Margin Trading and Stock Idiosyncratic Volatility: Evidence from. the Chinese Stock Market

Margin Trading and Stock Idiosyncratic Volatility: Evidence from the Chinese Stock Market Abstract We find that the idiosyncratic volatility (IV) effect is significantly exist and cannot be explained by other variables in Chinese stock market. Chinese stock market launched margin trading in March 2010, so we study the margin trading target stocks and non-margin trading target stocks respectively and find that IV effect exists in both stock groups. The IV effect of the margin trading target stocks can be explained by turnover ratio, whose mechanism is that the short sale constraints hinders the expression of the seller s heterogeneous beliefs. However, the IV effect of the non-margin trading target stocks cannot be interpreted by other variables. In comparison to margin trading target stocks, non-margin trading target stocks are more likely to have the characteristics of lottery-type stocks, and gambling behavior of which is more pronounced. Keywords: Idiosyncratic volatility; Margin trading; Short sale constraints; Heterogeneous belief; Gaming behavior 1. Introduction In the framework of the classic risk-return analysis, investors will require corresponding compensation as long as the risk increased additionally. Nevertheless, Ang, Hodrick, Xing, and Zhang (2006) document that stocks with high idiosyncratic volatility will produce low return in the future. Subsequently, they examine 23 countries and regions and find that this negative correlation still exists (Ang, Hodrick, Xing, and Zhang 2009). This phenomenon, which is contrary to the classic asset pricing theory, is called idiosyncratic volatility (IV) puzzle. China is not included in these 23 regions, so later marvelous scholars test IV effect in the Chinese market. As a result, they have various opinions on the IV effect. Yang and Han (2009), Zuo, Zheng, and Zhang (2011) follow the method of Ang, Hodrick, Xing, and Zhang (2006) to estimate the IV and obtain the similar result in Chinese stock market. Deng and Zheng (2011) use the ARMA model to estimate the IV and believe that there is no IV effect in China's stock market. To summarize, the controversy over whether the IV effect exists is based on the 1

estimation method of the expected IV and sample selection. The scholars who affirm its existence mainly explain it from short sale constraints and heterogeneous beliefs. But the logic between the short sale constraint, heterogeneous beliefs and IV is not clear enough. Yang and Han (2009) suppose that the lack of short mechanism and the unreasonable structure of Chinese stock market investors lead to the IV effect. Zuo, Zheng, and Zhang (2011) propose short sale constraints and heterogeneous beliefs are the reasons for IV effect of China's stock market. Yu, Zhang, and Zhao (2017) believe that heterogeneous beliefs can influence the IV effect and indicate that the introduction of short mechanism can reduce the IV puzzle and heterogeneous beliefs. This paper will clarify the logical relationship between heterogeneous beliefs and IV on the basis of predecessors, as well as the role of short mechanism. Some scholars also explain the IV effect from the perspective of maximum daily rate of return. Overall, the results are mixed. Kumar (2009) points out that investors prefer the lottery-type stocks which have low month ended price, high idiosyncratic volatility and high idiosyncratic skewness. Bali, Cakici, and Whitelaw (2011) find a negative and significant relationship between the maximum daily returns over the past one month (MAX) and expected stock returns. They point out that IV effect may not exist and IV itself is a proxy variable of MAX, which could be explained by MAX. Hou and Loh (2016) believe Max is another proxy of IV, as the time-series average of cross-sectional correlation is as high as 75% by Bali, Cakici, and Whitelaw (2011) s paper. Meanwhile, Nartea, Kong, and Wu (2017) argue that the MAX and IV are independent coexistence in the Chinese market, which is inconsistent with the United States and other European countries. Liu, Xing, and Zhang (2014) point out that the IV effect no longer exist under the combined effect of price range, MAX and turnover ratio. The preference for certain special stocks is the main reason for the existence of the IV puzzle. The arbitrage asymmetry caused by short sale constraints has become the focus of scholars' research in recent years. Stambaugh, Yu, and Yuan (2015) believe that the asymmetry of arbitrage leads to the IV effect. Buying undervalued stocks is easier than selling overvalued stocks, so undervalued mispricing is easy to correct, and overvalued mispricing is difficult to correct. In summary, the stock price is overvalued in general, thus IV puzzle is created. Chu, Hirshleifer, and Ma (2017) examine the causal relationship between arbitrage constraint and ten well-known asset pricing anomalies. The results clearly show that arbitrage limitations enhance the effects of asset pricing anomalies. China launched the margin trading mechanism in March 2

