly outperforms the lowest UEL decile portfolio by 0.36% at 10% significance level from May 2002 to October In addition, our factor model analysis shows that the highest UEL decile portfolio have higher factor loadings on SMB (small minus big size firms return), RMW (robust minus weak operating profit firms return), and 5

6 CMA (conservative minus aggressive capital expenditure firms return) of the Fama and French (2015) five factor model. Although high UEL firms also have higher liquidity risk betas such as commonality in liquidity with market liquidity, return sensitivity to market liquidity, and liquidity sensitivity to market return, UEL does not have additional explanation power on expected stock returns after controlling for the liquidity risk. Finally, we find the aggregate UEL is higher when the stock market return is lower, suggesting investors trading behavior are more sensitive to stock market volatility in a down market. Our study contributes to the market microstructure literature in the Chinese stock market in the following ways. First, we show that investors do care about the stock market volatility when they trade stocks. On average, there is a monthly 0.36% premium required by investors for holding stocks with high uncertainty elasticity of liquidity. Second, we find stocks with high UEL have characteristics related to high risk as shown in the literature such as smaller size, higher book to market ratio, higher momentum, and illiquid. Third, we find UEL in the Chinese stock market does not have additional explanation power on stock returns after controlling for liquidity risk although Chung and Chuwonganant (2014) conjecture the risk premium associated with UEL may be greater than the risk premium associated with liquidity commonality with the market liquidity. Finally, we show that the aggregate UEL is higher in a down market when the market volatility tends to be higher. This finding is complementary to the Bansal et al. (2014) who find an increase in market volatility is associated with an increase in discount rates. 6

7 The rest of the paper is organized as follows. Section 2 describes the background of market microstructure in the Chinese stock market. Section 3 describes our data and variable construction. Section 4 shows our empirical methodology and results. Section 5 concludes our paper. 2. Market microstructure in the Chinese stock market According to Jiang and Kim (2015), there are two main traded shares A-shares and B-shares in the Chinese stock market. A-shares are denominated in the Chinese currency RMB and B-shares are denominated in foreign currency (U.S. or Hong Kong dollar). B-shares were originally restricted to foreign investors. Since 2001, local Chinese can also own B-shares. Because only a small fraction of listed firms have B-shares, our study focuses on A-shares in the Chinese stock market. As of October 2014, there are four boards in the Chinese stock market. The Shanghai Main Board (with stock id 6xxxxx) was launched on December 19, The Shenzhen Main Board (with stock id 0xxxxx) was launched on July 3, The Shenzhen Small and Medium Sized Enterprises Board (with stock id 002xxx) was launched on May 17, The Shenzhen Growth Enterprise Market Board (with stock id 3xxxxx) was launched on October 30, As of April 2014, the average firm size is billion RMB (925 listed firms) on Shanghai Main Board, 7.40 billion RMB (445 listed firms) on Shenzhen Main Board, 5.28 billion RMB (684 listed firms) on Shenzhen Small and Medium Sized Enterprise Board, and 4.16 billion RMB (352 listed firms) on Shenzhen Growth Enterprise Market Board. The market opening days are from Monday to Friday and the daily trading period 7

8 is from 9:30 am to 11:30 am in the morning and 1:00 pm to 3:00 pm in the afternoon. The minimum price tick size is 0.01 RMB for A-shares. Since December 16, 1996, the stock price has a daily fluctuation limit of 10%. Hence, in order to have a consistent market microstructure, we started our sample in Unlike in the U.S. stock market, there are no market makers in the Chinese stock market and the trading mechanism is an order-driven system. According to Madhavan (1992), a quote-driven system is where dealers post prices before order submission and an order-driven system is where traders submit orders before prices are determined. Under the order-driven system, the Chinese stock s daily opening price is determined by a periodic auction from 9:15 am to 9:25 am and starts a continuous auction after 9:30 am. During the five minutes from 9:25 am to 9:30 am, traders cannot submit new orders nor withdraw their previous submitted orders. In our sample period from 1997 to 2014, the annual average trading days in the Chinese stock market is 242 days, which is about 10 days less than the annual average trading days in the U.S. stock market. The major reason for this number of trading day difference is from three major holiday weeks the Chinese New Year week in February, the Labor Day week in early May, and the National Day golden week in early October. Since February has less trading days than other months and the Chinese New Year week sometimes is in February, the average number of trading days in February is less than 15 days. In our study, we restrict our sample stocks to have at least 15 trading days in a month to estimate the average monthly market liquidity and market volatility. When the total market opening days are less than 15 days in a month 8

