short-sale constraint and return asymmetries in taiwan stock market

8/8/2019 Short-Sale Constraint and Return Asymmetries in Taiwan Stock Market

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International Research Journal of Finance and EconomicsISSN 1450-2887 Issue 15 (2008) EuroJournals Publishing, Inc. 2008http://www.eurojournals.com/finance.htm

Short-Sale Constraint and Return Asymmetries inTaiwan Stock Market

Ou Hu

Department of Economics, Youngstown State University

College of Arts and Sciences, One University Plaza, Youngstown, OH 44555

E-mail: [email protected]: (330) 941-2061

Zhaodan Huang

Department of Business and Economics, Utica College

E-mail: [email protected]: (315) 792-3247

Bih-shuang Liao

Department of Finance, Chihlee Institute of Technology, Taiwan

E-mail: [email protected]: (886-2) 2257-6167

Abstract

Using daily short interest data of the Taiwan Stock Exchange from January 1991 toSeptember 2004, we examine the asymmetries in the distribution of stock returns.Consistent with previous findings based on the U.S. stock market, our results show thatheavily shorted stocks generate less positive skewness and higher volatility. Moreover, inthe test of Hong and Stein (2003)s model, we find that the market relative short interestratio is positively correlated with the market turnover ratio. After orthogonalizing these twovariables, we find that the market relative short interest ratio has statistically significantpower in forecasting return skewness. However, the market turnover ratio does not seemimportant in the determination of the skewness of future market return.

Keywords: Return Skewness; Short Sale; Turnover Ratio; Emerging Financial MarketJEL Classification Codes: G12; G14

1. IntroductionThe phenomenon that aggregate stock market returns reveal negative asymmetry or negative skewnesshas been widely documented in the academic research [Chen, Hong, and Stein (2001)]. Hong and Stein(2003) develop a theory to address the question of why stock markets tend to have negative skewness,therefore vulnerable to crashes. The model suggests that bearish investors do not initially reveal theirinformation in the market until market declines due to two key assumptions of Hong-Stein model,namely the existence of difference of opinion among investors as well as short sale constraint.

Therefore, conditioned on short sale constraint and dispersion of opinions, the model predicts thatnegative skewness is most pronounced when short sale constraint is binding and the difference


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opinions are high. Finally, the model also predicts that the returns will be more negatively skewedconditioned on high trading volume.

Chen, Hong, and Stein (2001) provide some empirical evidence based on US stock markets tosupport the latter prediction by the model of Hong and Stein (2003). Their empirical work find that the

negative skewness is most pronounced in stocks that have experienced increase in trading volumerelative to trend over the prior six months. To our best knowledge, a direct test of the first predictionhas not been done until a recent paper by Chang, Cheng, and Yu (2006). One of their tests is toinvestigate whether stock returns are more negatively skewed when short sales are constrainted usingHong Kong stock market. However, they find the opposite evidence that the returns of individualstocks exhibit more negative skewness when short-sale constraint is removed.

Since there are two necessary and sufficient key assumptions in Hong and Stein (2003)smodel, yet Chang, Cheng, and Yu (2006) only controls the short-sale constraint of the stocks andignoring the second condition as of the need of different opinion, it might not be a surprise when onefailed to support the prediction by the model. In this paper, we empirically look at the determinants ofthe asymmetries in stock returns in Taiwan stock market. Both dispersion of opinions and short-sale

constraint are considered. Specifically, we use turnover ratio to measure the dispersion of opinionsamong investors [Chen et al. (2001)] and relative daily short interest ratio to measure the short-saleconstraint [See, e.g., Figlewski (1981); Desai et al. (2002)].

Our study is a comparable investigation of a stock market outside the U.S. Different from theU.S. stock market and the Hong Kong stock market, Taiwan stock market routinely release short saleinterest data as well as trading volume for individual stocks every day since 1991. Therefore, Taiwanstock market provides us a unique opportunity to directly test whether higher dispersion of opinionsand higher short-sale constraint lead higher negative skewness.

Contrary to the finding by Chang, Cheng, and Yu (2006), our results are consistent with theprediction by Hong and Stein (2003). Specifically, using the data from 1991 to 2004, we find that theportfolio with high relative short interest ratio has lowest subsequent average return, lowest average

positive skewness (or more negative skewness), and highest volatility. Since we find that the marketaverage relative short interest ratio is positively correlated with the market average turnover ratio, inorder to forecast skewness in market return, we first need to orthogonalize the market relative shortinterest ratio and the market turnover ratio. Finally, the generated error term (representing theorthogonalized dispersion of opinions) and the market short interest ratio are used to forecast marketskewness. We find that the estimated coefficient of market short interest ratio is negative andsignificant, and the error term which represents the information of market turnover ratio not shared bymarket short sale information has no power in forecasting market skewness.

