opinion divergence, unexpected trading volume and stock returns: evidence from china

International Review of Economics and Finance xxx (2014) xxx–xxx

REVECO-01002; No of Pages 9

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International Review of Economics and Finance

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Opinion divergence, unexpected trading volume and stockreturns: Evidence from China☆

Lin Chen⁎, Lu Qin, Hongquan Zhu⁎⁎School of Economics and Management, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China

a r t i c l e i n f o

☆ We are grateful for the helpful comments and valuab(71090402, 71171170, 71273040, and 71473206) from⁎ Correspondence to: L. Chen, School of Economics an⁎⁎ Correspondence to: H. Zhu, School of Economics anfax: + 86 28 87600543.

E-mail addresses: [email protected] (L. Che

http://dx.doi.org/10.1016/j.iref.2014.11.0121059-0560/© 2014 Elsevier Inc. All rights reserved.

Please cite this article as: Chen, L., et al., OpInternational Review of Economics and Finan

a b s t r a c t

Available online xxxx
Using the turnover decomposition model, we extract unexpected trading volume from tradingactivity to measure divergence in investors' opinions and explore the explanatory power of thatdivergence on stock returns. Portfolios built according to the magnitude of opinion divergenceare significantly profitable. The expected returns of portfolios with small opinion divergence aresignificantly higher than other portfolios, particularly for small companies. When this pricing fac-tor is included in the CAPM and the Fama–French three-factor model, the influence of opinion di-vergence on stock returns during the current month is significantly positive, but it is significantlynegative for the next month. When further considering liquidity, momentum reversal and otherfactors, the conclusion is still valid.
© 2014 Elsevier Inc. All rights reserved.

JEL classification:G12G14

Keywords:Opinion divergenceUnexpected trading volumeStock returnsTurnover decompositionChina stock market

1. Introduction

In this study, we analyze the role of divergence in investors' opinions in predicting the cross-section of future stock returns. Wefind that stocks with a higher degree of opinion divergence earn significantly lower future returns than similar stocks. In particular,a portfolio of stocks in the highest quintile of opinion divergence underperforms a portfolio of stocks in the lowest quintile of opiniondivergence by an average of 10.80% per year. This effect is the strongest in small stocks. After introducing this factor into the CAPMandthe Fama–French three-factor model, the results also show that the influence of opinion divergence on stock returns over a month issignificantly positive, whereas that on the stock returns of the followingmonth is significantly negative. The conclusion remains validwhen further considering liquidity, momentum reversal and other factors.

In empirical research, differences of opinion among investors are generally viewed as a proxy for heterogeneous beliefs. Afterrelaxing the standard assumption of homogeneous expectations in traditional asset pricing theory, differences of opinion havebeen included in numerous models (Basak, 2005; Harris & Raviv, 1993; Harrison & Kreps, 1978; Miller, 1977). Because of gradual in-formation flow, limited attention and heterogeneous prior beliefs, heterogeneous beliefs are closer to the real-world situation (Hong& Stein, 2007). When included in models in place of the standard assumption of homogeneous expectations, heterogeneous beliefscan alter the stock market equilibrium.

Miller (1977) provides an early theoretical analysis of the implications of divergence of opinion on stock returns. He argues that inamarket with short-sale constraints, the opinion of pessimistswould not be incorporated into the current price of a stock, whereas an

le suggestions of anonymous referee and editors. Hongquan Zhu thanks thefinancial support of research grantNational Natural Science Foundation of China. All errors are our own.dManagement, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR Chana. Tel.:+ 86 185 8398 0996.d Management, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR Chana. Tel.: + 86 28 87601865;

n), [email protected] (L. Qin), [email protected] (H. Zhu).

inion divergence, unexpected trading volume and stock returns: Evidence from China,ce (2014), http://dx.doi.org/10.1016/j.iref.2014.11.012

http://dx.doi.org/10.1016/j.iref.2014.11.012

mailto:[email protected]




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2 L. Chen et al. / International Review of Economics and Finance xxx (2014) xxx–xxx

optimistic opinion held by investors is easy to express through trading. Ultimately, this would lead to a higher current price than theintrinsic value of thefirm.Higher divergence of opinion leads to higher current prices and lower future returns.Miller (1977) providesa static model that allows only limited adjustments in expectations and trading activity when new information arrives. Based onMiller's (1977) theory, Harrison and Kreps (1978), Harris and Raviv (1993) and Basak (2005) develop dynamic asset pricing modelsthat incorporate heterogeneous beliefs.

In contrast, some research shows that upward bias in prices will disappear through the actions of rational agents. For example,Diamond and Verrecchia (1987) develop a model that depends on the existence of a perfectly rational market-maker with unlimitedcomputational abilities who can instantaneously estimate unbiased stock value, conditional on all publicly available information. Inaddition, Hong and Stein's (2003) findings rely on perfectly rational arbitrageurs that can eliminate mispricing. However, numerousstudies on limited arbitrage have questioned the assumption of perfectly rational arbitrageurs. For example, Shleifer and Vishny(1997), Gromb and Vayanos (2002) and Chen, Hong, and Stein (2002) provide compelling theoretical explanations of why arbitra-geurs may fail to close the arbitrage opportunity.

Subsequently, the burgeoning empirical literature is strongly supportedMiller's (1977) argument. Lee and Swaminathan's (2000)finding that higher trading volume, as a proxy for differences of opinion, predicts lower future returns is consistent withMiller's pre-diction. Chen et al. (2002) use breadth ofmutual fundownership as ameasure of themagnitude of disagreement among investors andcome to the same conclusion. They find that reductions (increases) in breadth of ownership lead to lower (higher) future returns, asMiller's model would predict. In addition, Diether, Malloy, and Scherbina (2002) use dispersion in analysts' earnings forecasts as analternative proxy of opinion divergence and also come to the same conclusion.