9 during our sample period from May 1997 to October 2014, we restrict our sample stocks to have the same trading days as the market opening days. According to Liao, Liu, and Wang (2014), the Chinese stock market has a unique split-share structure, a legacy of China s initial share issue privatization (SIP), in which state-owned enterprises (SOEs) went public to issue minority tradable shares to institutional and individual investors. Meanwhile, the Chinese government withheld control of these listed SOEs by owning majority non-tradable shares. In 2005, the Split-Share Structure Reform was initiated to dismantle the dual share structure by converting non-tradable shares into tradable shares. After this reform, the average non-tradable percentage of listed firms shares decreases from 60.22% in 2003 to 23.05% in Liao et al. (2014) argue that the Split-Share Structure Reform adopted a market mechanism that played an effective information discovery role in aligning the interests of the government and public investors. 3. Data and variable construction We use China Stock Market and Accounting Research (CSMAR) database to collect A-shares which are denominated in the Chinese currency RMB from May 1997 to October 2014 as our sample. Since we require a stock to have 60 months observations (at least 36 months) to calculate its uncertainty elasticity of liquidity and liquidity risk betas, our sample for return analysis is from May 2002 to October In addition, because Chinese public firms are required to disclose their annual financial statements before the end of April in the next year, we analyze yearly public firms characteristics sorted by UEL from April 2002 to April To calculate UEL, 9

10 we use Amihud (2002) illiquidity ratio to be the liquidity measure in our study. Since there is no similar stock market uncertainty measure such as VIX in the U.S. market until March 16, 2011 in the Chinese stock market, we follow Naes, Skjeltorp, and ØDegaard (2011) to take the cross-sectional average volatility of the sample stocks to be the market volatility, where volatility is calculated as the standard deviation of daily returns over the month. In order to make sure our sample stocks can represent the stock market condition, we require each individual stock has at least 15 trading days in a month to be included in our sample. For months with market trading days less than 15 days, we require each individual stock has the same trading days as the market opening days in a month. For macro variables such as term spread and default spread, we collect government bond and corporate bond information of China Central Depository & Clearing Co., Ltd (CCDC) from the WIND database. We define the term spread as the yield difference between the 10-year government bond and the 1-year government bond and the default spread as the yield difference between the BBB plus rated corporate bond and the AAA rated corporate bond Amihud (2002) illiquidity ratio We use Amihud s (2002) illiquidity ratio ILLIQ it, to be the major liquidity variable used in our study. Specifically, as shown in equation (1), where D T is the number of trading days in a month; and R is, and VOL is, are stock i s absolute return and dollar trading volume (in million RMB), respectively, on day s. ILLIQ it, DT 1 Ris, (1) D VOL T s 1 i, s Many research papers provide evidence to show that Amihud (2002) illiquidity 10