This short research note is organized as the follow. Section 2 provides the research design aswell as the data sample. Section 3 provides the empirical results. Section 4 provides a brief summary.

2. Data Sample and Research DesignAccording to the information provided by the Twaiwan Stock Exchange Corporation (TSEC), the firstsecurity market of Taiwan was established in 1961. The number of listed companies on the TWSEgrew from 119 in 1983 to 672 on June 30, 2004. The total market capitalization of companies listed onthe TWSE was approximately $374.2 billion as of June 30, 2004, which establishes the TWSE marketas one of the most important emerging financial markets.

For every firm in the TWSE, the monthly data includes shares outstanding and book value,spanning from 1988:01 to 2004:12. The daily data include short sale interest, daily returns, price, andthey span from 1991:01 to 2004:09. Since the short sale interest and the trading volume for eachindividual stock is released daily, we can use the information to calculate the daily relative shortinterest ratio as well as daily turnover ratio. Based on the established literature, the relative daily shortinterest (turnover ratio) is defined as the daily short interest (trading volume) divided by the totalshares outstanding.


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Starting from 1991:01, we form 4 portfolios on the basis of relative short interest ratio (shortsale interest divided by shares outstanding). Then, we report the realized average returns (equallyweighted and value weighted), average skewness in returns, and average volatility in returns for eachof the 4 portfolios. We repeat the same procedure for each month until the end of our sample

2004:09. In addition, we also conduct regression analyses to use relative short interest ratio andturnover ratio to forecast skewness in overall stock market returns. Our empirical model is as follows:

ttttcMKShbTurnoveraSkew 11 , (1)

where tSkew is the daily average market skewness measured for month t; tTurnover is the

daily average market turnover ratio for month t, which is used as a proxy for the difference of opinion;

and tMKSh is the daily average market relative short interest ratio for month t.

3. Empirical ResultsAs for the 4 portfolios, we find that from Table 1 and Table 2 the portfolio with high relative short

interest ratio (the fourth portfolio) has lowest subsequent risk-adjusted return, lowest averageskewness, and highest volatility. For example, panel A of Table 2 shows clearly that the meanskewness of portfolio 1 (with the lowest short sale ratios) is 0.1597, compared to 0.0612 of portfolio 4.In contrast to the lower level of skewness (more negative skewness), portfolio 4 has a higher averagelevel of standard deviation (2.85) than that of portfolio 1 (2.31).

Table 1: Risk-Adjusted Returns for the Quartile and Threshold PortfoliosThe sample ranges from 1991:01 to 2004:09. For every month, starting at 1991:01, we form quartileportfolios on the basis of the relative short interest level. For three holding periods: one month, sixmonths, we calculate risk-adjusted equally-weighted and value-weighted returns using the Fama-French Three-Factor model:

ptthtsftmtmpftpt HMLSMBrrarr )(

p -values are in the parentheses.

Horizon

One-month Six-month One-year

Portfolio Equally-weighted Value-weighted Equally-weighted Value-weighted Equally-weighted Value-weighted

QuartileAdj-

2R

Adj-2R

Adj-2R

Adj-2R

Adj-2R

Adj-2R

0.772 0.89 1.505 0.89 0.504 0.92 0.973 0.89 0.292 0.92 0.623 0.921

(0.0522) (0.0026) (0.0888) (0.0266) (0.2963) (0.0912)

-0.235 0.86 0.333 0.84 -0.404 0.87 0.257 0.87 -0.427 0.88 0.282 0.892

(0.4532) (0.2756) (0.1571) (0.3298) (0.1293) (0.2592)

-0.776 0.86 -0.066 0.83 -1.142 0.87 -0.344 0.87 -1.231 0.87 -0.512 0.883

(0.0078) (0.8369) (0.0001) (0.2345) (0.0000) (0.0686)

-1.406 0.94 -0.390 0.97 -1.336 0.94 -0.201 0.97 -1.300 0.95 -0.134 0.984 (0.0000) (0.0127) (0.0000) (0.1614) (0.0000) (0.3241)

Table 2: Average Skewness/Variance of Quartile PortfoliosStocks are sorted into quintiles based on their short sale ratio. The portfolio with the highest (lowest)short sale ratios is named as 4 (1).