The Chinese stockmarket is an ideal experimental platform because of the absolute short-selling constraints existing up to March31, 2010. To date, however, there has been no empirical research on howdifferences of opinion affect asset prices in the Chinese stockmarket except for that carried out by Opie and Zhang (2013). Opie and Zhang (2013) use mutual fund ownership, breadth of mutualfund ownership and breadth of all investors as measures of opinion divergence. Their third proxy measures divergence among theentire investor population rather than institutional investors, but their conclusion is inconsistent with Miller (1977) and subsequentempirical studies. However, it is well known that investors' trading activity is driven bymarket information, firm-specific informationand divergence of opinion among investors (Bessembinder, Chan, & Seguin, 1996; Garfinkel & Sokobin, 2006). Thus, mutual fundownership, breadth of mutual fund ownership and breadth of all investors perhaps contain homogeneous expectations for stockand are not accurate proxies of opinion divergence. In this study, unexpected trading volume is excluding the trading activitiesbased on homogeneous belief of information. We believe that unexpected trading volume is a more precise measure of divergencein investors' opinions. Garfinkel (2009) has demonstrated that unexplained volume is the preferred proxy for opinion divergence.

Our study contributes to the literature in several ways. First, one of our main contributions is the construction of opinion diver-gencemeasurement. Ourmeasurement is quite new and different from the existingmeasurements, such as analysts' forecasts disper-sion. Garfinkel (2009) has demonstrated that unexplained volume is the preferred proxy for opinion divergence. To date, there is nostudy that has explored the relationship of opinion divergence and stock return using unexplained volume. Although Opie and Zhang(2013) have performed similar research usingmutual fund ownership, breadth ofmutual fund ownership and breadth of all investorsasmeasurements of opinion divergence, their conclusion is inconsistentwith the argument ofMiller (1977) and subsequent empiricalstudies. It is well known that investors' trading activity is driven by market information, firm-specific information and divergence ofopinion among investors (Bessembinder et al., 1996; Garfinkel & Sokobin, 2006). Therefore, mutual fund ownership, breadth of mu-tual fund ownership and breadth of all investors are more likely the homogeneous expectations for stock and not accurate proxies ofopinion divergence. Furthermore, mutual fund ownership, breadth of mutual fund ownership only reflect the information at the endof each quarter, not that of the whole quarter. He, Ng, andWang (2004) emphasize that window-dressing their portfolios is popularfor mutual fund managers. In the Chinese stock market, mutual funds only need to report the top ten stocks, rather than all of thestocks in their quarterly portfolios. This practice would result in great bias if the quarterly data are used. In our paper, unexpectedtrading volume is that of the trading activities that are driven by heterogeneous belief of investors. Therefore, the unexpected tradingvolume is a more precise measure of investors' opinion divergence.

Second, we empirically investigate the effect of investors' opinion divergence on stock returns in the Chinese stock market. TheChinese stockmarket is quite different from the U.S. stockmarket. It is relatively young and is dominated by inexperienced individualinvestors (Mei, Scheinkman, & Xiong, 2009). Therefore, the level of investors' opinion divergence should be more severe in Chinesestock market than in other developed markets. When the opinion divergence as a factor is introduced into the CAPM and theFama–French three-factor model, the models' explanatory power on stock returns improves significantly. Third, we further controlthe impacts from liquidity and momentum and loosen the short-sale constraints on returns as a robustness test; the results remainthe same. Our study confirms the importance of investors' opinion divergence on asset pricing in Chinese stock markets.

The remainder of this study is organized as follows. Section 2 constructs the measurement of divergence in investor's opinions.Section 3 describes the data sample and reports the empirical results. Section 4 covers the robustness testing, and Section 5 summa-rizes the major findings and provides conclusions.

2. Measurement of divergence in investor's opinions

Because opinion divergence is related to cognition and behavior, it cannot bemeasured directly. In the existing literature, indirectvariables are used as proxies for investors' divergence of opinion. For example, bid–ask spread, stock return volatility and analysts'forecast dispersion are proxies commonly used in the literature. Bid–ask spreadmay reflect either information asymmetry or liquidity(Amihud&Mendelson, 1989; Glosten&Harris, 1988;He, Lepone, & Leung, 2013). Stock return volatility is affected by information and

Please cite this article as: Chen, L., et al., Opinion divergence, unexpected trading volume and stock returns: Evidence from China,International Review of Economics and Finance (2014), http://dx.doi.org/10.1016/j.iref.2014.11.012


3L. Chen et al. / International Review of Economics and Finance xxx (2014) xxx–xxx

risk. Both are noisy measures of divergence in investors' opinions. Although analysts' forecast dispersion appears to be a better proxyfor divergence in investors' opinions (Basak, 2005; Diether et al., 2002; Moeller, Schlingemann, & Stulz, 2007; Verardo, 2009; Yu,2011), there are still two potential problemswith this measure. First, not all investors will make a decision according to the forecastsof analysts; analysts' forecast dispersionmerely represents the differences in beliefs between professional investors. Second, analysts'forecast dispersion is subject to the impact of uncertainty. For example, analysts may issue biased forecasts due to their own interests.This leads to information distortion of opinion divergence measured by forecast divergence. We extract opinion divergence from un-expected trading volume,which is a cleanermeasure of opinion divergence because the literature has shown that unexpected volumestrongly reflects diversion in investors' opinions (Garfinkel, 2009).

Theoretically, trading is usually caused by three factors: (i) investors' exogenous liquidity needs; (ii) information impacts,including public information, private information, macro information and firm-specific information; and (iii) investors' opiniondivergence (Bessembinder et al., 1996; Garfinkel & Sokobin, 2006). Expected trading volume, thus, is that due to information. The re-mainder is unexpected volume, a measure of opinion divergence. The difference between ourwork and that of Garfinkel and Sokobin(2006) and Garfinkel (2009) is that they use daily returns of individual stock to fit expected volume, whereas we use a Fama–Frenchthree-factor model to obtain market information and firm-specific information and then fit the expected volume.

Information can be subdivided intomarket information andfirm-specific information.Whenwe use the Fama–French three-factormodel tofit stock returns, the size and value factors capture covariation in returns and variation in expected returns that aremissed bythemarket portfolio (Fama & French, 2004). Furthermore, the size and value factors also capture leverage and the earning-price ratio,which contain information about expected returns that is missed by market betas (Fama & French, 1992). If the market portfolio isused as a proxy for market information, it is reasonable to attribute the size and value factors to firm-specific information.