11 ratio is a valid proxy to measure a stock s liquidity. Acharya and Pedersen (2005) use Amihud (2002) illiquid ratio to measure a stock s transaction cost. Goyenko, Holden, and Trzcinka (2009) run horse races of annual and monthly liquidity estimates and conclude Amihud (2002) illiquidity ratio does well measuring price impact. Brennan, Huh, and Subrahmanyam (2013) decompose the Amihud (2002) measure into elements that correspond to positive and negative return days and find only the down-day element commands a return premium. Lou and Shu (2015) find that the pricing of the Amihud measure is driven by its trading volume component instead of its construct of the ratio of absolute return to volume. Huo (2009) uses ShangZhen 180 index component stocks to show that the average trading cost in the Chinese stock market is about 0.25%. After we cross-sectionally winsorsize each stock s Amihud (2002) illiquidity ratio to top 10% in each month, we find the Amihud (2002) illiquidity ratio could proxy for the transaction cost in the Chinese stock market. We take the equally-weighted average of each sample stock s transaction cost to be the market transaction cost in every month Uncertainty elasticity of liquidity UEL from monthly data Since the Chinese stock market does not have VIX index until March 16, 2011 when CBOE applies its proprietary CBOE Volatility Index methodology to options on ishares Trust FTSE China 25 Index Fund with Ticker: VXFXI, we follow Naes, Skjeltorp, and ØDegaard (2011) to take the cross-sectional average volatility of the sample stocks to be the market volatility. As shown in equation (2) and (3), we take 11

12 the logarithm of in each stock s monthly illiquidity ratio divided by previous month s illiquidity ratio and the logarithm of the market volatility divided by previous month s market volatility to measure the change in illiquidity ratio and the change in the market volatility. dilliq t ln( ILLIQ t / ILLIQ t 1) (2) dmkt _ Volat ln( Mkt _ Volat / Mkt _ Volat 1) (3) We then calculate each individual stock s uncertainty elasticity of liquidity as shown in equation (4), the coefficient on dmkt_vola t is defined as UEL i. A qualified stock in our sample needs to have past 60 months (at least 36 months) observations of both dilliq t and dmkt_vola t in the end of April from April 2002 to April dilliq i, t i UELi * dmkt _ Volat ei (4) In the firm-level excess return Fama and MacBeth (1973) regression test, to avoid the errors-in-variable problem, we use the portfolio approach to calculate the individual stock s UEL. Specifically, in the end of April in year t from 2002 to 2014, we sort stocks by their UEL and apply their UEL rank to May in year t to April in year t+1 to form ten equally-weighted portfolios and calculate each portfolio s change in illiquidity ratio. Next, we calculate each portfolio s UEL during the sample period from May 2002 to October Finally, we assign the portfolio s UEL back to individual stocks based on their UEL rank UEL from daily data In order to examine how the monthly aggregate UEL changes through time, we use daily data of Shanghai stock exchange index to calculate the market s daily 12

13 volatility. Specifically, we use the method Corwin and Schultz (2012) to calculate the high-low variance estimator from the index s daily high and low price. The market s daily volatility HL is a by-product in the process to calculate the daily high-low spread of the market. We then run equation (4) for each stock in a month to get each individual sample stock s monthly UEL. Next, we take the equally-weighted average of each individual stock s UEL to be the aggregate UEL of the market Liquidity risk Pastor and Stambaugh (2003) first propose the concept of liquidity risk and document the average on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5% annually from 1966 through 1999 in the U.S. stock market. Acharya and Pedersen (2005) then derive a liquidity-adjusted capital asset pricing model and show that two additional sensitivities: stock liquidity to market liquidity and stock liquidity to market return also explains expected stock returns well. Liu (2006) applies his turnover adjusted non-trading days liquidity measure to create a liquidity factor and finds that his liquidity-augmented capital asset pricing model explains size, book to market, long-term contrarian investment, and fundamental to price ratios related equity risk premium well. Lam and Tam (2011) also show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. Lee (2011) applies Lesmond, Ogden, and Trzcinka (1999) zero-return probability as the transaction cost proxy and uses Acharya and Pedersen (2005) liquidity-adjusted capital asset pricing model to examine the price of liquidity risk in the global stock market. Lee (2011) 13