Panel A: Average Skewness of the Portfolios Sorted by Short Sale Ratios

Portfolio 1 2 3 4

Number of Observations 165 164 165 165MEAN 0.160 0.125 0.105 0.061STD 0.316 0.320 0.304 0.266

Panel B: Average Standard Deviation of the Portfolios Sorted by Short Sale Ratios

Number of Observations 165 164 165 165MEAN 2.311 2.337 2.536 2.847STD 0.702 0.621 0.639 0.664


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In search of the possible correlation between short-sale constraint and dispersion of opinions,we use the follow model:

ttt MKSHbaTurnover (2)

In the regression analysis, we find that the market average relative short interest ratio is

positively correlated with the market average turnover ratio. Table 3 shows the results. The coefficientof tMKSh is 0.00145 ( t-stat = 6.41), which clearly indicates that there is a positive correlation between

the market relative short interest ratio and the market turnover ratio.

Table 3: Orthogonalize the market relative short interest ratio and the market turnover ratio

ttt MKSHbaTurnover

itTurnover is the daily average turnover ratio for month t and for stock i ; itMKSh is the

daily average relative short interest ratio for month t and for stock i .

Variable Parameter Estimate t-statistics Adjusted 2R

Intercept 0.0078 12.96 0.196lmksh 0.0015 6.41

Given that there is positive correlation between the market relative short interest ratio and themarket turnover ratio, one must first orthogonalize market relative short interest ratio and marketturnover ratio in order to using equation (1) to forecast the negative skewness in market return. To doso, we first generate the error term through regression (2). We then use the error term and market shortinterest ratio to forecast market skewness. Statistically, the error term represents the information ofmarket turnover ratio not shared by market short sale information.

Table 4 shows the results based on equation (1). It shows clearly that the short-sale constraint,represented by the market short sale ratio, has significant negative impact on skewness (coefficient = -

0.044; t -stat = -3.69), which implies that the overall maket exhibit more negative skewness whenmarket short sale ratio is high. This finding is basically consistent with the prediction by Hong-Steinmodel. Chen, Hong, and Stein (2001) do not use short sale data (not available) in their study. However,they find the detrended turnover ratio can forecast skewness in returns. Our study gives us a uniqueopportunity to directly test the effect of short sale on skewness of future returns. We find that when weemploy both short sale and trading volume, trading volume does not seem important in determining theskewness in stock returns. As shown in Table 4, the coefficient for the measurement of dispersion ofopinions (the orthogonalized turnover ratios) is not significant, although it has a negative sign which isconsistent with Chen et al. (2001).

Table 4: Predicting Market Skewness Based on the Orthogonalization between Market Turnover Ratio andMarket Relative Short Ratio

tttt cMKShbTurnoveraSkew 11

whereitTurnover is replaced by the residuals generated by the regression (2).

Variable Parameter Estimate t-statistics Adjusted 2RIntercept 0.21768 6.78 0.078Mksh -0.04429 -3.69Turnover -6.29743 -1.51

4. ConclusionsIn this research note, we examine the asymmetries in the distribution of stock returns. Using a unique

data set from the Taiwan stock exchange which provides daily short interest data from January 1991 toSeptember 2004, our study produces some interesting results. First of all, consistent with previous


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findings based on the U.S. stock market, our results show that heavily shorted stocks generatesignificant and negative risk-adjusted abnormal returns. Moreover, heavily shorted stocks generate lesspositive skewness and higher volatility. In the test of Hong and Stein (2003)s model, we find that themarket relative short interest ratio is positively correlated with the market turnover ratio. After

orthogonalizing these two variables, we find that the market relative short interest ratio has statisticallysignificant power in forecasting return skewness. However, the market turnover ratio does not seemimportant in the determination of the skewness of future market return.

References[1] Chang, E.C., Cheng, J.W., and Y. Yu, 2006, Short-sale constraint and price discovery: evidence

from the Hong Kong market,Journal of Finance, forthcoming.[2] Chen J., H. Hong, and J. C. Stein, 2001, Forecasting Crashes: Trading Volume, Past Returns

and Conditional Skewness in Stock Prices,Journal of Financial Economics 61, 345 - 381.[3] Desai, H., K. Ramesh, S. R. Thiagarajan, and B. V. Balachandran, 2002. An investigation of

the informational role of short interest in the Nasdaq market, Journal of Finance 57, 2263-2287.

[4] Figlewski, S., 1981, The informational effects of restrictions on short sales: Some empiricalevidence, Journal of Financial and Quantitative Analysis 16, 463-476.

[5] Hong, H and J. C. Stein, 2003, Difference of opinion, short-sales constraints, and marketcrashes, The Review of Financial Studies 16, No.2, 487-525.

short-sale constraint and return asymmetries in taiwan stock market

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