First, we estimate the Fama–French three-factor model for each stock based on daily stock returns for each month:

PleasInter

Ri; j−Rf ; j

� �¼ αi þ βi RM; j−Rf ; j

� �þ siSMBj þ hiHMLj þ εi; j; ð1Þ

where Ri,j and RM,j are the daily returns of stock i and market index on day j, respectively. Rf,j is the daily risk-free rate. SMBj (smallminus big) and HMLj (high minus low) are the size and value factors respectively. Based on the estimation of Eq. (1), we note thatRMi; j ¼ βi RM; j−Rf ; j

� �andRF

i; j ¼ αi þ siSMBj þ hiHMLj. Ri,jM and Ri,j

F are the returns related tomarket information and firm-specific infor-mation, respectively.

FollowingGarfinkel and Sokobin (2006) andGarfinkel (2009), we use daily turnover rate as the proxy for trading volume. Becausepositive and negative returns have different impacts on trading volume (Karpoff, 1987), we treat them differently in the regression ofthe turnover rate on the absolute value of returns in Eq. (2):

TOi; j ¼ κ i þ γþ1 RM

i; j

��þ þ γ−

1 RMi; j

��− þ γþ

2 RFi; j

��þ þ γ−

2 RFi; j

��− þ εi; j; ð2Þ

where TOi,j is the turnover rate of stock i on day j. When Ri,jM is positive, |Ri,jM|+ = Ri,j

M, and at the same time, |Ri,jM|− = 0; when Ri,jM is

negative, |Ri,jM|− = |Ri,jM|, and at the same time |Ri,jM|+ = 0. The values for |Ri,jF |+ and |Ri,jF |− are obtained by the same method.We run regression (2) based on the previous 36 months for each month with rolling once per month. The coefficient κ i

denotes trading activity caused by investors' exogenous liquidity needs. The trading activity that is caused by information is denoted

as TOIi; j ¼ γþ

1 RMi; j

��þþ γ−

1 RMi; j

��−þ γþ

2 RFi; j

��þþ γ−

2 RFi; j

��−. The remainder is trading activity caused by opinion divergence, denoted as

ODi,j = TOi,j − TOi,jI , which is daily divergence of opinion. Empirically, the opinion divergence of an individual stock i in month t is

ODi;t ¼∑Ni;t

j¼1ODi; j=Ni;t , where Ni,t is the number of trading days of individual stock i in month t.

3. Data and empirical results

3.1. Data and descriptive statistics

We collected daily andmonthly data from the Chinese StockMarket and Accounting Research (CSMAR) database for all of the do-mestic (i.e., A) shares (excluding special treatment stocks) listed on the Shanghai or Shenzhen stock exchanges. To be included in oursample, we required firms to have at least four years ofmonthly observations. Because the Chinese stockmarkets did not enforce rulesrelating to price change limitation before 1997, we select our sample period as 1997 to 2011 to avoid probable policy bias. To obtainreliable model estimations, we exclude the first month of data following any initial public offering and delete the firm/month if thereare fewer than 10 daily observations in that firm/month. Because the accounting ratios offinancial companies are different from thoseof other companies, financial companies are excluded. The final samples consist of 3,162,768 daily data items and 160,018 monthlydata items for 1233 listed companies.

Table 1 provides descriptive statistics for the variables. The sample period is from January 2000 to December 2011. Becausewe runregression (2) based on theprevious 36 months to estimate parameter, the 1997–1999 data are eliminated.OD represents themonth-ly differences of opinion among investors (average of the daily opinion divergence for individual stock in eachmonth); R is themonth-ly return of individual stock; RM is monthlymarket return; SMB andHML are the size factor and value factor, respectively (see Fama &French, 1993); ILLIQ is the illiquidity factor used by Amihud (2002) and Martínez, Nieto, Rubio, and Tapia (2005), as defined inSection 4; Ln(ME) is the natural logarithm of company market capitalization of the previous year (unit: RMB100 million); and BM

e cite this article as: Chen, L., et al., Opinion divergence, unexpected trading volume and stock returns: Evidence from China,national Review of Economics and Finance (2014), http://dx.doi.org/10.1016/j.iref.2014.11.012


Table 1Descriptive statistics for variables.

Mean Median Std. dev 25th 75th

OD −0.040 −0.270 1.378 −0.884 0.575R (%) 1.231 0.400 12.510 −6.940 8.442RM (%) 0.917 1.320 8.781 −5.122 5.334SMB (%) 0.616 0.990 4.040 −1.650 3.200HML (%) 0.275 0.220 2.845 −1.430 2.130ILLIQ 0.221 0.092 0.313 0.035 0.265Ln(ME) 3.354 3.255 0.897 2.710 3.893BM 0.436 0.372 0.259 0.237 0.577

This table presents the descriptive statistics of the variables. The sample period is from January 2000 to December 2011. Because we run regression (2) based on theprevious 36 months to estimate the parameter, the 1997–1999 data are eliminated. OD measures the monthly differences of opinion among investors (average ofthe daily opinion divergence for individual stocks in each month); R is the monthly return of the individual stock; RM is the monthly market return; SMB and HMLare the size factor and value factor, respectively (see Fama & French, 1993); ILLIQ is the liquidity factor (Amihud (2002) illiquidity index, as defined in Section 4);Ln(ME) is the natural logarithm of the company's market capitalization of the last year (unit: RMB100 million); and BM is the book-to-market ratio. To eliminate thepotential influence of extreme values on regression analysis, we winsorize OD, ILLIQ, Ln(ME) and BM by 1% from both top and bottom.


represents the book-to-market ratio. To eliminate the potential impact of extreme values on the regression analysis, wewinsorizeOD,ILLIQ, Ln(ME) and BM by 1% from both top and bottom.

Table 2 presents the Pearson correlation coefficients of the variables (probability values in parentheses). The opinion divergenceindex (OD) has a significantly positive correlation with the stock returns in the current month. The Amihud illiquidity factor (ILLIQ)has a significantly negative correlation with the same stock returns. That is, the higher the illiquidity of the stock, the larger the trans-action cost and the smaller the returns in the currentmonth. The correlation coefficients also reflect the effects of size and value factorson stock returns. The data show that R has a significantly positive correlation with BM and a significantly negative correlation withLn(ME).

