Hedging or Speculation, What can we Learn from the ...

Hedging or Speculation: What Can We Learn from the Volume-Return Relationship?

Lin Huang and Dayong Zhang* Research Institute of Economics and Management Southwestern University of Finance and Economics April 2014

ABSTRACT: This study investigates the volume-return relationship using data from the Chinese stock market. Based on the model set up by Llorente et al. (2002), we test empirically whether investors in China are hedging oriented or motivated by speculation. A two-state Markov switching model was used to augment the basic model. Allowing the underlying model to switch between two regimes reveals further information that investors' motivation in the Chinese stock market is sensitive to the general market conditions.

KEY WORDS: Chinese stock market, information asymmetry, Markov switching, stock return, trading volume.

JEL Classification G12 G14 C22

-------------Lin Huang ([email protected]) is an associate professor of finance at the Research Institute of Economics and Management, Southwestern University of Finance and Economics, China. Dayong Zhang ([email protected]), corresponding author, is an associate professor of finance at the Research Institute of Economics and Management, Southwestern University of Finance and Economics, China. The authors thank the editor, Ali M. Kutan, and anonymous referees for their valuable comments. Any remaining errors are the authors’. * Corresponding author: Dayong Zhang, Research Institute of Economics and Management, Southwestern University of Finance and Economics, 55 Guanghuacun Street, Chengdu, China, 610074. Email: [email protected]; Phone: +86-28-87352967 1

Electronic copy available at: http://ssrn.com/abstract=2199322

Hedging or Speculation: What Can We Learn from the Volume-Return Relationship?

April 2014

ABSTRACT: This study investigates the volume-return relationship using data from the Chinese stock market. Based on the model set up by Llorente et al. (2002), we test empirically whether investors in China are hedging oriented or motivated by speculation. A two-state Markov switching model was used to augment the basic model. Allowing the underlying model to switch between two regimes reveals further information that investors' motivation in the Chinese stock market is sensitive to the general market conditions.

KEY WORDS: Chinese stock market, information asymmetry, Markov switching, stock return, trading volume.

JEL Classification G12 G14 C22

1

Electronic copy available at: http://ssrn.com/abstract=2199322

Researchers have long been interested in studying the relationship between trading volume and stock returns. It is believed that the trading volume of a stock contains important information and has a crucial role in forecasting future returns. Previous studies in this area focus on the contemporaneous relationship between trading volumes and return (see Karpoff, 1987 for a survey of relevant literature) and show a strong positive correlation between price change and volume. Since the 1990s, the focus has moved to the dynamic relationship between price changes and volume. In other words, scholars investigate the causal relationship, such as whether volume helps forecast stock returns or whether investors trade more when stock prices rise. Antoniewicz (1993) found that the returns for individual stocks on high-volume days were more persistent than the returns on low-volume days. Others such as Stickel and Verrecchia (1994), Chordia and Swaminathan (2000), Gervais et al. (2001), Connolly and Stivers (2003), Kaniel et al. (2008), Hutson et al. (2008) and Chuang et al. (2009) also report a significant dynamic relationship between returns and trading volumes via different methods. Darrat et al. (2003) used intraday trading information for Dow Jones industrial average (DJIA) component stocks and found that the majority of the DJIA stocks showed no contemporaneous correlation between volume and volatility. However, the authors found evidence of significant lead-lag relations between these two variables. Griffin et al. (2007) examined the data from 46 developed and developing countries that showed a strong positive relation between turnover and past returns in many markets. More recently, scholars have begun to examine whether the return-volume dynamics change in different phases of the stock market cycle. Ning and Wirjanto (2009) discovered an 2

extreme asymmetric return-volume dependence in six emerging East Asian equity markets. 1 Chen (2012) used a regime switching model to identify the U.S. bull and bear stock market. He found that stock returns are negatively correlated with volume in a bear market, while the correlation is positive in a bull market. Liu et al. (2012) proposed a two-state Markov switching model to examine the explanatory and predictive power of price and trading volume for return volatility. As the stock market in China has grown, more attention has been drawn to investigating similar problems in China. Lee and Rui (2000) examined contemporaneous and causal relationships between trading volume, stock returns and volatility in the Chinese stock market. They found that trading volume does not cause Granger stock market returns in each market. Chan et al. (2007) compared the information content of stock trades by domestic and foreign investors in the Chinese stock market. The authors found that the A-share volume had strong predictive ability for B-share returns before February 2001 when domestic investors were not allowed to invest in the B-share market. Our research fits into this line of literature and further adopts a regime-switching strategy for investigating the volume-return relationship in China. We set up our baseline model based on a theoretical model by Llorente et al. 2 (2002, hereafter referred to as LMSW). The model allows us to identify investors' motivation for trading through the volume-return relationship and thus provide more information than simply examining the lead-lag relationship or causal 1