14 documents a security s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. Since stocks in the Chinese stock market seldom have non-trading days, we apply Amihud (2002) illiquidity ratio to be stocks transaction cost proxy. Similar to Acharya and Pedersen (2005) and Lee (2011), we use equation (5), (6), (7), (8), and (9) to calculate the stock return and market return correlation risk 1, stock liquidity innovation and market liquidity innovation correlation risk 2, stock return and market liquidity innovation correlation risk 3, stock liquidity innovation and market return correlation risk 4, and the total liquidity risk rt rt rt rt rt i M cov r, 1 t rt var c i M M t i cov c, 2 t c var c i M M t i cov, c 3 t var c M t M i M M t i cov c, 4 t rt var c M i M M t 5. (5) (6) (7) (8) (9) i i i i where r i t represents the individual stock return, M rt represents the market return, i c t represents the individual stock's liquidity innovation, and represents the market liquidity innovation. To calculate stocks beta (1 to 4) in the April end from 2002 to 2014, we require our sample stock to have 60 months (at least 36 months) return and Amihud (2002) illiquidity ratio. We follow Pastor and Stambaugh (2003), Acharya M c t 14

15 and Pedersen (2005), and Liu (2006) to use the AR(2) model as shown in equation (10) to calculate a stock s illiquidity innovation i c t or the market s illiquidity innovation M c t. ILLIQ * ILLIQ * ILLIQ c (10) im ( ) i( M ), t 1 i( M ), t 1 2 i( M ), t 2 t Similar to the way we use to calculate UEL in the firm-level excess return Fama and MacBeth (1973) regression test, we use the portfolio approach to calculate the individual stock s 1 2 3,,, and 4. Specifically, in the end of April in year t from 2002 to 2014, we sort stocks by their beta (1 to 4) and apply their beta rank to May in year t to April in year t+1 to form ten equally-weighted portfolios and calculate each portfolio s return, portfolio s illiquidity innovation, and market illiquidity innovation through the whole sample period from May 2002 to October We then calculate each portfolio s beta (1 to 4) and assign each portfolio s UEL back to individual stocks based on their beta (1 to 4) rank. 4. Empirical methodology and results 4.1. Number and size of sample stocks Table 1 reports the total firm number and the average firm size of the total listed stocks and our sample stocks in the end of April in year t from 2002 to We require our sample stocks to have at least 15 trading days when the market opening day is above 15 days and to have the same trading days as the market opening days when the market opening days are less than 15 days. In addition, our sample stocks also need to have past 60 months (at least 36 months) return and Amihud (2002) illiquidity ratio. After this data screening, the number of our sample stocks is 811 in 15

16 2002 and 1875 in The average firm size in our sample is 3.46 billion RMB in 2002 and billion RMB in For our sample stocks as of April 2014, Shanghai Main Board has 826 stocks and the average firm size is billion RMB; Shenzhen Main Board has 396 stocks and the average firm size is 7.41 billion RMB; Shenzhen SME Board has 505 stocks and the average firm size is 5.50 billion RMB; Shenzhen GEM Board has 148 stocks and the average firm size is 4.98 billion RMB. (Insert Table 1 here) 4.2. Uncertainty elasticity of liquidity of A-shares Characteristics of decile portfolios sorted by UEL We sort our sample stocks by stocks uncertainty elasticity of liquidity (UEL) into equally-weighted 10 portfolios in the end of April from 2002 to 2014 and report characteristics of these decile portfolios in table 2. The average UEL increases from of the lowest UEL decile portfolio to 0.99 of the highest UEL decile portfolio. For risk related characteristics, the average stock price decreases monotonically from RMB of the lowest UEL decile portfolio to 9.02 RMB of the highest UEL decile portfolio, showing that investors who invest in the low price stocks are more sensitive to the market volatility when they trade. In addition, the average firm size also decreases from billion RMB of the lowest UEL decile portfolio to 3.92 billion RMB of the highest UEL decile portfolio. We winsorize our sample stocks book to market ratio to the closest non-negative value if the stock s book to market ratio is negative. Although the highest UEL decile portfolio has lower book to market ratio of 0.41, there is not an obvious trend in stocks book to market ratio from the 16