3.2. Portfolio strategies based on opinion divergence

According to the theoretical analysis above, the higher the degree of opinion divergence, the higher the current stock returns andthe lower the future returns. In this section,we use portfolio strategies to verify the theoretical analysis.We assign stocks to portfoliosbased on certain characteristics, such as difference of opinion, to compare the difference between the average returns of these stockportfolios. Additionally, taking into consideration the effects of size and value factors on stock returns (Fama & French, 1993), the sizeand book-to-market ratios of firms are controlled for during sorting and grouping.

Each month, we assign stocks to five quintiles based on stock market capitalization at the end of the previous year. In each group,we further divide stocks into five quintiles based on opinion divergence in the month. After assigning the stocks into 25 portfolios,they are held for onemonth. We calculate themonthly portfolio return as the value-weighted average (there is no qualitative differ-ence if portfolio return is based on equal-weighted average). This strategy is repeated at the end of each month.

As Table 3 shows, Panel A andPanel B give the average return in the currentmonth and in the subsequentmonth for each portfolio.The results not only clearly demonstrate a size effect but also show that the degree of opinion divergence has a significant impact onboth current returns and expected subsequent returns. The last column of Table 3 shows a strong negative relationship betweenaverage returns and opinion divergence if the stocks are sorted by opinion divergence only. The current month return for the OD1–OD5 strategy is −3.53%, whereas the corresponding subsequent month return is 0.90%. Both are strongly significant. That is, wecan obtain an unexpected return by using a portfolio strategy based on opinion divergence. Within each size group, the higher the

Table 2Pearson correlation matrix.

R OD RM SMB HML ILLIQ BM

OD 0.339⁎⁎⁎

(0.000)RM 0.673⁎⁎⁎

(0.000)0.357⁎⁎⁎

(0.000)SMB 0.289⁎⁎⁎

(0.000)0.080⁎⁎⁎

(0.000)0.136⁎⁎⁎

(0.000)HML 0.058⁎⁎⁎

(0.000)−0.019⁎⁎⁎

(0.000)0.186⁎⁎⁎

(0.000)−0.278⁎⁎⁎

(0.000)ILLIQ −0.191⁎⁎⁎

(0.000)−0.145⁎⁎⁎

(0.000)−0.184⁎⁎⁎

(0.000)−0.205⁎⁎⁎

(0.000)0.136⁎⁎⁎

(0.000)BM 0.144⁎⁎⁎

(0.000)0.287⁎⁎⁎

(0.000)0.222⁎⁎⁎

(0.000)−0.053⁎⁎⁎

(0.000)0.032⁎⁎⁎

(0.000)−0.008⁎⁎

(0.012)Ln(ME) −0.103⁎⁎⁎

(0.000)−0.259⁎⁎⁎

(0.000)−0.154⁎⁎⁎

(0.000)0.056⁎⁎⁎

(0.000)−0.072⁎⁎⁎

(0.000)−0.318⁎⁎⁎

(0.000)−0.290⁎⁎⁎

(0.000)

This table reports the Pearson correlation of all of the variables. The probabilities are shown in parentheses. ⁎⁎⁎ and ⁎⁎ indicate significance at the 1% and 5% levels,respectively.



Table 3Mean portfolio returns by size and opinion divergence.

Divergence quintiles Small Large All stocks

S1 S2 S3 S4 S5

Panel A: current month average returnOD1 (low) −0.28 −0.18 −0.39 −0.12 0.55 −0.05OD2 0.04 −0.07 −0.12 −0.31 0.09 −0.04OD3 0.69 0.52 0.36 0.32 0.17 0.31OD4 1.72 1.67 1.44 1.44 0.94 1.25OD5 (high) 4.36 4.06 3.73 3.31 2.59 3.48OD1–OD5(t-Statistic)

−4.63⁎⁎⁎

(−14.01)−4.24⁎⁎⁎

(−13.69)−4.12⁎⁎⁎

(−11.91)−3.43⁎⁎⁎

(−9.32)−2.04⁎⁎⁎

(−5.16)−3.53⁎⁎⁎

(−10.19)

Panel B: subsequent month average returnOD1 (low) 2.10 1.71 1.56 1.15 0.69 1.03OD2 1.95 1.90 1.43 1.21 0.96 1.19OD3 1.52 1.37 1.27 1.08 1.13 1.10OD4 0.99 0.96 1.07 1.05 1.03 1.02OD5 (high) 0.00 −0.03 −0.34 0.06 0.36 0.13OD1–OD5(t-Statistic)

2.11⁎⁎⁎

(7.48)1.74⁎⁎⁎

(6.32)1.90⁎⁎⁎

(5.62)1.09⁎⁎⁎

(3.36)0.33(0.86)

0.90⁎⁎⁎

(2.73)

Eachmonth stocks are sorted infive groups based on the level ofmarket capitalization at the end of the previous year. Stocks in each size group are then sorted into fiveadditional groups based on the opinion divergence of eachmonth. After assigning stocks into 25groups, they are held for onemonth.We calculate themonthly portfolioreturn as the value-weighted average. Panel A reports the average return in the currentmonth, and Panel B gives the return of the subsequentmonth. The t-statistics inparentheses test whether the mean of differences is equal to zero. ⁎⁎⁎ indicates significance at the 1% level.


degree of opinion divergence, the higher the current stock returns and the lower the expected subsequent returns. The currentmonthreturn for theOD1–OD5 strategy ranges from−4.63% for small stocks to−2.04% for large stocks, whereas the corresponding range forexpected subsequent returns is 2.11% to 0.33%. Table 3 also shows that the difference in average monthly return between low- andhigh-divergence portfolios declines as the average size increases. That is, the influence of opinion divergence on stock returns(both current month and expected subsequent month) is greater for small companies.

To control for the possible influence of the value effect on stock returns, we triple-sort on size, book-to-market ratio (BM) andopinion divergence. In eachmonth, all stocks are divided into three groups based on stockmarket capitalization at the end of the pre-vious year. Each group is then divided into three groups based on BM. Lastly, each of these nine groups is further divided into threegroups according to the degree of opinion divergence. Thus, we obtain 27 portfolios. All portfolios are held for one month, and thereturns of each are then calculated for current and subsequent months as described above.