Some papers have studied the volume-return relationships in emerging markets, for example, Gündüz and Hatemi-j (2005), Yilmaz and Gulay (2006), Huang et al. (2012). 2 A significant number of theoretical studies try to explain volume-return relationships. For example, Chordia and Subrahmanyam (2004) use order imbalance, Liu (2006) connects with liquidity, Statman et al. (2006) offer an behavioral approach etc. LMSW belongs to the strand of asymmetric information literature, which includes Brown and Jennings (1989), Grundy and McNichols (1989), Blume et al. (1994), Wang (1994), He and Wang (1995), Holden and Subrahmanyam (2002), Schneider (2009), Biais et al. (2010) and Albuquerque and Miao (2014). Gagnon and Karolyi’s (2009) empirical evidence supports an explanation for the volume-return relationship based on asymmetric information. 3

relationship. LMSW suggest two reasons why investors trade: first, to hedge and rebalance their portfolios and, second, to speculate using their own private information. Trading based on these motives may result in different patterns in return dynamics. When a group of investors sells a stock for hedging, the stock price must decrease to attract others to buy. Since there is no change in the expected future payoff of the stock, a decreasing price will cause a low return in the current period and a high expected return in the next period. If a group of investors sells stocks for speculative reasons, the decreasing price will reflect the group’s private information about future payoffs. With the asymmetric information in the market, price only partially reveals the investors’ private information. The low return in the current period will be followed by a low return in the next period. Thus, hedging trading is more likely to generate negative autocorrelation in returns, and speculative trading is more likely to lead to positive autocorrelation in returns. By examining the serial correlation of returns combined with the trading volume, we can learn which trading motive is the most important and gain insight into the future movement of the price. To reveal existing multiple regimes, we adopt a simple Markov switching model, which allows the baseline model to switch between multiple regimes. Investors’ trading motives may be different under different market conditions. In a regime with high volatility, given the investors’ risk-averse behavior, they may not want to speculate even they have an information advantage. Thus, in a high-volatility regime, the positive serial correlation in returns would be not obvious compared with the low-volatility regime. In other words, investors will show strong hedging motives in a high-volatility regime, and the returns will be negatively correlated with the high trading volume. Our hypothesis is that investors may change their 4

trading strategy when they are faced with different levels of risk or general market conditions. Another contribution of this paper is that we apply the LMSW model to the market index, though LMSW examine their theory using individual stock data. We believe the hedging motive and the speculative motive exist at the portfolio level, and market-level trading motives are more important to dig out. The reasons are as follows: First, since market capitalization is a proxy for measuring information asymmetry, we can group individual stocks according to their size. We hypothesize that there are more speculative trades in smaller portfolios. Second, there are two trading exchanges in the Chinese stock market: Shanghai and Shenzhen. Most of the big firms are listed on the Shanghai stock exchange, while middle and small firms are listed on the Shenzhen stock exchange. Given size as the information asymmetry measure, we argue that the firms listed on the Shenzhen stock exchange have an information asymmetry problem and investors are more likely to trade based on speculation. The Shenzhen Composite Index, as a combination of middle and small stocks, shows different return-volume dynamics compared with the Shanghai Composite Index. Examining these two market indices can provide a method for studying trading motives in different markets at the same time. Finally, from investors’ point of view, especially fund managers, they often care more about a market-wide phenomenon, not specific securities. The possible different trading motives implied in the market index can help investors forecast index movements. Our major findings can be summarized as follows. In the one-regime case, hedging generates more trading for the Shanghai and Shenzhen stock exchanges. After we consider the time-varying market conditions in the regime-switching model, we find two regimes exist in 5

both markets. The high-volatility regime is dominated by more hedging trades than the low-volatility regime in the Shanghai stock exchange. However, there is no dominant strategy in the Shenzhen market. Our findings are consistent with the fact that the Shanghai stock exchange has more big firms listed and with investors’ risk-aversion behavior.