17 lowest UEL decile portfolio to the highest UEL decile portfolio. In terms of momentum Ret t-12, t-2 and the recent month s return Ret t-1, there is no significant difference between the highest UEL decile portfolio and the lowest UEL decile portfolio. Finally, the highest UEL decile portfolio has higher daily volatility of 2.97% than the daily volatility of 2.84% of the lowest UEL decile portfolio at 10% level although the difference does not seem economically important. For liquidity characteristics, there is no significant difference in non-tradable percentage between the highest UEL decile portfolio and the lowest UEL decile portfolio and the average non-tradable percentage of those decile portfolios is about 35% during our sample period. The Amihud (2002) illiquidity ratio increases almost monotonically from of the lowest UEL decile portfolio to of the highest UEL decile portfolio, showing that the portfolio of higher UEL has a higher transaction cost. The monthly RMB trading volume also decreases almost monotonically from 2.33 billion RMB of the lowest UEL decile portfolio of to 0.87 billion RMB of the highest UEL decile portfolio. However, the average monthly turnover (shares traded divided by total shares outstanding) increases from 20.81% of the lowest UEL portfolio to 27.68% of the highest UEL portfolio. Johnson (2008) shows that volume and liquidity seem unrelated over time in the data and argues that volume is positively related to the variance of liquidity or liquidity risk. Therefore, the argument from Johnson (2008) suggests the highest UEL decile portfolio has higher liquidity risk because the highest UEL decile portfolio has a higher turnover ratio. Overall, our results show portfolios with higher UEL are less liquid. 17

18 For investor attention variables, there is no significant difference in listing months between the highest UEL decile portfolio and the lowest UEL decile portfolio. The institutional ownership decreases almost monotonically from 18.37% of the lowest UEL decile portfolio to 13.07% of the highest UEL decile portfolio, suggesting less recognized stocks by institutional investors tend to have higher UEL. In addition, the number of analysts following decreases monotonically from of the lowest UEL decile portfolio to 3.35 of the highest UEL decile portfolio, showing that analysts may play an important role to reduce a stock s liquidity sensitivity to the market volatility because analysts produce valuable pricing information for investors. Finally, we find the number of employees decrease from of the lowest UEL decile portfolio to 2915 of the highest UEL decile portfolio. Our results suggest stocks with lower investor attention have higher UEL. (Insert Table 2 here) The determinants of UEL We examine which firm characteristics affect a stock s uncertainty elasticity of liquidity (UEL) in table 3. Specifically, we run firm-level Fama and MacBeth (1973) regression each year from 2002 to To avoid the multicollinearity problem arising from including all liquidity variables simultaneously, we separate a stock s Amihud (2002) illiquidity ratio, monthly turnover, and non-tradable percentage into three different regressions. Our results show that stocks with lower price, smaller market capitalization, higher book to market ratio, higher past year return, higher Amihud (2002) illiquidity ratio, higher non-tradable percentage, and less analysts 18

19 following have higher UEL. One interesting point is that institutional ownership does not have significant explanation power on UEL although Chung and Chuwonganant (2014) find institutional ownership significantly negatively explains UEL in the U.S. market. Because Kamara, Lou, and Sadka (2008) argue that the increase in institutional ownership of large firms in the U.S. market also increases the commonality in liquidity, institutional investors seem to play an important role to affect the correlation risk between stock liquidity innovation and market liquidity innovation or change in market volatility. However, since the average institutional ownership of stocks is below 20% in the Chinese stock market, currently institutional investors do not have enough influence on a stock s UEL. Another interesting point is the difference in investors behavior towards value stocks in the Chinese and U.S. stock market. Different from our result in the Chinese stock market, Chung and Chuwonganant (2014) find higher market to book ratio stocks have higher UEL, suggesting investors in the Chinese stock market more hesitate to trade value stocks when the market is becoming more volatile and investors in the U.S. stock market more hesitate to trade growth stocks when the market is becoming more volatile. It is also interesting to see that liquidity of stocks with better past year return performance are more sensitive to the change in the stock market volatility. Furthermore, since smaller firms may also have lower share price, higher transaction cost (Amihud (2002) illiquidity cost in our study), and less analysts following, our results show that liquidity of small firms is more sensitivity to the change in the stock market liquidity. Finally, our result shows that stocks of firms with 19