Table 4 provides the average returns of all portfolios in the currentmonth (Panel A) and the subsequentmonth (Panel B). It can beobserved from Table 4 that when the impact of size and value factors is controlled for, opinion divergence still has a significant impacton stock returns in the current and subsequentmonths. The current return of a portfolio based on a high degree of opinion divergenceis significantly higher than that based on a low degree of opinion divergence. The reverse relationship is observed for expected sub-sequent returns.

Table 4Mean portfolio returns by size, book-to-market and opinion divergence.

Divergence quintiles Small cap Mid cap Large cap

Low BM High BM Low BM High BM Low BM High BM

Panel A: the current month average returnOD1 (low) −0.25 −0.19 −0.02 −0.09 −0.34 −0.23 0.25 0.17 0.40OD2 0.42 0.66 0.88 0.39 0.42 0.59 0.00 0.27 0.55OD3 (high) 2.88 3.35 3.56 2.17 2.85 3.11 1.32 2.08 2.77OD1–OD3(t-Statistic)

−3.13⁎⁎⁎

(−10.61)−3.54⁎⁎⁎

(−12.26)−3.58⁎⁎⁎

(−11.53)−2.26⁎⁎⁎

(−7.93)−3.19⁎⁎⁎

(−10.67)−3.34⁎⁎⁎

(−11.40)−1.06⁎⁎⁎

(−2.73)−1.92⁎⁎⁎

(−5.63)−2.37⁎⁎⁎

(−7.77)

Panel B: the subsequent month average returnOD1 (low) 1.72 1.92 2.05 1.42 1.43 1.70 0.40 0.92 1.30OD2 1.22 1.75 1.60 1.09 0.96 1.27 0.94 1.13 1.28OD3 (high) 0.09 0.21 0.76 −0.13 0.49 0.53 0.04 0.45 1.04OD1–OD3(t-statistic)

1.63⁎⁎⁎

(6.52)1.71⁎⁎⁎

(6.60)1.29⁎⁎⁎

(5.07)1.55⁎⁎⁎

(5.25)0.94⁎⁎⁎

(3.09)1.18⁎⁎⁎

(4.85)0.36(1.02)

0.47(1.51)

0.26(0.92)

Each month's stocks are sorted into three groups based on the level of market capitalization at the end of last year. Each size group is then sorted into three book-to-market groups. The book-to-market ratio is computed by financial figures of last year. Lastly, these nine groups are divided into three groups according to the degree ofopinion divergence. Thus, we obtain 27 portfolios. Each portfolio is held for one month, and we calculate its returns for the current and subsequent months. This tableprovides the value-weighted average returns of all portfolios in the current month (shown in Panel A) and subsequent month (shown in Panel B). The t-statistics inparentheses test whether the mean of differences are equal to zero. ⁎⁎⁎ indicates significance at the 1% level.




3.3. Time-series analysis

The statistical results of Tables 3 and 4 demonstrate that regardless of whether the size and value factors are controlled for, thedegree of opinion divergence is always an important factor influencing stock returns. In this section, we further verify these resultsby introducing an opinion divergence factor into the asset pricing model based on time-series analysis.

As CAPM and the Fama–French three-factor model are the most commonly used fundamental asset pricing models (Fama &French, 2004; Perold, 2004), and many improvements are all developed based on these models (Acharya & Pedersen, 2005;Carhart, 1997). Thus, we follow a similar path to construct the followingmulti-variable regressionmodel to test the pricing capabilityof opinion divergence.

We introduce the opinion divergence factor into CAPM and the Fama–French three-factormodel to obtainmodels (3) and (4).Wethen run time-series regression for each stock's monthly data and obtain the regression coefficients, intercepts and adjusted sums ofsquared residuals (Adj-R2). Table 5 reports the averages of the intercepts, coefficients and Adj-R2. The t-statistics in parentheses testwhether the mean of the coefficients is equal to zero.

Table 5Time-se

Interc

CAPM0.005(14.00.007(11.90.006(11.80.007(11.3

Fama−0.0(−0.40.000(0.480.000(0.340.002(2.44

We introbtain tt-statist

PleasInter

Ri;t−Rf ;t

� �¼ αi þ βi RM;t−Rf ;t

� �þ γiODi;t þ ηiODi;t−1 þ εi;t ð3Þ

Ri;t−Rf ;t

� �¼ αi þ βi RM;t−Rf ;t

� �þ siSMBi þ hiHMLi þ γiODi;t þ ηiODi;t−1 þ εi;t ð4Þ

The estimated results of CAPM and the Fama–French three-factormodel shown in Table 5 indicate thatmarket risk, size factor andvalue factor all have significant influences on the returns of individual stock. CAPMhas an average explanatory power of 44.42% for thereturns of individual stock, whereas that of the Fama–French three-factor model is 51.83%. When opinion divergence in the currentmonth (ODt) is introduced into both models, its regression coefficient is significantly positive at the 1% level. The averages of theODt coefficients in the CAPM and the Fama–French three-factor model are 1.050 and 0.852, respectively. That is, every one unit in-crease in the degree of opinion divergence will increase monthly stock returns by 0.852% to 1.050%. The impact of a one-month lagin opinion divergence (ODt − 1) on stock returns is negative and significant at the 1% level. The averages of the ODt − 1 coefficientsin CAPM and the Fama–French three-factor model are 0.465 and −0.481, respectively; i.e., every one unit increase in the degree ofopinion divergence will decrease the average stock returns in the subsequent month by 0.665% to 0.481%. These results all showthat the higher the degree of opinion divergence among investors, the higher the stock returns in the current month and the lowerthe returns in the subsequentmonth. This conclusion is still tenablewhen both current and lagging opinion divergence are introducedinto the regression model. Furthermore, with the introduction of the opinion divergence factor, the degrees of fit (Adj-R2) of themodels all increase. Thus, when market risk, size factor and value factor have been controlled for, the index of opinion divergenceis capable of supplying incremental information.

ries test of CAPM and three-factor models for opinion divergence I.