Theoretical Background and the LMSW Model The LMSW Model In this model, LMSW assume two tradable securities, one risk-free and one risky asset. They introduced a non-traded asset in the investors’ portfolio to generate hedging requirements. The non-traded asset is correlated with the risky asset. As investors’ holding of the non-traded asset changes, each investor will want to adjust his stock holdings to maintain an optimal portfolio strategy. In addition, some investors may have private information about future stock payoffs. These investors trade on their information and generate speculative trading. Volume provides a way to identify the underlying trading motives and the possible future price movement. If speculative trading is dominant in the market, together with high trading volume, the return tends to exhibit positive autocorrelation. If more investors trade for hedging reasons, with the observed high trading volume, the return will be more likely to reverse itself. Our baseline model is taken from Proposition 3 in LMSW's paper, and the testable empirical model takes the following form (Equation 1). The original model looks at individual stocks. We modify it by referring to a market version of the LMSW model:

Rt +1 =C0 + C1 Rt + σ C2Vt Rt + ε t +1 , ε t ~ iidN(0, ) , 6

(1)

where Rt is the market return for the current period, and Vt is a measure of volume. In this model, returns are generated by three sources: public information about future payoffs, investors’ hedging trades and speculative trades. Different trading motivations exhibit different return and volume dynamics. When public information arrives, the returns generated by public news about future payoffs are independent over time; i.e., C1 is 0. The stock price fully reflects public information, and the price change has no impact on the investor’s stock demand under the assumption of exponential utility. LMSW suggest that the results for the coefficient C1 are complex and sensitive to the specification of the underlying model. In the imperfect market, where information asymmetry exists, price only partially reflects the private information. Therefore, we expect to have a momentum effect and a positive C1. The results for C2 are more robust in the LMSW model. Because investors hold the non-traded asset, they have to trade to hedge against the associated risk. They need to reallocate their portfolio holdings to maintain an optimal risk profile, and they have to decrease (increase) the price to attract other investors to buy (sell). Returns generated by hedging trades give rise to volume and are serially negatively correlated; i.e., C2 < 0. However, speculation-dominated trades will result in a statistically positive coefficient.

Markov Switching Model Because market conditions vary over time, investors’ trading behavior may also change accordingly. Their trading strategy changes when they are faced with different levels of risk or economic status. In the following, we adopt the Markov regime-switching (Hamilton, 1994) 7

model to investigate this problem. Assuming there are m unobservable states of nature ( st = 1, 2, m ), Model 1 can be written as:

Rt +1 = C0 ( st ) + C1 ( st )σs Rt + C2 ( st )Vt Rt + ε t +1 , ε t | st ~ iidN(0, ( t )) .

(2)

The evolution depends on the data states. In the Markov switching (hereafter referred to as MS) model, we assume the regime-switching process is an ergodic Markov chain defined by the transition probabilities:

pij = Pr( st +1 = j | st = i ), ∀i, j ∈ {1, 2, m} m

where

∑p j =1

ij

= 1 . The m-state transition matrix P is therefore

 p11   P=   p  m1 

p1n    . pmn 

Data Description The data used in our analysis was collected from the RESSET Finance Database 3, with weekly data from the period July 1, 2000, to July 12, 2012. Taking a broader snapshot of trading by using weekly data, rather than daily data, lessens the chance of inaccuracies arising, for example, from a particular day during the week. We use return data for the Shanghai Composite Index (SHCI) and the Shenzhen Composite Index (SZCI). The weekly turnover rate for both markets following LMSW’s methodology is defined as the weekly aggregate of the daily turnover weighted by market capitalization (tradable shares). The primary data is transformed by taking a natural logarithm. 3

http://www.resset.cn/en/ Beijing Gildata RESSET Data Tech Co., Ltd. 8

[Insert Figures 1 and 2 about here]

In Figures 1 and 2, the logarithm of turnover for both markets is trending or likely to be non-stationary. Using the LMSW methodology, we de-trend the turnover data by subtracting its historical mean. The horizon used in this de-trending is taken as 10 weeks, and the following equation shows how the volume variable is calculated:

Vt = log turnovert −

1 −1 ∑ log turnovert + s . 10 −10

[Insert Table 1 about here] Table 1 provides the summary statistics of our variables. On average, the return for the SHCI is lower than that of the SZCI. The volatility of the SZCI is also higher than that of the SHCI. Generally, stock capitalization on the Shenzhen Stock Exchange is smaller than that on the Shanghai stock exchange, and therefore, they produce higher returns and are more risky. Since speculation is more likely occur with smaller stocks, we expect speculation-oriented trading on the Shenzhen stock exchange to exceed that on the Shanghai stock exchange. We perform unit root tests on the return, log turnover and the de-trended series. The results are shown in Table 2. The returns are generally stationary. The ADF tests on turnover show that the series is stationary. However, the KPSS 4 tests suggest the unit root. These results are consistent with the graphic illustration of turnover data in both markets and

4

The null hypothesis of the ADF test is nonstationary or the series contains a unit root, whereas the KPSS test uses stationarity as the null hypothesis. 9

provide motivation for de-trending the series. We arbitrarily choose 10 weeks 5 as the historical average following the LMSW principle, and the unit root tests and graphics prove the stationarity of the new volume measure.

[Insert Table 2 about here]

Empirical Results We report the estimated coefficients for a single regime model in Table 3. For both markets, the return without volume coefficient C1 is significant and positive, suggesting that there is a positive autocorrelation in the returns holding volume at the average level, which is consistent with the momentum effect in general. We are more interested in the return with volume coefficient C2. Taking the SHCI as an example, the parameter C2 is significantly negative, which indicates that on the Shanghai stock exchange, the general trading behavior is dominated by hedging. Unlike LMSW, we use the aggregate-level market return and volume instead of individual stocks. One of the problems with using macro-level data is the inability to distinguish the number of stocks dominated by different types of trades. Instead, our results provide a market-wide view of the dominant trading strategy. The estimated absolute value of C2 for the Shenzhen stock exchange is smaller than the C2 value for the Shanghai stock exchange, in the sense that there is less hedging-motivated trading or stronger speculative behavior in the Shenzhen stock exchange. This is consistent with our hypothesis that more hedging trades occur on the Shanghai stock exchange since the market capitalization of the

5

We also try the 20- and 30-week moving average and find similar results. 10

stocks traded on the Shanghai stock exchange is larger than that on the Shenzhen stock exchange. The Shanghai Composite Index return is more likely to reverse following high volume.

[Insert Table 3 about here]

The stock market has experienced periods of boom and crash in the preceding decades. More than one state can exist, which means investors may follow different dominant strategies over time. When the market is more volatile, investors have more incentive to hedge even they have information advantages. To motivate the regime-switching model empirically, we use the Inclan and Tiao (1994) test on volatility switching for each regression residual 6. The results reported in Table 3 provide clear evidence of the structural instability in the variance of the regression residuals. There is not only one structural break but also potentially multiple breaks. The existence of such breaks will eventually affect the regression, and therefore provide evidence for the Markov switching model.

[Insert Table 4 about here]

Table 4 shows the results for a two-state MS model 7. Both markets have two distinctive states and subsequently different trading patterns in each state. In general, regime 1 is a high-volatility regime, and regime 2 is a low-volatility regime. For both markets, the standard 6

We thank an anonymous referee for his valuable comments, and we give a brief introduction to the Inclan and Tiao (1994) method in Appendix 1. 7 Liu et al. (2012) also adopt a two-state MS model to study stock returns. 11

deviations for the estimated residuals in regime 1 are approximately twice as high as in regime 2. For example, the standard deviation in the SHCI is 0.0468 in regime 1 and 0.0214 in regime 2. The signs of these coefficients are not different from those in the single regime case; however, there are significant differences between the two regimes. For the SHCI results, the key parameter for the return-volume interaction term in regime 1 (high volatility) is statistically significantly negative, and the impact is bigger than that in the single regime case. The coefficient C22 in the low-volatility regime is negative but insignificant. This indicates that investors have a stronger motive to trade due to hedging when the market is more volatile. Ignoring the existence of different regimes may disguise the real underlying trading motives. And the market return is more likely to exhibit reversals in the volatile period when high trading volumes are observed. However, in the SZCI estimate, the return-volume coefficients C21 and C22 for the two regimes are insignificantly negative; in the one-regime case, C2 is marginally significantly negative at 10%. Thus, stocks on the SZCI are more likely to be traded for speculative reasons since the stocks’ market values are much smaller than those of the stocks traded on the Shanghai stock exchange. Comparing the estimated values of C21 and C22, C21 is more negative than C22, which indicates that the hedging strategy is still more in the high-volatility regime. However, the insignificance demonstrates that there is no dominant strategy on the Shenzhen stock exchange. It is hard to forecast the direction of the SZCI movement even when high volume occurs. For the autocorrelation coefficient conditional on volume, C11 is not significant; but in regime 2, C12 is more than twice as much as C11 and statistically significantly positive in the 12