20 higher non-tradable percentage have higher UEL, suggesting the Split-Share Structure Reform launched in 2005 to convert non-tradable shares to tradable may help reduce the overall stocks UEL. (Insert Table 3 here) Factor model analysis for decile portfolios sorted by UEL We rank stocks UEL in the end of April in year t from 2002 to 2014 and apply their UEL rankings to May in year t to April in year t+1 for 150 months from May 2002 to October We then form 10 equally-weighted portfolios on stocks UEL ranking and examine portfolio returns for those 10 decile portfolios. As shown in Panel A of table 4, average monthly returns of UEL sorted decile portfolios increase from 1.28% to 1.64%. The highest UEL portfolio earns monthly 0.36% more than the least UEL portfolio at 10% level from May 2002 to October We then use CAPM model as shown in equation (11), Fama and French (1993) three factor model as shown in equation (12), Carhart (1997) four factor model as shown in equation (13), and Fama and French (2015) five factor model as shown in equation (14) to analyze the portfolio returns of those 10 UEL ranked portfolios. To calculate monthly factors such as SMB (small size minus big size), HML (high book to market minus low book to market), UMD (up return minus down return), RMW (robust operating profitability minus weak operating profitability), and CMA (conservative in investment minus aggressive in investment), we follow Fama and French (2015) to apply firm characteristics in the end of April in year t to form value-weighted portfolios from May in year t to April in year t+1. Basically, except 20

21 for Size (divided into two groups), we use top 30%, middle 40%, and bottom 30% to separate characteristics such as book to market ratio BM, past performance Ret t-12,t-2, operating profit OP (difference between total revenue and total cost divided by total equity), and investment INV (change in total asset divided by previous total asset) into three groups and take the return difference between top and bottom groups to be monthly factors. r r MKTRF (11) pt ft pt MTKRF, pt * t pt r r * MKTRF * SMB * HML (12) pt ft pt MTKRF, pt t SMB, pt t HML, pt t pt r r * MKTRF * SMB * HML * UMD (13) pt ft pt MTKRF, pt t SMB, pt t HML, pt t UMD, pt t pt r r * MKTRF * SMB * HML pt ft pt MTKRF, pt t SMB, pt t HML, pt t * RMW * CMA RMW, pt t CMA, pt t pt (14) The factor model analysis shows that the highest UEL decile portfolio has significant factor loadings on SMB, RMW, and CMA than the lowest UEL decile portfolio. This result shows that returns of stocks with higher UEL behave more close to firms with smaller size, more robust operating profits, and more conservative in capital expenditure than stocks with smaller UEL. (Insert Table 4 here) 4.3. UEL and liquidity risk Liquidity risk betas sorted by UEL In April end from 2002 to 2014, table 5 shows the UEL sorted decile portfolios 21

22 average correlation risks between stock return and market return (Beta 1), stock liquidity innovation and market liquidity innovation (Beta 2), stock return and market liquidity innovation (Beta 3), stock liquidity innovation and market return (Beta 4), and total liquidity risk (Beta 5 = Beta 2 Beta 3 Beta 4). We require our sample stocks to have 60 months (at least 36 months) past monthly return and Amihud (2002) illiquidity ratio. Although the highest UEL decile portfolio has similar correlation between stock return and market return to the lowest UEL decile portfolio, the highest UEL decile portfolio has 1% level significant higher liquidity risk betas such as correlation risk between stock liquidity innovation and market liquidity innovation, stock return and market liquidity innovation, stock liquidity innovation and market return, and total liquidity risk than the lowest UEL decile portfolio. This result shows stocks with higher uncertainty elasticity of liquidity also have higher systematic liquidity risk. (Insert Table 5 here) Can UEL subsume liquidity risk in explaining expected stock returns? To avoid the errors-in-variable problem in our cross-sectional firm-level return analysis, we follow Lee (2011) to form decile portfolios on the basis of one dimensional sorting determined solely on individual stocks betas estimated from past 60 months (at least 36 months). We then calculate those ten portfolios whole sample period correlation risk betas from May 2002 to October 2014 and assign portfolios betas back to individual stocks based on their beta rankings estimated in the end of April from 2002 to Table 6 reports the correlation risk betas estimated from the 22