ept ODt ODt − 1 RM–Rf SMB HML Adj-R2

+ OD⁎⁎⁎

8)0.970⁎⁎⁎

(154.46)44.42%

⁎⁎⁎

1)1.050⁎⁎⁎

(14.33)0.913⁎⁎⁎

(141.35)45.89%

1)−0.465⁎⁎⁎

(−12.74)0.982⁎⁎⁎

(149.07)45.02%

⁎⁎⁎

2)2.126⁎⁎⁎

(27.06)−1.645⁎⁎⁎

(−35.90)0.900⁎⁎⁎

(131.22)48.73%

–French + OD007)

0.936⁎⁎⁎

(142.88)0.681⁎⁎⁎

(35.06)0.012(0.57)

51.83%

)0.852⁎⁎⁎

(10.83)0.884⁎⁎⁎

(84.41)0.667⁎⁎⁎

(35.27)0.078⁎⁎⁎

(3.12)53.12%

)−0.481⁎⁎⁎

(−9.23)0.951⁎⁎⁎

(136.56)0.683⁎⁎⁎

(33.37)0.006(0.29)

52.65%

⁎⁎

)1.805⁎⁎⁎

(22.56)−1.474⁎⁎⁎

(−28.90)0.880⁎⁎⁎

(119.28)0.656⁎⁎⁎

(30.15)0.064⁎⁎⁎

(3.03)55.61%

oduce the opinion divergence factor into CAPM and the Fama–French three-factor model. We then run time-series regression for each stock'smonthly data andhe regression coefficients, intercept and adjusted sum of squared residuals (Adj-R2). This table reports the average of intercepts, coefficients and Adj-R2. Theics in parentheses test whether the mean of coefficients is zero. ⁎⁎⁎ and ⁎⁎ indicate significance at the 1% and 5% levels, respectively.




4. Robustness test

4.1. Further analysis taking liquidity into consideration

The literature shows that the liquidity of an asset is also an important factor influencing its returns (Acharya & Pedersen, 2005;Constantinides, Harris, & Stulz, 2003; Márquez, Nieto, & Rubio, 2014). The higher the liquidity of an asset is, the lower the transactioncost is and the smaller the return required by investors is.With other conditions unchanged, an assetwith a higher liquiditywill offer alower future return. Thus, the liquidity of an asset is positively correlated to its current returns and negatively to its future returns. Tomeasure the liquidity of assets, we have adopted the illiquidity index (ILLIQ) of Amihud (2002) and Martínez et al. (2005). Thismeasurement index is based on daily data, so it is applicable to a relatively long time analysis andwill yield a good fit whenmeasuringthe liquidity of assets and forecasting their future returns (Goyenko, Holden, & Trzcinka, 2009).

Note that |Ri,j| is the absolute value of the daily return of individual stock i on day j, and Voli,j is the trading volume (unit: RMB1billion) of individual stock i on day j. The illiquidity of individual stock i on day j is ILLIQi,j = |Ri,t|/Voli,j. The illiquidity of individualstock i in month t is ILLIQi;t ¼ ∑Ni;t

j¼1ILLIQi; j=Ni;t , where Ni,t is the number of trading days of individual stock i in month t.To test whether opinion divergence still has an influence on stock returns after having controlled for liquidity, we introduce the

previous month illiquidity index (ILLIQt − 1) of individual stocks into models (3) and (4) and repeat the time-series regression; theresults are shown in Table 6.

The results in Table 6 show that when market risk, size factor, value factor and illiquidity have been controlled for, opiniondivergence still has a significant impact on stock returns. This impact is significantly positive on current returns and significantly neg-ative on the subsequent month's returns. In some regressions, the coefficients for illiquidity index are significantly positive, which isconsistentwith the existing results and indicates that an assetwith a lower liquiditywill offer a higher future return. After introducingthe illiquidity index into regression, the degree of model fit also increased.

4.2. Cross-sectional regression analysis

Analysis of both the portfolio strategy and the time-series regression show that opinion divergence is an important factor influenc-ing stock returns. The results of portfolio strategy analysis (Tables 3 and 4) indicate that the size and value factors also have amarkedinfluence on stock returns. Additionally, momentum and contrarian strategy are another important factors (Alwathainani, 2012;Jegadeesh & Titman, 1993). It is thus necessary to further discuss the impact of opinion divergence on stock returns after these poten-tial influencing factors are controlled for. We thus set up the following cross-sectional regression model:

Table 6Time-se

Interc

−0.0(−0.10.003(2.080.007(5.38−0.0(−7.5−0.0(−6.2−0.0(−1.0

To test windividu

PleasInter

Ri;t−Rf ;t

� �¼ c0 þ c1HBi;t þ c2HBi;t−1 þ c3βi;t þ c4Ln MEð Þ þ c5BMi;t þ c6ILLIQi;t−1

þc7Ri;−1 þ c8Ri;−12:−2 þ c9Ri;−36:−13 þ εi;t :ð5Þ

Here, βi,t is the beta coefficient of individual stock i, which is obtained from CAPM regression based on the previous 36 months ofreturnswith rolling once permonth.Ri,− 1 is the return of individual stock i inmonth t− 1,. Ri,− 12 :− 2 and Ri,− 36 :− 13 are the averagereturns from month t − 12 to month t − 2 and from month t − 36 to month t − 13 for individual stock i, respectively. These threecontrol variables are added to capture the momentum and contrarian factor of stock returns (Diether et al., 2002). Other variablesare as previously defined.