2010, which undoubtedly provided a natural experimental base for scholars to study the influence of short-selling constraints. Yang, Hua, and Chen (2016) refer to Fu (2009) using EGARCH model to calculate the IV. They classify and discuss both situations of margin trading, and study their impacts on stock IV effect. It is empirically concluded that margin financing will increase the IV effect of stocks, while securities lending will reduce the IV effect of stocks. However, Guo, Kassa, and Ferguson (2014) prove that the IV estimation in Fu (2009) is wrong. The EGARCH model, used by Fu (2009), uses the return of t month when estimating the IV in t month. Therefore, there is a false positive correlation between the two. Li, Xu, and Zhu (2014) use the plasticizer incident in the liquor industry to find that short sale constraint leads to the overvaluation of stock prices, while margin trading are conducive to correcting overvalued stock prices. Li, Du, and Lin (2015) compare the IV effect of margin trading target stock (target stock) and non-margin trading target stocks (non-target stock) and the IV of stocks before and after the stocks are listed or kicked out. They find that the IV of the target stocks are lower than that of the non-target stocks. The stocks IV decrease after the stocks are included in the margin trading institutions, and increase after being excluded. China has strict requirements for the screening of stocks under the margin of financing and securities lending. The stocks selected usually have the large circulation, high fluidity and good stability, and the information of such stocks is more transparent, so it s reasonable to have lower IV. Therefore, due to the company's own characteristics, it cannot fully demonstrate that introducing margin trading mechanism reduces the target stocks IV. This paper will use the difference in differences model to test the impact of margin trading on target stocks IV. First of all, we use the last month s IV as the proxy of current month s IV and study the IV effect of the Chinese stock market, and found that IV effect exists in Chinese stock market generally. Based on previous research, this article will focus on the following three aspects. First, this article will try to explain IV effect from two aspects: heterogeneous beliefs and gambling behavior. The IV is an overall risk measure of abnormal returns. We suspect that gambling behavior and heterogeneous beliefs are the main causes of IV effect. Kumar (2009) believes investors prefer lottery stocks. We call this is gambling behavior. Gaming behavior tends to overestimate expected returns, which can lead to abnormal negative returns. In this paper the gambling behavior is represented by the MAX. Heterogeneous beliefs mean that people have inconsistent views on stocks, buyers believe that stock prices will rise, and sellers believe stock prices will fall. The stronger heterogeneous beliefs of people, the more active stock trading are, and the turnover ratio of stocks is higher. Therefore, similar to Zuo, Zheng, 3

and Zhang (2011), Liu, Xing, and Zhang (2014), we use turnover to represent heterogeneous beliefs. Second, this paper will study the difference between gambling behavior and heterogeneous beliefs of investors of margin trading stocks and non-margin trading stocks. According to the relevant regulations of the China Securities Regulatory Commission, stocks that can become the subjects of margin trading have large market value, high liquidity and good stability generally. And there are monitoring and elimination mechanisms. Therefore, these stock information transparency should be higher than others, heterogeneity belief of investors should be weaker and the gambling behavior will be less. Third, this article will explore the impact of short sale constraints on stock IV. Stambaugh, Yu, and Yuan (2015) think buying is easier than selling. Buying will push the stock price up, while selling will cause the stock price decrease. The former will lead to the IV to be negatively correlated with the expected return. The latter will contribute to the IV to be positively correlated with the expected return. Overall, it will give rise to a negative correlation between IV and expected returns as the existence of the short sale constraint. Li, Xu, and Zhu (2014) believe that the short sale constraint causes stock price overvaluation, and margin trading can slow down this phenomenon. Li, Du, and Lin (2015) also examined the IV of margin trading target stocks and non-target stocks. Our paper will further use the difference in differences model to test the effect of margin trading on stock IV. Additionally, we speculate that the abnormality of returns caused by heterogeneous beliefs is partly due to the short sale constraint. Because of the asymmetry of buying and selling, buyers can express their own beliefs, and sellers cannot express their beliefs and can only withdraw from the market, which will inevitably lead to overvaluation of the overall stock price and succeeding in turn trigger the abnormal return. The remainder of the paper is organized as follows. Section 2 presents data description and variable definitions. Section 3 provides the major empirical results. Section 4 concludes. 2. Data and variables The firm-level daily and monthly stocks data are derived from the CASMAR database. Fama- French three factors (market factor MKT, size factor SMB, book to market ratio factor HML) come from the China Asset Management Research Center of the Central University of Finance 4

and Economics. The sample selected all A shares of the Shanghai Stock Exchange and the Shenzhen Stock Exchange. Since the Shanghai and Shenzhen Stock Exchanges began to implement the price limit up or down system on December 16, 1996, therefore the sample period is from January 1997 to March 2017. In order to reduce the impact of outliers, we removed the stock of the company's IPO trading day. And the stocks with less than 10 trading days in the month are excluded for the volatility calculation in order to ensure the accuracy. Due to the constraint imposed by China's price limit system, the up and down range of the stock closing price on each trading day is the closing price of the previous trading day times [-10%, 10%], two rounds are reserved. Therefore, when the abnormal value is deleted, the price fluctuation range is rounded off and the two decimal places are retained. This paper will carry out research on full sample stocks, target stocks, and non-target stocks. A total of 2,387 stocks from Shanghai and Shenzhen from January 1997 to March 2017 are selected as full samples data. In March 2010, China officially launched margin trading, and gradually expanded the size of the margin trading stocks list. Meanwhile, there are also stocks that are removed from the list. In order to guarantee the number of samples, the list of target stocks issued by the Shanghai Stock Exchange and the Shenzhen Stock Exchange on January 25, 2013 will be used as the benchmark. Then exclude stocks that are later removed from the target stocks list. The 461 stock data obtained finally will be used as stock samples for target stocks. 1,420 stocks that have never participated in margin trading are used as stock samples of non-target stocks. 1 Considering the timing of margin financing and the timing of target stock samples selected, our paper takes the period from January 1997 to March 2010 as the first stage, and from February 2013 to March 2017 as the second stage, and conducts a comparative study on the two stages before and after the margin financing. All variables in the Fama-MacBeth regression are winsorized at 0.5% and 99.5% to handle extreme values. We calculate the maximum daily rate of return following the method used by Nartea, Kong, and Wu (2017) MAX. And refer to Zuo, Zheng, and Zhang (2011), Liu, Xing, and Zhang (2014) and others to calculate the turnover ratio (TURNOVER) by dividing the monthly cumulative transaction amount by the month-end circulation market value. Idiosyncratic volatility (IV), 1 Exclude stocks in the list of target stocks issued by the Shanghai Stock Exchange on the July 7th, 2017 and the Shenzhen Stock Exchange on January 5, 2018 and the stocks that have been removed from the list after they have joined the list. In short, only consider stocks that have never participated in the margin trading. 5