SHCI and the SZCI. In the empirical literature, the negative return correlation evidence is mainly observed in daily data and small stocks (e.g., French and Roll 1986, Lo and MacKinlay 1988, Jegadeesh and Titman 1995). French and Roll (1986) and Jegadeesh and Titman (1995) found that the first-order correlation of daily returns is negative for small firms but positive for large firms. The LMSW empirical results also showed that for small stocks, C1 is negative while for large stocks C1 is positive. They argue that C1 is model sensitive, requiring additional theoretical input to understand. French and Roll (1986) suggested that the positive autocorrelation rises when the market incorporates information slowly. One possible explanation for our finding is that in a low-volatility regime, the market responds to information more slowly than in a volatile regime.

[Insert Figures 3 and 4 about here]

Now let’s look at the regime-switching properties over time. Figures 3 and 4 plot the smoothed probability of regime 1 with the price index and returns for the SHCI, respectively. The shaded area is defined as if the probability in regime 1 is greater than 0.8. These figures provide a more straightforward view of how two states evolve over time. Regime 1 occurred predominantly between 2007 and 2010, including the speedy price increase period in 2007 and the period of the global financial crisis. Not only a market crash but also rapid increases in stock prices can cause hedging-oriented trading. A clearer view could be had by referring to the plot of the return and regime probabilities. Clearly, regime 1 is associated with the more volatile financial crisis period as well as temporary high-volatility periods. 13

[Insert Figures 5 and 6 about here]

The estimated results for the Shenzhen stock exchange follow a similar pattern as the Shanghai stock exchange. Furthermore, the plots for the price index, return, and smoothed probability of staying in regime 1, as seen in Figures 5 and 6, also tell a similar story to the Shanghai case. In both markets, the log likelihood ratio (LR) statistics are strongly in favor of the regime-switching model as opposed to the single-regime model.

Conclusion In this paper, we apply the Markov regime-switching model based on the theoretical framework developed by LMSW to identify investors’ trading behavior in the Chinese stock market. When we examine the one-regime case in the Shanghai and Shenzhen stock exchanges, the results show that the interaction coefficient of return with volume is negative. This suggests that hedging motivations generate more trading, though the Shenzhen stock exchange behaves differently from the Shanghai stock exchange. After we consider the regime-switching model to capture the time-varying market conditions, we find that two regimes exist in both markets. One regime (the high-volatility regime) has twice the volatility of the low-volatility regime. The trading behaviors are very different between these two regimes. The high-volatility regime is dominated by more hedging trades compared to the low-volatility regime. This indicates that investors are more likely to trade to hedge risks during the volatile period, which is consistent with the investors’ risk-aversion behavior. 14

Although in the low-volatility regime volume seems to have less predicting power for future returns, there is a significantly positive autocorrelation, which indicates a strong momentum effect. What can we learn from the empirical results regarding the volume-return relationship? First, two regimes have existed over time. When investors wish to use volume as a factor in making investment decisions, an appropriate evaluation of the market conditions is required. The relationship differs significantly between a riskier market and a relatively safer market. Second, when the market is relatively stable (or less volatile), volume information is less useful in predicting future returns, and previous returns are likely to persist instead. However, when the market is more volatile, because of either rapid price increases (such as a bubble period) or a market crash, trading volume can yield useful information, and investors are more likely to trade for hedging rather than speculation. In such conditions, the return momentum is not significant. One caveat here when interpreting these empirical results is that we cannot rule out speculative trading in the market for individual stocks. The conclusions drawn from our empirical analysis give only the overall market situation. However, this general market observation is very important for fund managers and investors when they make market-wide decisions.