The upper part of Table 7 (Panel A) gives the results of regression based on the Fama andMacBeth (1973)method, run eachmonth.The results show that when the market risk, size factor, value factor, liquidity factor and momentum and contrarian factor are con-trolled for, the impact of an individual stock's degree of opinion divergence among investors is positive on its return in the currentmonth but negative on its return in the subsequent month, both significant at the 1% level. In addition, when opinion divergence is

ries test of CAPM and three-factor models for opinion divergence II.

ept ODt ODt − 1 RM–Rf SMB HML ILLIQt − 1 Adj-R2

002)

1.160⁎⁎⁎

(15.57)0.909⁎⁎⁎

(139.57)0.014⁎

(1.69)46.62%

⁎⁎

)−0.402⁎⁎⁎

(−8.35)0.981⁎⁎⁎

(148.14)0.011(1.42)

45.16%

⁎⁎⁎

)2.160⁎⁎⁎

(27.43)−1.611⁎⁎⁎

(−28.99)0.897⁎⁎⁎

(131.73)−0.000(−0.05)

49.02%

07⁎⁎⁎

1)0.955⁎⁎⁎

(11.98)0.881⁎⁎⁎

(82.86)0.669⁎⁎⁎

(34.05)0.054⁎⁎

(2.09)0.004⁎

(1.87)53.55%

05⁎⁎⁎

3)−0.377⁎⁎⁎

(−6.74)0.953⁎⁎⁎

(134.85)0.691⁎⁎⁎

(33.54)−0.012(−0.58)

0.004⁎⁎

(2.00)52.72%

019)

1.823⁎⁎⁎

(22.70)−1.396⁎⁎⁎

(−25.39)0.879⁎⁎⁎

(117.64)0.661⁎⁎⁎

(29.27)0.054⁎⁎

(2.44)−0.001(−0.27)

55.69%

hether opinion divergence still influences stock return when the liquidity factor is controlled for, we introduce the last month illiquidity index (ILLIQt − 1) ofal stock, based on Table 5, into regression models (3) and (4). ⁎⁎⁎, ⁎⁎ and ⁎ indicate significance at the 1%, 5% and 10% levels, respectively.



Table 7Fama–McBeth regressions: explaining the cross-section of individual stock returns.

Intercept ODt ODt − 1 βi,t Ln(ME) BM ILLIQt−1 R−1 R−12:−2 R−36:−13 Adj-R2

Panel A: entire sample, January 2000 to December 20110.017(1.65)

−0.005(−1.37)

−0.002(−1.16)

0.010⁎⁎

(2.14)5.56%

0.017⁎

(1.88)2.960⁎⁎⁎

(28.56)−2.187⁎⁎⁎

(−22.72)−0.003(−0.97)

−0.002(−1.36)

0.007⁎

(1.74)15.37%

0.012(1.32)

2.959⁎⁎⁎

(28.91)−2.124⁎⁎⁎

(−21.31)−0.003(−0.90)

−0.001(−0.81)

0.008⁎

(1.85)0.013(1.31)

16.00%

0.015⁎

(1.73)3.043⁎⁎⁎

(30.39)−2.080⁎⁎⁎

(−21.78)−0.004(−1.25)

−0.002(−1.30)

0.006⁎

(1.77)0.002⁎

(1.79)−0.073⁎⁎⁎

(−6.55)0.074⁎

(1.72)−0.011(−0.30)

19.88%

Panel B: 181 stocks without short-sale constraints, April 2010 to December 2011−0.003(−0.04)

−0.011(−0.60)

0.000(0.00)

−0.005(−0.22)

20.79%

−0.008(−0.10)

3.914⁎⁎⁎

(3.35)−2.988⁎⁎

(−2.67)−0.010(−0.51)

0.001(0.06)

−0.003(−0.14)

26.50%

−0.028(−0.38)

4.011⁎⁎⁎

(3.33)−2.769⁎⁎

(−2.43)−0.008(−0.41)

0.003(0.28)

−0.006(−0.22)

0.062(0.69)

26.75%

−0.050(−0.64)

3.697⁎⁎⁎

(2.98)−2.479⁎⁎

(−2.30)−0.001(−0.04)

0.004(0.35)

−0.001(−0.03)

0.090(0.80)

−0.102(−1.34)

0.595⁎⁎⁎

(3.12)−0.189(−0.81)

32.42%

Fama and MacBeth (1973) cross-sectional regressions are run every month. Panel A reports all results from January 2000 to December 2011. Because the beta coeffi-cients are obtained from CAPM regression based on the previous 36 months' returns, the 1997–1999 data are eliminated. Panel B reports the Fama–McBeth regressionresults of 181 stocks without short-sale constraints, from April 2010 to December 2011. ⁎⁎⁎, ⁎⁎ and ⁎ indicate significance at the 1%, 5% and 10% levels, respectively.


introduced into the CAPM and the Fama–French three-factor model, the goodness of fit is increased for both models. Thus, opiniondivergence among investors in the China stock market significantly influences asset pricing.

4.3. Analysis of different sample periods

Miller's (1977) study on the influence of opinion divergence on changes in stock price is based on short-sale constraints. The Chi-nese stock market was subject to strict short-sale constraints from its establishment up to March 31, 2010, but since that date, stockmargin trading pilots for 90 stocks have been carried out and the short-sale constraints on partial stocks have gradually loosened.When strict short-sale constraints are eliminated in a market, does opinion divergence still have an impact on stock returns? Accord-ing to the experience of theU.S. market, evenwhen there is no absolute short-sale constraint in themarket, factors such as transactioncost or market friction will limit free expression of investors' bearish opinions. Hence, studies on the influence of opinion divergenceon asset pricing in the U.S. market are still able tomake robust conclusions. We divided our sample period into two sub-periods, fromJanuary 1997 to March 2010 and from April 2010 to December 2011, to explore the possible impact of short-sale constraints on ourresults.

Regardless of whether time-series regression or cross-sectional regression is carried out, the results for the sub-period January1997 toMarch 2010 are identical to those in Table 5 and the upper part of Table 7 (the data are not reported due to space limitations).Our attention is thus focused on the results following loosening of the short-sale constraints since March 31, 2010. Because of therelatively short period (two years) of data collection, only the results of cross-sectional regression are presented (in the lower partof Table 7, Panel B). These data demonstrate that the impact of opinion divergence on stock returns remains significant for this sampleof 181 stocks.

5. Conclusion

Weestablish a turnover decompositionmodel by usingunexpected trading volume to obtain the degree of divergence in investors'opinions (i.e., heterogeneous beliefs). The opinion divergence is directly extracted from trading activity, ensuring that 1) the opiniondivergence obtained has been translated into actual trading activity and exerted an impact on asset prices and 2) such problems asincomplete information or overlap with other exogenous measurement indices of opinion divergence are avoided. We are thusable to investigate the effect of investors' opinion divergence on stock returns and draw the following conclusions.