size (SIZE), book-to-market ratio (BM), CAPM beta (BETA), short-term reversal (REV), momentum effect (MOM), and idiosyncratic skewness (ISKEW) are all referenced to Bali, Engle, and Murray (2016). The residual standard deviation of the individual stock data obtained by the CAPM model is used to obtain the monthly stock idiosyncratic volatility (IV). In order to ensure the accuracy of the IV, the stock data with less than 10 trading days in a month is excluded, and we use last month s standard deviation of the daily return reside to proxy the current month IV. The size (SIZE) is measured using the natural logarithm of the market value of equity at the end of month t. The book-to-market ratio (BM) is the book market value divided by the market capitalization value. The CAPM beta (BETA) is the covariance of stock returns and market returns divided by market risk, and all returns are deducted risk-free returns. Shortterm reversal (REV), momentum effect (MOM) and idiosyncratic skewness (ISKEW) are calculated following Bali, Engle, and Murray (2016). The financing balance (FB) and the shorting balance (SB) represent the impact of margin trading respectively. 3. Empirical test 3.1 The existence of the IV puzzle Using portfolio analysis, stocks are divided into ten portfolios according to IV each month. And we only hold these portfolios holdings for one month, and change the holding every month. Then we report the equal-weighted averages, CAPM alpha, and Fama-French three-factor alpha of stock returns for each decile and the return spread between the highest-and lowest-iv portfolios in Table 1. The second column shows that the portfolio IV is negatively correlated with the average return. The difference among average return of the portfolio of highest and lowest IV is -1.685% and the Newey-West-t is -6.24. The third and fourth columns show that the portfolio IV is negatively correlated with the risk-adjusted expected return, for the return spread between the highest-and lowest-iv portfolios is statistically and economically significant negative. Therefore, the IV effect exists, and IV is negatively related with expected returns. However, for the value-weighted holding portfolio, averages, CAPM alpha, and Fama- French three-factor alpha of the return spread between the highest-and lowest-iv portfolios are insignificant. We also analyze the target stocks and non-target stocks separately. It is found that 6

the target stocks average return and the Fama-French three-factor alpha of the return spread between the highest-and lowest-iv portfolios from January 1997 to March 2017 is significantly positive, and the spread of CAPM alpha is insignificant. In comparison, the averages, CAPM alpha, and Fama-French three-factor alpha of the stocks return spread between the highest-and lowest-iv portfolios for non-target stocks are significantly negative. Therefore, for the valueweighted univariate portfolios, the reason why the IV effect does not exist is due to the target stocks. We speculate that this is because the target stocks have high market value, so the weight ratio is high, and the stability of the stock itself is good, which makes the overall portfolio stability better. To save space, we put the results of the value-weighted portfolio analysis in the Internet Appendix. Table 1 Returns on portfolio sorted by IV At the beginning of every month we sort stocks into quintiles according to their idiosyncratic volatility (IV) in the past calendar month. We compute each portfolio s equal-weighted excess returns for the current month. We also estimate each portfolio s CAPM alpha and Fama-French 3-factor alpha using the full sample of monthly equalweighted returns for each portfolio. The last two row shows the return and alpha spread between the highest- and lowest IV portfolios together with Newey-West t-statistics which reported in parenthesis. We conduct the analysis for the full sample period January 1997 to March 2017. Significance at the 1% level is indicated by ***. decile Average return (%) CAPM alpha (%) FF-3 alpha (%) low IV 1.733 0.843 0.385 2 1.912 0.96 0.433 3 1.941 0.961 0.394 4 1.842 0.866 0.306 5 1.704 0.727 0.187 6 1.529 0.527-0.096 7 1.39 0.399-0.275 8 1.135 0.128-0.483 9 0.851-0.153-0.78 high IV 0.048-0.946-1.543 high-low -1.685*** -1.789*** -1.929*** (-6.24) (-6.78) (-7.57) In addition to the single sorting method, we also use the Fama-MacBeth regression analysis at the firm level. Taking the expected excess return of the stock as the dependent variable, and IV, MAX, SIZE, BM, BETA, REV, TURNOVER, MOM, ISKEW as independent variables. Set 7