15

References Albuquerque, R., and J. Miao. 2014. “Advance Information and Asset Prices.” Journal of Economic Theory 149: 236-275. Antoniewicz, R. 1993. “Relative Volume and Subsequent Stock Price Movements.” Working paper, Board of Governors of the Federal Reserve System. Biais, B.; P. Bossaerts.; and C. Spatt. 2010. “Equilibrium Asset Pricing and Portfolio Choice under Asymmetric Information.” Review of Financial Studies 23, no. 4: 1503-1543. Blume, L.; D. Easley; and M. O’Hara. 1994. “Market Statistics and Technical Analysis: The Role of Volume.” Journal of Finance 49, no. 1: 153-181. Brown, D., and R. Jennings. 1989. “On Technical Analysis.” Review of Financial Studies 2, no. 5: 527-551. Chan, K.; A. Menkveld; and Z. Yang. 2007. “The Informativeness of Domestic and Foreign Investors’ Stock Trades: Evidence from the Perfectly Segmented Chinese Market.” Journal of Financial Market 10, no. 4: 391-415. Chen, S. 2012. “Revisiting the Empirical Linkages between Stock Returns and Trading Volume.” Journal of Banking and Finance 36, no. 6: 1781-1788. Chordia, T., and A. Subrahmanyam. 2004. “Order Imbalance and Individual Stock Returns: Theory and Evidence.” Journal of Financial Economics 72, no. 3: 485-518. Chordia, T., and B. Swaminathan. 2000. “Trading Volume and Cross-Autocorrelations in Stock Returns.” Journal of Finance 55, no. 2: 913-935. Chuang, C.C.; C.M. Kuan; and H.Y. Lin. 2009. “Causality in Quantiles and Dynamic Stock Return-Volume Relations.” Journal of Banking and Finance 33, no. 7: 1351-1360. Connolly, R., and C. Stivers. 2003. “Momentum and Reversals in Equity-Index Returns during Periods of Abnormal Turnover and Return Dispersion.” Journal of Finance 58, no. 4: 1521-1555. Darrat, A.; S. Rahman; and M. Zhong. 2003. “Intraday Trading Volume and Return Volatility of the DJIA Stocks: A Note.” Journal of Banking and Finance 27, no. 10: 2035-2043. French, K., and R. Roll. 1986. “Stock Return Variances: The Arrival of Information and the Reaction of Traders.” Journal of Financial Economics 17, no. 1: 5-26. Gagnon, L., and G. Karolyi. 2009. “Information, Trading Volume, and International Stock Return Comovements: Evidence from Cross-Listed Stocks.” Journal of Financial and Quantitative Analysis 44, no. 4: 953-986. Gervais, S.; R. Kaniel; and D. Mingelgrin. 2001. “The High-Volume Return Premium.” Journal of Finance 56, no. 3: 877-919. Griffin, J.; F. Nardari; and R. Stulz. 2007. “Do Investors Trade More When Stocks Have Performed Well? Evidence from 46 Countries.” Review of Financial Studies 20, no. 3: 905-951. 16