23 portfolio approach. The correlation risks between stock liquidity innovation and market liquidity innovation (Beta 2), stock return and market liquidity innovation (Beta 3), and stock liquidity innovation and market return (Beta 4) preserve stocks original Beta 2, Beta 3, and Beta 4 rankings, suggesting stocks with higher liquidity risk in the past also have higher liquidity risk in the future. However, UELs estimated from the portfolio approach does not preserve their original rankings, suggesting the characteristic of stocks uncertainty elasticity of liquidity may not be a stable variable; i.e. past UEL may not proxy for future UEL of a stock well. (Insert Table 6 here) As shown in table 7, we then use the liquidity risk betas and UEL estimated from the portfolio approach to explain firm level stock excess returns (raw return minus risk free rate) with Fama and MacBeth (1973) regression from May 2002 to October Model 1 shows that UEL does not have a significant explanation power on stocks excess returns. In addition, from Model 2 to Model 5, our results show that only correlation risk between stock liquidity innovation and market liquidity innovation Beta 2, stock liquidity innovation and market return Beta 4, and total liquidity risk Beta 5 have significant explanation power on stocks excess returns. This result is consistent with Lee (2011) who argues that a security s required rate of return depends on the covariance of its own liquidity with aggregate local market liquidity, as well as the covariance of its own liquidity with local and global market returns. Model 6, Model 8, and Model 9 show that UEL does not subsume the explanation power of Beta 2, Beta 4, and Beta 5 on stocks excess returns. Although 23

24 Chung and Chuwonganant (2014) conjecture stocks with greater UEL command higher return premium after controlling for other liquidity-related risk factors, our result shows that UEL does not have additional explanation power on the stock risk premium after controlling for the liquidity risk in the Chinese stock market. Interestingly, Model 7 shows that UEL has a 10% significant explanation power on excess stock return after controlling the correlation risk between stock return and market liquidity innovation Beta 3. This result suggests a stock s uncertainty elasticity of liquidity may capture the liquidity risk dimensions of liquidity commonality (Beta 2) and flight-to-quality (Beta 4) in explaining stock returns after we control the stock return sensitivity to market liquidity innovation (Beta 3) because Model 9 shows that the coefficient on UEL decreases from significant to insignificant after we control for the overall liquidity risk (Beta 5 = Beta 2 Beta 3 Beta 4). (Insert Table 7 here) 4.4. Aggregate UEL and macro variables Correlation matrix among UEL and macro variables Our final task is to examine when the aggregate UEL is higher under different macro conditions. Specifically, we regress the monthly aggregate UEL of stocks on macro variables such as stock market return, stock market volatility, stock market illiquidity, term spread, and default spread. However, in order to avoid a serial correlation among monthly UEL estimated from past 60 months (at least 36 months) stock illiquidity ratio and market volatility, we apply Corwin and Schultz (2012) daily high-low volatility estimator of Shanghai stock exchange index s daily high and low 24

25 prices to proxy for the stock market volatility. For each month from May 2002 to October 2014, we calculate each stock s monthly UEL by regressing each stock s daily change in Amihud (2002) illiquidity ratio on daily change in the high-low volatility estimator and use the coefficient on the change in market volatility to be each stock s monthly UEL. We then take the equally-weighted UEL of each stock to be the aggregate UEL. Table 8 shows the Pearson correlation coefficients among UEL and macro variables such as monthly stock market return Mkt_Ret, stock market volatility (equally-weighted average of stocks daily return volatility in a month) Mkt_Vola, stock market illiquidity (equally-weighted average of stocks Amihud (2002) illiquidity ratio Mkt_Illiq, term spread (the yield difference between the 10-year government bond and the 1-year government bond) Term_Spread, and default spread (the yield difference between the BBB plus rated corporate bond and the AAA rated corporate bond) Default_Spread. Because China Central Depository & Clearing Co., Ltd (CCDC) from the WIND database starts to report the BBB plus rated corporate bond from January 2009, our Term_Spread and Default_Spread are from January 2009 to October During our sample period, there are 8 significant correlation coefficients among UEL and macro variables. The aggregate UEL significantly negatively correlates with the stock market return with correlation coefficient of The stock market return negatively correlates with the stock market illiquidity with correlation coefficient of and positively correlates with the term spread with correlation 25