up the model: R r IV MAX SIZE BM BETA i, t f, t 0, t 1 1, t 1 i, t 1 2, t 1 i, t 1 3, t 1 i, t 1 4, t 1 i, t 1 5, t 1 i, t 1 REV TURNOVER MOM ISKEW 6, t i, t 1 7, t 1 i, t 1 8, t 1 i, t 1 9, t 1 i, t 1 i, t 1 (1) First, using the full sample data of all stocks from January 1997 to March 2017, stock return at month t is the dependent variable, and IV, MAX, SIZE, BM, BETA, REV, TURNOVER, MOM, ISKEW at month t-1 are independent variables. We do univariate regression analysis first. Table 2 shows the time series average of the regression coefficients for a single variable. The results show that the IV and expected return are significantly negatively correlated. The t-value is -7.27, and the IV effect in the Chinese market exists. The MAX is significantly negatively correlated with the expected return of stocks, with a t-value of -4.58, confirming that the Chinese stock market has the MAX effect too. Both findings supports Nartea, Kong, and Wu (2017) s document. At the same time, SIZE, REV, TURNOVER, ISKEW are significantly negatively correlated with stock expected return; BM, BETA are significantly positively correlated with stock expected return; there is no significant relationship between mom and expected return. Table 2 All stock univariate Fama-MacBeth regression results We run a firm-level univariate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from January 1997 to March 2017. We report the time-series averages of the slope coefficients and their associated t-statistics in a single row, but each variable is independently regressed on stock returns. IV and the other control variables are defined in the Appendix. Significance at the 1% and 5% levels is indicated by *** and **, respectively. MAX SIZE BM BETA REV TURNOVER MOM ISKEW IV -0.091*** -0.569*** 0.310*** 0.591*** -0.000*** -2.034*** -0.000-0.256*** -0.687*** (-4.58) (-3.42) (2.85) (2.78) (-3.70) (-6.67) (-1.60) (-4.37) (-7.27) Then, still focus on the full sample data, the stock's expected return is used as the dependent variable. Multivariate regression analysis is performed using Fama-MacBeth regression to test the robustness of MAX effect and the relationship between MAX and IV. The results are shown in Table 3. It can be found that IV can explain the MAX since MAX effect disappears when controlling for IV in the regression, which is different from the finding by Nartea, Kong, and 8

Wu (2017). Nartea, Kong, and Wu (2017) observe that the MAX effect and the IV effect of the Chinese market are independent coexist, In addition, we also find the turnover ratio can explain MAX. Table 3 Full sample data of all stocks bivariate and multi-variate Fama MacBeth regression results with MAX For all stocks, we run a firm-level bi-variate and multi-variate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the MAX and other control variables using monthly data from January 1997 to March 2017. Each row reports the time-series averages of the slope coefficients and their associated t-statistics. MAX and the other control variables are defined in the Appendix. Significance at the 1%, 5% and 10% levels is indicated by ***, ** and *, respectively. MAX SIZE BM BETA REV TURNOVER MOM ISKEW IV -0.097*** -0.576*** (-5.34) (-3.50) -0.086*** 0.267** (-4.52) (2.55) -0.130*** 0.863*** (-7.02) (4.15) -0.081*** -0.000* (-3.50) (-1.96) -0.022-1.934*** (-1.26) (-6.97) -0.099*** -0.000 (-4.82) (-1.39) -0.097*** -0.150** (-4.61) (-2.58) 0.001-0.701*** (0.03) (-6.18) 0.046*** -0.722*** 0.029 0.658*** -0.000-2.565*** -0.000-0.264*** -0.371*** (2.61) (-4.73) (0.32) (3.63) (-1.42) (-10.04) (-0.93) (-5.55) (-3.99) Again, following the previous practice, taking the full sample from January 1997 to March 2017 as a sample, and the stock's expected return is used as the dependent variable. Multivariate regression analysis is performed using Fama-MacBeth regression to test the robustness of IV effect. The results are shown in Table 4. When adding other control variables in the regression, the IV effect always exist and cannot be explained by other variables in Chinese stock market. According to the previous literature, gambling behavior represented by MAX and the heterogeneous belief represented by the TURNOVER, to a certain extent, can explain IV. However, the results show that after controlling the TURNOVER and the MAX, although the 9

t-value of the IV is greatly reduced, from -7.27 to -3.12, its effect is still significantly exist, indicating that gambling behavior and heterogeneous beliefs cannot fully explain the IV effect. For multi-variate regression, IV effect remains after controlling other variables. Table 4 Full sample data of all stocks bivariate and multi-variate Fama MacBeth regression results with IV For all stocks, we run a firm-level bi-variate and multi-variate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from January 1997 to March 2017. Each row reports the time-series averages of the slope coefficients and their associated t-statistics. IV and the other control variables are defined in the Appendix. Significance at the 1%, 5% and 10% levels is indicated by ***, ** and *, respectively. IV SIZE BM BETA REV TURNOVER MOM ISKEW MAX -0.763*** -0.606*** (-8.73) (-3.71) -0.659*** 0.127 (-7.26) (1.20) -0.706*** 0.540** (-7.61) (2.56) -0.748*** -0.000 (-7.45) (-1.18) -0.327*** -1.724*** (-3.50) (-6.22) -0.700*** -0.000 (-7.30) (-1.45) -0.678*** -0.162*** (-7.15) (-2.85) -0.357*** -1.695*** 0.007 (-3.12) (-6.16) (0.31) -0.371*** -0.722*** 0.029 0.658*** -0.000-2.565*** -0.000-0.264*** 0.046*** (-3.99) (-4.73) (0.32) (3.63) (-1.42) (-10.04) (-0.93) (-5.55) (2.61) Compared with the non-target stocks, the target stocks have large market value, high liquidity, good stability, and the transparency of corporate information disclosure is higher. Therefore, the IV effect of the target stocks should be weaker than that of non-target stocks. Then, the significance of the IV of the two types of stocks, as well as the explanatory effect of gambling behavior and heterogeneous beliefs on the IV of the two types of stocks are examined separately. We use Fama-MacBeth cross-section regression for the target stocks and non-target stocks analysis, respectively, from January 1997 to March 2017. The results shown in Table 5 and Table 6. For target stocks, when the turnover ratio is controlled, the IV becomes completely 10

