Short-sales constraints and stock return asymmetry: evidence from the Chinese stock markets

Abstract

The difficulty of short-selling stocks in the Chinese markets conforms to the assumption of the ‘Differences-of-Opinion’ theory and therefore, provides an empirical framework for testing the theory. The results show evidence supporting the theory: heavier trading predicts a more negatively skewed return.

Notes

¹ Most of this literature, however, is focused on the effects of future trading on volatilities (e.g., Bologna and Cavallo 2002), rather than on skewness as is considered here.

² For a detailed description of the Chinese stock markets, see Seddighi and Nian (2004).

³ The lag length m is chosen by the Ljung–Box Q tests as the minimum lag that renders serially uncorrelated residuals (at the 5% significance level) up to 22 lags (approximately a month) from an OLS autoregression of y_t . To keep the model parsimonious, the lags with insignificant estimated coefficients based on the OLS autoregression are removed. The OLS autoregression is used only to determine the number of lagged returns included in the conditional mean. The coefficients in the conditional mean equation will be jointly estimated with the conditional variance equation using full information maximum-likelihood (FIML) estimation.

⁴ This study also tries to include a Monday dummy as in Hueng and McDonald (2005), but it is never statistically significant. Therefore, to keep the model parsimonious, this dummy is not included in the final specification.

⁵ An alternative modelling strategy would be the one proposed by Harvey and Siddique (1999). They specify a conditional skewness process that is similar to the conditional variance process; i.e., the conditional skewness is a function of its own past value and the cube of the past residuals.

⁶ There exist many methods for modelling an asymmetric distribution, including kernel estimators, semi-nonparametric (SNP) methods, and flexible parametric methods. A parametric method is adopted in order to directly derive the effects of forecasting variables on skewness. There are also many parametric distributions that can capture the skewness of a random variable. Examples include the skewed-t distribution used by Hansen (1994), Degiannakis (2004), and Hueng and McDonald (2005), the skewed-GT distribution used by Theodossiou (1998) and Harris et al. (2004), and the log-generalized gamma distribution used by Brännäs and Nordman (2003). The AGT distribution is used because it has a simple parametric form and is more flexible. Comparisons among different choices of distributions are out of the scope of this study.

⁷ Cont and Bouchaud (2000) propose a theoretical model where stock kurtosis depends on the herding behaviours of the investors. However, the data do not provide information on the construction of measures of herding. Furthermore, specifications are experimented where p and q are modelled as time-varying variables as well. But the calculation of the standard errors on this set of parameters fails, which indicates that there is not enough information in the data to identify these parameters, or these parameters cannot be identified in the specification. Including a lag in the dynamics causes the same problem. Since the focus is on the skewness, it was decided to use the current specification. Adding dynamics to p and q, though, does not change the significance of the effect of prior trading volume on market skewness.