Grundy, B., and M. McNichols. 1989. “Trade and the Revelation of Information through Prices and Direct Disclosure.” Review of Financial Studies 2, no. 4: 495-526. Gündüz, L., and A. Hatemi-j. 2005. “Stock Price and Volume Relation in Emerging Markets.” Emerging Markets Finance & Trade 41, no. 1 (January-February): 29-44. Hamilton, J. 1994. Time Series Analysis. Princeton: Princeton University Press. He, H., and J. Wang. 1995. “Differential Informational and Dynamic Behavior of Stock Trading Volume.” Review of Financial Studies 8, no. 4: 919-972. Holden, C. and A. Subrahmanyam. 2002. “News Events, Information Acquisition, and Series Correlation.” Journal of Business 75, no. 1: 1-32. Huang, P.Y.; Y.S. Ni; and C.M. Yu. 2012. “The Microstructure of the Price-Volume Relationship of the Constituent Stocks of the Taiwan 50 Index.” Emerging Markets Finance & Trade 48, supp. 2: 153-168. Hutson, E.; C. Kearney; and M. Lynch. 2008. “Volume and Skewness in International Equity Markets.” Journal of Banking and Finance 32, no. 7: 1255-1268. Inclan, C., and G.C. Tiao. 1994. “Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance.” Journal of American Statistical Association 89, no. 427: 913-923. Jegadeesh, N., and S. Titman. 1995. “Short-Horizon Return Reversals and the Bid-Ask Spread.” Journal of Financial Intermediation 4, no. 2: 116-132. Kaniel, R.; G. Saar; and S. Titman. 2008. “Individual Investor Trading and Stock Returns.” Journal of Finance 63, no. 1: 273-310. Karpoff, J. 1987. “The Relation between Price Changes and Trading Volume: A Survey.” Journal of Financial and Quantitative Analysis 22, no. 1: 109-126. Lee, C.F., and O.M. Rui. 2000. “Does Trading Volume Contain Information to Predict Stock Return? Evidence from China’s Stock Market.” Review of Quantitative Finance and Accounting 14, no. 4: 341-360. Liu, W. 2006. “A Liquidity-Augmented Capital Asset Pricing Model.” Journal of Financial Economics 82, no. 3: 631-671. Liu, X.; D. Margaritis; and P. Wang. 2012. “Stock Market Volatility and Equity Returns: Evidence from a Two-State Markov-Switching Model with Regressors.” Journal of Empirical Finance 19, no. 4: 483-496. Llorente, G.; R. Michaely; G. Saar; and J. Wang. 2002. “Dynamic Volume-Return Relation of Individual Stocks.” Review of Financial Studies 15, no. 4: 1005-1047. Lo, A., and A. MacKinlay. 1988. “Stock Market Prices Do not Follow Random Walks: Evidence from a Simple Specification Test.” Review of Financial Studies 1, no. 1: 41-66. Ning, C., and T.S. Wirjanto. 2009. “Extreme Return-Volume Dependence in East-Asian Stock Markets: A Copula Approach.” Finance Research Letters 6, no. 4: 202-209. Schneider, J. 2009. “A Rational Expectations Equilibrium with Informative Trading 17

Volume.” Journal of Finance 64, no. 6: 2783-2805. Statman, M.; S. Thorley; and K. Vorkink. 2006. “Investor Overconfidence and Trading Volume.” Review of Financial Studies 19, no. 4: 1531-1565. Stickel, S., and R. Verrecchia. 1994. “Evidence that Trading Volume Sustains Stock Price Changes.” Financial Analyst Journal 50, no. 6: 57-67. Wang, J. 1994. “A Model of Competitive Stock Trading Volume.” Journal of Political Economy 102: 127-168. Yilmaz, A., and G. Gulay. 2006. “Dividend Policies and Price-Volume Reactions to Cash Dividends on the Stock Market: Evidence from the Istanbul Stock Exchange.” Emerging Markets Finance & Trade 42, no. 4 (July-August): 19-49.

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Appendix 1 Inclan and Tiao’s (1994) method is one of the earliest attempts to deal with changes in volatility. They start with an investigation of changes in the variance of a sequence of independent observations. Their test statistic is the centered cumulative sums of squares. Consider a sequence of independent random variables of {ν t }, t = 0,1,T with zero mean and time varying variance σ t2 . The statistics (we call them the DK statistics) are written as: C k Dk = k − , k =1,......, T , with D0 =DT =0 CT T

(A.1)

where Ck = ∑ t =1ν t2 is the CUSUM. For a series with homogeneous variance, Inclan and k

Tiao (1994) prove that the adjusted DK statistics

T / 2 ⋅ Dk are distributed asymptotically as

a Brownian bridge. To investigate whether there is a shift in variance, we need to look at the significance of the maximum of the adjusted DK statistics where the position of the maximum value of the statistics identifies the timing of the shift in volatility. Inclan and Tiao also add to the literature a systematic way of detecting multiple breaks (the ICSS algorithm). This method, as claimed by Inclan and Tiao (1994), can be applied to regressions as a diagnostic analysis of residuals.

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Table 1. Descriptive statistics Shenzhen

Shanghai Return

Turnover

Vol.

Return

Turnover

Vol.