insignificant (t-value is -0.53), indicating that the heterogeneous beliefs can explain the IV effect. For the non-target stocks, the situation is similar to the full sample stock analysis that IV effect exists and cannot be explained by other variables. The result is documented in Table 6, IV cannot be explained by either TURNOVER or MAX, both the magnitude and the t-value of the IV coefficient reduced, but still significant, which means the turnover ratio and MAX cannot fully explain the IV effect. For the full sample, we find that heterogeneous beliefs can partially explain the IV effect, and gambling behavior represented by MAX can be explained by IV. Table 5 Target stocks bivariate and multi-variate Fama MacBeth regression results with IV For target stocks, we run a firm-level bi-variate and multi-variate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data. Each row reports the timeseries averages of the slope coefficients and their associated t-statistics. IV and the other control variables are defined in the Appendix. Significance at the 1%, 5% and 10% levels is indicated by ***, ** and *, respectively. IV SIZE BM BETA REV TURNOVER MOM ISKEW MAX -0.400*** (-3.55) -0.553*** -0.491*** (-5.16) (-3.15) -0.384*** 0.062 (-3.62) (0.42) -0.441*** 0.428 (-4.04) (1.48) -0.553*** -0.000 (-4.64) (-0.09) -0.068-1.669*** (-0.53) (-4.14) -0.380*** -0.000 (-3.24) (-0.41) -0.385*** -0.163* (-3.40) (-1.80) -0.449*** -0.004 (-3.55) (-0.13) -0.293** -0.593*** 0.023 0.345-0.000-2.610*** -0.000-0.294*** 0.069** (-2.16) (-4.01) (0.19) (1.24) (-0.09) (-6.16) (-0.31) (-3.31) (2.22) Table 6 Non-target stocks bivariate and multi-variate Fama MacBeth regression results with IV For non-target stocks, we run a firm-level bi-variate and multi-variate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data. Each row reports the time- 11

series averages of the slope coefficients and their associated t-statistics. IV and the other control variables are defined in the Appendix. Significance at the 1%, 5% and 10% levels is indicated by ***, ** and *, respectively. IV SIZE BM BETA REW TURNOVER MOM ISKEW MAX -0.884*** (-9.40) -0.901*** -1.143*** (-10.16) (-6.46) -0.855*** 0.188* (-9.25) (1.90) -0.896*** 0.564*** (-9.65) (2.79) -0.864*** -0.000** (-8.73) (-2.39) -0.483*** -1.908*** (-5.01) (-6.98) -0.914*** -0.000 (-9.60) (-0.89) -0.883*** -0.182*** (-9.29) (-2.77) -0.859*** -0.009 (-7.29) (-0.41) -0.472*** -1.913*** -0.002 (-3.97) (-7.02) (-0.11) -0.350*** -1.440*** -0.038 0.798*** -0.000** -2.935*** -0.000-0.276*** 0.048** (-3.42) (-8.28) (-0.43) (4.23) (-2.56) (-11.52) (-0.94) (-4.91) (2.22) 3.2 Gaming behavior and heterogeneous beliefs In order to study the impact of the margin trading mechanism on IV, TURNOVER, and MAX, and further explore the existence of gambling behavior and heterogeneous beliefs on the two types of stocks, the cross-sectional regression analysis is carried out for the target stocks and non-target stocks in two stages (Chinese stock market launched margin trading in March 2010, our paper takes the period from January 1997 to March 2010 as the first stage, and from February 2013 to March 2017 as the second stage). The results are shown in Table 7 and Table 8. Comparison of time, in the second stage, the IV, TURNOVER and MAX of target stocks are significantly weaker than the first stage. However, only the level of significance for the turnover ratio is weakened in the second stage for non-target stocks. If we compare these two different stocks groups, the IV, TURNOVER and MAX in the two stages of non-target stocks are stronger than those of the target stocks. It shows that IV effect can be reduced by the margin trading, heterogeneous beliefs and gambling behaviors of the target stocks. The non-target stocks are almost unaffected by the margin trading. 12

Table 7 Target stocks two-stage Fama-MacBeth regression results We select target stocks. For the left part, we run a firm-level univariate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from January 1997 to March 2010 (first stage). Each row reports the time-series averages of the slope coefficients and their associated t-statistics, but each variable is independently regressed on stock returns. IV, MAX and TURNOVER are defined in the Appendix. For the right part, we run a firm-level univariate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from February 2013 to March 2017(the second stage). Significance at the 1%, 5%, and 10% levels is indicated by ***, **, and *, respectively. The first stage The second stage IV MAX TURNOVER IV MAX TURNOVER -0.440*** -0.445* (-3.21) (-1.80) -0.075** -0.010 (-2.20) (-0.18) -1.887*** -0.935 (-3.71) (-1.38) Table 8 Non-target stocks two-stage Fama-MacBeth regression results We select non-target stocks. For the left part, we run a firm-level univariate Fama MacBeth crosssectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from January 1997 to March 2010 (first stage). Each row reports the time-series averages of the slope coefficients and their associated t-statistics, but each variable is independently regressed on stock returns. IV, MAX and TURNOVER are defined in the Appendix. For the right part, we run a firm-level univariate Fama MacBeth cross-sectional regression of the return on that month with 1-month lagged values of the IV and other control variables using monthly data from February 2013 to March 2017(the second stage). Significance at the 1% and 5% levels is indicated by *** and **, respectively. The first stage The second stage IV MAX TURNOVER IV MAX TURNOVER -0.928*** -0.791*** (-7.51) (-4.01) -0.140*** -0.098*** (-5.14) (-2.90) -2.991*** -1.086** (-7.17) (-2.48) The MAX effect of the non-target stocks are stronger than target stocks in both stages, indicating that the gambling behavior on the non-target stocks is stronger than the target stocks. 13