First, portfolio strategies developed according to the degree of opinion divergence have significant profitability. The expected re-turn in the subsequent month of a portfolio with a low degree of opinion divergence is significantly higher than that of other portfo-lios, and this difference is most obvious with stocks of smaller companies. When factors of size and value are controlled for, theexpected average return in the subsequentmonth of a portfolio based on small-company stocks and with a low degree of opinion di-vergence is significantly higher than that of portfolios based on large-company stocks and with a high degree of opinion divergence.

Second, from the perspective of asset pricingmodels, empirical results demonstrate that opinion divergence is an important factorinfluencing asset pricing. When the opinion divergence (OD) factor is introduced into the CAPM and the Fama–French three-factormodel, both time-series regression and cross-sectional regression show that the degree of opinion divergence has a significantly pos-itive correlation with the current month stock returns and a significantly negative correlation with the subsequent month stockreturns. In the robustness test, we further control for the impact of liquidity and the momentum factor on asset pricing and discuss




the potential impact of the loosening of short-sale constraints on the results. The results all indicate that opinion divergence is not onlyan important factor in asset pricing but is also more important than these other factors influencing asset pricing and is capable ofsupplying incremental information.

References

Acharya, V. V., & Pedersen, L. H. (2005). Asset pricing with liquidity risk. Journal of Financial Economics, 77, 375–410.Alwathainani, A. M. (2012). Consistent winners and losers. International Review of Economics & Finance, 21(1), 210–220.Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time-series effects. Journal of Financial Markets, 5, 31–56.Amihud, Y., & Mendelson, H. (1989). The effects of beta, bid–ask spread, residual risk, and size on stock returns. Journal of Finance, 44, 479–486.Basak, S. (2005). Asset pricing with heterogeneous beliefs. Journal of Banking & Finance, 29, 2849–2881.Bessembinder, H., Chan, K., & Seguin, P. J. (1996). An empirical examination of information, differences of opinion, and trading activity. Journal of Financial Economics,

40, 105–134.Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52, 57–82.Chen, J., Hong, H., & Stein, J. C. (2002). Breadth of ownership and stock returns. Journal of Financial Economics, 66, 171–205.Constantinides, G. M., Harris, M., & Stulz, R. M. (2003). Handbook of the economics of finance: Corporate finance, Vol. 1A, Elsevier.Diamond, D. W., & Verrecchia, R. E. (1987). Constraints on short-selling and asset price adjustment to private information. Journal of Financial Economics, 18, 277–311.Diether, K. B., Malloy, C. J., & Scherbina, A. (2002). Differences of opinion and the cross-section of stock returns. Journal of Finance, 57, 2113–2141.Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427–465.Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56.Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18, 25–46.Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81, 607–636.Garfinkel, J. A. (2009). Measuring investors' opinion divergence. Journal of Accounting Research, 47, 1317–1348.Garfinkel, J. A., & Sokobin, J. (2006). Volume, opinion divergence, and returns: A study of post-earnings announcement drift. Journal of Accounting Research, 44, 85–112.Glosten, L. R., & Harris, L. E. (1988). Estimating the components of the bid/ask spread. Journal of Financial Economics, 21, 123–142.Goyenko, R. Y., Holden, C. W., & Trzcinka, C. A. (2009). Do liquidity measures measure liquidity? Journal of Financial Economics, 92, 153–181.Gromb, D., & Vayanos, D. (2002). Equilibrium and welfare in markets with financially constrained arbitrageurs. Journal of Financial Economics, 66, 361–407.Harris, M., & Raviv, A. (1993). Differences of opinion make a horse race. Review of Financial Studies, 6, 473–506.Harrison, J. M., & Kreps, D. M. (1978). Speculative investor behavior in a stock market with heterogeneous expectations. Quarterly Journal of Economics, 92, 323–336.He, W. P., Lepone, A., & Leung, H. (2013). Information asymmetry and the cost of equity capital. International Review of Economics & Finance, 27, 611–620.He, J., Ng, L., & Wang, Q. (2004). Quarterly trading patterns of financial institutions. The Journal of Business, 77, 493–510.Hong, H., & Stein, J. C. (2003). Differences of opinion, short-sale constraints and market crashes. Review of Financial Studies, 16, 487–525.Hong, H., & Stein, J. C. (2007). Disagreement and the stock market. Journal of Economic Perspectives, 21, 109–128.Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.Karpoff, J. M. (1987). The relation between price changes and trading volume: A survey. Journal of Financial and Quantitative Analysis, 22, 109–126.Lee, C. M. C., & Swaminathan, B. (2000). Price momentum and trading volume. Journal of Finance, 55, 2017–2069.Márquez, E., Nieto, B., & Rubio, G. (2014). Stock returns with consumption and illiquidity risks. International Review of Economics & Finance, 29, 57–74.Martínez, M. A., Nieto, B., Rubio, G., & Tapia, M. (2005). Asset pricing and systematic liquidity risk: An empirical investigation of the Spanish stock market. International

Review of Economics & Finance, 14(1), 81–103.Mei, J. P., Scheinkman, J. A., & Xiong, W. (2009). Speculative trading and stock prices: Evidence from Chinese A–B share premia. Annals of Economics and Finance, 10,

225–255.Miller, E. M. (1977). Risk, uncertainty, and divergence of opinion. Journal of Finance, 32, 1151–1168.Moeller, S. B., Schlingemann, F. P., & Stulz, R. M. (2007). How do diversity of opinion and information asymmetry affect acquirer returns? Review of Financial Studies, 20,

2047–2078.Opie, W., & Zhang, H. F. (2013). Investor heterogeneity and the cross-sectional stock returns in China. Pacific-Basin Finance Journal, 25, 1–20.Perold, A. F. (2004). The capital asset pricing model. Journal of Economic Perspectives, 18, 3–24.Shleifer, A., & Vishny, R. (1997). The limits of arbitrage. Journal of Finance, 52, 35–55.Verardo, M. (2009). Heterogeneous beliefs and momentum profits. Journal of Financial and Quantitative Analysis, 44, 795–822.Yu, J. (2011). Disagreement and return predictability of stock portfolios. Journal of Financial Economics, 99, 162–183.


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opinion divergence, unexpected trading volume and stock returns: evidence from china

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