Mean

0.0014

1.8208

-0.0045

0.0021

2.0282

0.0040

Median

0.0003

1.8048

-0.0092

0.0025

2.0531

0.0194

Maximum

0.1496

3.4854

1.7252

0.1669

3.5447

1.6468

Minimum

-0.1384

0.0243

-1.969

-0.1519

-0.3738

-1.9959

Std. Dev.

0.0355

0.6554

0.4303

0.0397

0.6582

0.4315

Skewness

0.2756

0.0693

-0.0599

0.0156

-0.2668

-0.2450

Kurtosis

4.8456

2.6838

4.8387

4.6061

2.8239

4.9852

96.9278***

3.1151

88.7003***

67.4147***

8.2463**

109.2269***

JB statistic

Note: The superscript *** indicates significance at 1%, ** indicates significance at 5% and * indicates significance at 10%. Turnover is the natural logarithm of the weekly turnover rate. Vol. is the de-trended turnovers defined in the paper.

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Table 2. Unit root test

Shanghai

Shenzhen

Return

Log turnover

Vol. (de-trended)

ADF

-24.0207***

-4.3157***

-13.6662***

KPSS

0.1231

0.3880*

0.0943

ADF

-23.5334***

-4.5399***

-13.4235***

KPSS

0.1252

1.0615***

0.0533

Note: The superscript *** indicates significance at 1%, ** indicates significance at 5% and * indicates significance at 10%.

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Table 3. Single regime estimate Variables

Shanghai

Shenzhen

C0

0.0021 (0.0015)

0.0027 (0.0016)

C1

0.0755* (0.0425)

0.0820* (0.0419)

C2

-0.1917** (0.0799)

-0.1429* (0.0842)

R2

0.0107

0.0082

1207.839

1136.417

Inclan and Tiao (1994) test

3.158*** (01/12/2006)

3.782*** (17/11/2006)

ICSS test on multiple break

B.1: 14/12/2007 B.2: 19/03/2010

B.1: 28/12/2007 B.2: 19/03//2010 B.3: 18/11/2011

Log likelihood

Notes: Standard errors are in brackets. For the Inclan and Tiao (1994) test, the estimated break points are in brackets. The superscript *** indicates significance at 1%, ** indicates significance at 5% and * indicates significance at 10%.

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Table 4. Two-regime MS estimate Variable

Shanghai

Shenzhen

C01

0.0064** (0.0027)

0.0077* (0.0043)

C11

0.0560 (0.0572)

0.0385 (0.0695)

-0.2398**

(0.1178)

-0.1882 (0.1443)

0.0468*** (0.0024)

0.0563*** (0.0035)

C02

-0.0012 (0.0014)

-0.0001 (0.0014)

C12

0.1257** (0.0635)

0.1740*** (0.0575)

C22

-0.0820 (0.1214)

-0.0521 (0.1188)

Sigma2

0.0214*** (0.0013)

0.0259*** (0.0013)

P(1,1)

0.9441

0.9391

p(1,2)

0.0450

0.0332

1258.2469

1190.4526

100.8158***

108.0712***

Regime 1 (high volatility) C21 Sigma1

Regime 2 (low volatility)

Transition probabilities Log likelihood LR statistic

Note: The superscript *** indicates significance at 1%, ** indicates significance at 5% and * indicates significance at 10%.

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Figure 1. Turnover and de-trended turnover for the Shanghai stock exchange

Figure 2. Turnover and de-trended turnover for the Shenzhen stock exchange

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Figure 3. Shanghai Composite Index and the smoothed probability of regime 1 Note: The solid line is the smoothed probability of regime 1, and the dashed line is the Shanghai Composite Index. The shaded area is defined as if the probability in regime 1 is greater than 0.8.

Figure 4. Shanghai index returns and the smoothed probability of regime 1 Note: The solid line is the smoothed probability of regime 1, and the dashed line is the return for the SHCI. The shaded area is defined as if the probability in regime 1 is greater than 0.8.

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Figure 5. Shenzhen Composite Index and the smoothed probability of regime 1 Note: The solid line is the smoothed probability of regime 1, and the dashed line is the Shenzhen Composite Index. The shaded area is defined as if the probability in regime 1 is greater than 0.8.

Figure 6. Shenzhen index returns and the smoothed probability of regime 1 Note: The solid line is the smoothed probability of regime 1, and the dashed line is the return for the SZCI. The shaded area is defined as if the probability in regime 1 is greater than 0.8.

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