On the one hand, we believe that it is related to the requirements of investors in the margin trading rules. Both the Shanghai Stock Exchange and the Shenzhen Stock Exchange have regulated that investors who open credit accounts must meet the requirements of no less than 500,000 RMB securities trading assets per day in nearly 20 trading days. We refer to investors who have reached the requirements for opening a credit account as qualified investors. Others are called unqualified investors. The investment strength, experience and analysis level of qualified investors are at a high level, and investment decisions are more based on rational analysis, so there are probably fewer gambling behaviors. In comparison, unqualified investors have more gambling behavior. On the other hand, it is related to the margin trading choice of target stocks. Through the screening of margin trading rules, the target stocks are basic in line with the characteristics of large market value, high liquidity and less volatile, so the lottery characteristics of these stocks are weaker. Investors will be more gambling on non-target securities. According to Kumar (2009) definition of lottery stocks: lottery stocks have low prices, high volatility and high volatility skewness. We descriptively test these three characteristics of the target stocks and non-target stocks, and use the independent sample t test to observe the level of significance of the difference. Table 9 shows that the non-target stocks are lower in price, higher in volatility, higher in volatility skewness, and the differences are statistically significant. Therefore, both the nature of the stock and the empirical test indicate that the lottery-type characteristics of the target stocks are weaker and the gambling behavior is less. Table 9 Lottery type description statistics The table provides descriptive statistics on the price, IV and ISKEW characteristics of the target stocks and non-target stocks from five aspects: mean, standard deviation (sd), minimum (min), median (median) and maximum (max). And use the independent sample t test to observe the level of significance for the difference. We conduct the analysis from January 1997 to March 2017. Target stocks Non-target stocks Independent sample t test (t value) price IV ISKEW price IV ISEKW price IV ISKEW mean 14.57 1.980 0.370 11.77 2.140 0.410 53.714-46.942-15.924 sd 14.71 0.980 0.690 8.620 1.030 0.710 min 0.680 0.0200-3.370 0.500 0.0100-3.540 median 10.71 1.790 0.350 9.560 1.940 0.390 max 386.4 22.64 3.550 169.5 20.62 3.840 We suppose that the heterogeneous beliefs of non-target stocks are stronger than the target 14

stocks, because the heterogeneous beliefs of investors in such stocks cannot be expressed. Combining the result above-mentioned that the IV effect of target stocks is explained by the turnover ratio, and IV and turnover of target stocks in the second stage decreased significantly (Table 7). We speculate that the introduction of the margin trading mechanism can make the heterogeneous belief of the investors of the target stocks to be expressed, thus reducing the IV. Next, we will further study the impact of margin trading mechanism on the IV effect of stocks. 3.3 Short sale constraint From the two-stage comparison in Table 7, the stock IV, the MAX, and the turnover ratio of the target stocks are significantly lower. The significance level of the IV decreased from 1% to 10%, the significance level of the MAX fell from 5% to insignificant. And the turnover ratio coefficient s level of significance decreased from 1% to insignificant. Based on the document by Table 8, the significance level of TURNOVER of non-target stocks decreased a bit, from 1% to 5%, but the significance level of IV and MAX remain the same. Based on this, it is clear that the introduction of the margin trading mechanism can significantly decrease the IV, gambling behavior and heterogeneous beliefs of the target stocks, but not for non-target stocks. In order to further study the effect of margin trading on the IV, a difference in differences model analysis is conducted on two types of stocks. First we have the dummy variable T, let T=0 for the first stage, and T=1 for the second stage; then introduce the dummy variable D, let D=0 for non-target stocks and D=1 for target stocks; last, let the interaction item DID=T*D. The model is as follows: IV= T D DID+ (2) 1 2 3 where 3 represents the effect of margin trading on the IV. The results are shown in Table 10. It is found that the implementation of margin trading has a significant decrease effect on the stock IV (t = -25.79). In order to test the robustness of the results, we selected 254 stocks, respectively, from target stocks and non-target stocks with the closest SIZE to conduct common trend test and other influencing factors testing after controlling the SIZE of stocks. First, using the difference in differences model after controlling the scale, the results are shown in Table 11. After controlling the scale variable, the IV of target stocks is still significantly lower than the IV of non-target stocks. Second, the common trend test. Figure 1 shows the line chart of equivalent weighted IV of 15