26 coefficient of The stock market volatility negatively correlates with the stock market illiquidity with correlation coefficient of , positively correlates with the term spread with correlation coefficient of , and negatively correlates with the default spread with correlation coefficient of The stock market illiquidity negatively with the term spread with correlation coefficient of Finally, the term spread negatively correlates with the default spread with correlation coefficient of This result is consistent with Fama and French (1989) who find that a term premium is low near peaks and high near troughs and that the default spread is high during periods when business is persistently poor and low during periods when the economy is persistently strong. (Insert Table 8 here) When is the aggregate UEL higher? Table 9 shows when the aggregate UEL is higher during our sample period. Model 1 is from May 2002 to October 2014 (150 months) and Model 2 is from January 2009 to October 2014 (70 months). The general message is that the stock market return significantly negatively explains the concurrent aggregate UEL. The average stock s liquidity sensitivity to the stock market volatility is higher when the stock market return is lower. In addition, Model 2 also shows that the aggregate UEL is higher when the stock market illiquidity is higher (close to 10% significance). Therefore, the average UEL is higher in a down market when the stock market liquidity is lower. (Insert Table 9 here) 5. Conclusion 26

27 We examine the determinants of the change in a stock s liquidity given the change in the stock market volatility (uncertainty elasticity of liquidity) and how the UEL correlates with stocks expected returns and stocks liquidity risk in the Chinese stock market from May 2002 to October We find stocks with lower share price, smaller size, higher book to market ratio, past year stock return performance, higher Amihud (2002) illiquidity ratio, higher non-tradable percentage of outstanding shares, less analyst coverage have higher UEL in the Chinese stock market. Fama and French (2015) five factor model analysis shows that stocks with higher UEL have higher factor loadings on SMB, RMW, and CMA, demonstrating that returns of stocks with higher UEL comove with returns of stocks with smaller size, robust operating profits, and less capital expenditures. Although stocks with high UEL have higher liquidity risk, UEL does not have additional explanation power on expected stock returns after controlling for the liquidity risk. Finally, UEL is higher when the stock market return is lower, suggesting investors in the Chinese stock market more care about the market volatility in a down market. We find several interesting points which are different in the U.S. market in the Chinese stock market. First of all, institutional ownership does not seem to be important for a stock s UEL. Since the average institutional ownership is below 20% in the Chinese stock market while the average institutional ownership is above 50% in the U.S. stock market, we expect the importance of institutional ownership will increase as the average institutional ownership gradually increases in the Chinese stock market. Secondly, we find that investors of growth stocks in the Chinese stock 27

28 market care less about stock market volatility than investors of growth stocks in the U.S. stock when they trade. The difference in behavior may result from the significant difference between the turnover rate between the Chinese stock market and the U.S. stock market. Because investors in the Chinese stock market trade more often than investors in the U.S. stock market and growth stocks normally have higher turnover rate in both markets, investors of growth stocks in the U.S. market hold growth stocks much longer than investors of growth stocks in the Chinese stock market and therefore care more about growth stocks liquidity sensitivity to the stock market volatility. Thirdly, the non-tradable percentage of outstanding shares feature plays an important role in explaining UEL. As the Chinese government is engaging the Split-Share Structure Reform, we expect the aggregate UEL will decrease as more shares become tradable. Finally, analyst coverage plays an important role in explaining UEL in the Chinese stock market. Since the financial analyst also plays an important role in disseminating information, we expect the aggregate UEL will also decrease in a more information efficient market with more analyst coverage. 28

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