the two types of stocks and time. The line chart from March 2010 to February 2013 is only for the continuity of time and has no reference value. The difference of IV is equal to the IV of target stocks minus the IV of non-target stocks. In the first stage, the IV of the two types of stocks is almost exactly the same, and the difference of IV is close to zero. In the second stage, the difference of IV drops. It shows that in the first stage, the two types of stocks have a common trend, and in the second stage, after the implementation of the margin trading mechanism, there is a difference between the two. Table 10 Difference in differences Model Introduce the dummy variable T, T=0 for the first stage (January 1997 to March 2010), and T=1 for the second stage (February 2013 to March); then create the dummy variable D, let D=0 for 1420 non-target stocks and let D=1 for 461 target stocks; last, we have the interaction item DID=T*D. Significance at the 1% level is indicated by ***. IV DID -0.263*** (-25.79) time 0.164*** (28.51) treated -0.088*** (-15.13) Table 11 Difference in differences model after controlling scale variables We select 254 stocks from target stocks and nontarget stocks with the closest SIZE, respectively. The settings of the variables are the same as in Table 10. Significance at the 1% level is indicated by ***. IV DID -0.108*** (-6.08) time -0.082*** (-6.41) treated 0.037*** (3.44) Figure 1 IV of target stocks and non-target stocks The difference of IV is equal to the IV of target stocks minus the IV of non-target stocks 16

Third, the placebo test. The sample interval is from January 1997 to February 2010 before the margin financing and financing are allowed. Assume that the margin trading is carried out in January 2003. The first phase is from January 1997 to December 2002, and the second phase is from January 2003 to February 2010. The rest remained unchanged. The results of the double difference model are shown in Table 12. Under this condition, the introduction of margin trading mechanism has significantly increased the IV of target stocks. Therefore, it cannot be said that there are other factors that make the previous results untrustworthy. Table 12 Placebo test The sample is from January 1997 to March 2017. Assume that the margin trading is carried out in January 2003.The first stage is from January 1997 to Jannuary 2003 and the second stage is from March 2003 to February 2010. We select 254 stocks from target stocks and non-target stocks with the closest SIZE, respectively. The settings of the variables are the same as in Table 10, apart from the stocks number. Significance at the 1% level is indicated by ***. IV DID 0.082*** (4.87) time 0.395*** (33.98) treated -0.044*** (-3.31) In summary, the development of the margin trading mechanism can effectively reduce stocks IV. The margin trading mechanism is divided into two parts: financing and securities lending. In order to explore whether the IV is inhibited by financing or securities lending, this paper uses the financing balance (FB) and the short balance (SB) as the independent variables and the stock s IV as the dependent variable, and runs Fama-MacBeth regression to test whether FB and SB is significantly related with IV. The results are shown in Table 13. We find that both FB and SB are significantly negative correlated with IV, but SB is more significant, indicating that the main role of reducing the IV of stocks comes from securities lending. Chinese stock market introduced the securities lending mechanism, which eliminated short-selling constraint for target stocks and reduced its IV. Therefore, the IV effect of Chinese stocks is partially due to the short-selling constraint. 17

Table 13 Finance balance and short balance Fama-MacBeth regression We use target stocks to run a firm-level bi-variate Fama MacBeth cross-sectional regression of the IV on that month with the same month values of the FB and SB using monthly data from February 2013 to March 2017. The result reports the time-series averages of the slope coefficients and their associated t-statistics. IV and the other variables are defined in the Appendix. Significance at the 1% and 10% levels is indicated by *** and *, respectively. FB SB -0.002* -0.525*** (-1.76) (-3.63) According to the research results of Stambaugh, Yu, and Yuan (2015), Li, Xu, and Zhu (2014), short sale constraint will cause arbitrage asymmetry between buyers and sellers; Chu, Hirshleifer, and Ma (2017) also mention that the cost of selling is infinitely compared to buying because of the existence of short selling constraint. We believe that heterogeneous beliefs are normal phenomena in the stock market, otherwise there will be no buying nor selling. However, if the heterogeneous belief cannot be expressed, it can cause an abnormal return. Before the introduction of margin trading, buying is much easier than selling. The buyer's beliefs can be well expressed in the market, and the seller has no way to express his or her beliefs in the market. As a result, the stock price will be overestimated and the negative abnormal return will be obtained in the future. Under other similar conditions, the target stocks are more in line with the assumption that the all investors can obtain sufficient market information in a timely manner in the assumption of the classic capital asset pricing model comparing to the non-target stocks. Therefore, the market can react to the information more quickly, which can drive the stock price into a reasonable position. And the abnormalities caused by other interference items are weak. When the buying and selling is asymmetric, the seller s belief of shorting is suppressed. After the introduction of the margin financing mechanism, the seller s beliefs can be fully expressed. The IV and TURNOVER of target stocks in the second stage are reduced. Therefore, the IV effect of margin trading target stock can be explained by heterogeneous beliefs, which mechanism is that the short sale constraint hinders the expression of the seller's heterogeneous beliefs. 3.4 Robustness test 18

We will conduct a robustness test by eliminating common factors after deleting all financial industry stocks. The financial industry is highly leveraged and will have an impact on the outcome, thus we delete all financial industry stocks at the beginning. Then, we use Fama- French three-factor model to eliminate common factors. The formula for the yield is shown in equation (3). It can be seen that the rate of return comes from two parts: the common factor related return and the abnormal return. After removing the common risk factors (market factor MKT, size factor SMB, and book to market ratio factor HML), we can get the risk-adjusted rate of return rit, _ adj, showed in equation (4). r MKT SMB HML (3) i, t i MKT, i t SMB, i t HML, i t i, t r _ adj (4) i, t i i, t The risk-adjusted rate of return can eliminate the influence of common factors, leaving only the idiosyncratic part and unexplained part to test the robustness of the results, and can avoid the estimation error of CAPM beta (introduced by Brnnan, Chorida, and Subrahmanyam, 1998). We will retest all above empirical parts. The major results are almost consistent with before. And there are two differences here. Firstly, Table 3 shows that controlling the turnover can make the MAX completely insignificant, but now it can only reduce its significance level to 10% (see Table IA.4 of the Internet Appendix). This shows that turnover can only partially explain the MAX. Secondly, the robust test results of the two-stage cross-sectional regression analysis of target stocks are shown in Table IA.5 of the Internet Appendix. Compare the two stage overtime, all IV, MAX and TURNOVER did not change two much. It is hard to see whether the short sale constraint has an impact on the three. Compare the two groups of stocks, it can be seen that the significant level of target stocks MAX effect is 5%, which is lower than the significant level of 1% of the non-target stocks. 2 It indicates that there are more gambling behaviors for the non-target stocks. 4. Conclusion Overall, the IV effect of Chinese stock market exists and cannot be explained by other variables. However, if we separate stocks into target and non-target, the IV effect of the target stocks can 2 Because in this part the results of the non-target stocks are almost the same as before, so table is not listed. 19

be explained by the turnover ratio. This shows that the IV effect of the target stocks is mainly derived from heterogeneous beliefs. And the reason is that the short-selling constraint hinders the expression of heterogeneous beliefs. The IV effect of non-target stocks cannot be explained, and it is largely affected by other factors besides heterogeneous beliefs. The occurrence of gambling on the target stocks is less than that of non-target stocks. On one hand, because the target stocks are large in circulation, good in liquidity, and less volatile, so weak in all lottery characteristics. On the other hand, from the perspective of investors, some investors have been subject to the short-selling constraint, so they are more likely to conduct gambling on non-target stocks. Through the double difference model, we find that the introduction of margin trading mechanism can significantly reduce the IV of the target stocks. And the result is robust after consideration of several additional tests. The inhibition of stock IV mainly comes from securities lending. Therefore, the introduction of short selling mechanism is conducive to the stock s price correction in China. 20

Appendix Variable definition and specific processing method The monthly IV, MAX, ISKEW data is calculated from the daily data. The following i represents the i -th stock, d represents the d -th day, t represents the t -th month, y represents the y -th year R i is the return of stock i, r m is the market return, r f is the riskfree return, rr m f is the market return minus the risk-free return. (1) Idiosyncratic volatility (IV): First use the CAPM model to find the idiosyncratic return of stock id, i on day d.the IV of the t -month of the stock i is defined as the standard deviation of the idiosyncratic returns for the month. R r ( R r ), IVi, t var( i, d ) i, d f, d i i m, d f, d i, d (2) Maximum daily return (MAX): Due to the implementation of the ups and downs in China, the stock price fluctuations in one day may not be fully expressed. If directly refer to the method of Bali, Cakici, and Whitelaw (2011) to find the maximum daily rate of return, it will cause error. Therefore, according to the practice of Nartea, Kong, Wu (2017), this paper seeks the cumulative daily maximum rate of return as a substitute for the maximum daily rate of return. Specifically, if the stock returns 10% on the first day and 5% on the second day, the cumulative return on the first day of the stock is 15%. Similarly, if the stock's return on the first day is 10%, the yield on the second day is 10%, and the return on the third day is 5%, then the cumulative return on the first day of the stock is 25%. (3) Short-term reversal (REV): The short-term reversal of period t is defined as the return of period t multiplied by 100. REV 100 R i, t i, t (4) Momentum effect (MOM): The momentum effect of the t -th period is calculated from the yield of t 1 to t 11. MOM 100 ( R 1) 1 i, t i 11: 1, m m t t (5) Size (SIZE): Firm size at each month t is measured using the natural logarithm of the market value of equity at the end of month t. SIZE ln( MktCap ) i, t i, t 21

(6) Book to market ratio (BM): It is defined as the book market value divided by the market capitalization, and then calculate the logarithm. Twelve months book market value of in year y is using the book market value of month 12 th in year y-1. Market capitalization is the market value of equity at the end of month t. BM it, BE i,y 1 ln( ) BE is the book market value, ME is the outstanding market value. (7) CAPM beta (BETA): Defined as the covariance of stock i 's return and market return ME it, divided by market risk. BETA it, cov( Ri, t rf, t, rm, trf, t ) var( r r ) m, t f, t (8) Turnover ratio (TUNOVER): Defined as the monthly cumulative transaction amount divided by the market capitalization at the end of the month. TURNOVER it, svolume it, MktCap (9) Idiosyncratic skewness (ISKEW): First calculate the residual of the market-valued weighted three-factor model, then use the following formula to calculate idiosyncratic skewness. r MKT SMB HML i, d i MKT, i d SMB, i d HML, i d i, d ISKEW it, 1 n 3 d 1 id, n 1 n ( ) d 1 n 2 3/2 id, (10) Finance balance (FB): The finance balance refers to the difference between the monthly financing purchase and the repayment of the loan by investor. (11) Short balance (SB). The short balance is the differences between monthly short selling and buying and repaying. it,, 22

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