A Rearch On The Skewness Of Chinese Stock Market Yields

In the capital markets, asset returns often exhibit asymmetric distribution, namely skewness. The research on skewness phenomenon has been nearly four decades. However, in practical applications and research, it is often assumed that the assets yield obey symmetry distribution, namely normal distribution, etc., ignoring the skewness characteristics. If skewness phenomenon truly exists, and can not be ignored, then the simple normal distribution assumption is likely to be misleading the true returns and risk characteristics. As we all know, the yield affects asset pricing, portfolio, risk prediction and market participants’behavior. As an inherent property of the asset yields, skewness thus affects asset pricing, influences the allocation of assets, impacts the behavior of market participants and the regulation, and so on Therefore, researching the skewness of the capital market returns has great theoretical and practical significance.Take Chinese stock market between 2006 and 2013 as the sample, the stochastic volatility models (SV) based on the eight different distributions as the models in the paper, to demonstrate the existence of skewness in the stock market and its main features. And, the eight different probability distributions, namely:normal distribution (N), skew normal distribution (SN), Student’s t-distribution distribution (T), skew Student t distribution (ST), generalized error distribution (GED), skew generalized error distribution (SGED), mixed normal distribution (MN) and mixed skew normal distribution (MSN). Based on study, we get some conclusions as follows:(1) normal distribution is the worst, the assumption of normal distribution is not the best choice; (2) SN and N, ST and T, SGED and GED, MN and MSN are four pairs of the eight distribution, the distribution containing the skewness parameter is at least not worse than the one without skewness; (3) compared to N and SN distributions, the distributions with fat tails are better, indicating that China’s stock market is not only skewed, but also accompanied by fat tail; (4) On the whole, mixed skew normal distribution (MSN) is the best, it is not only able to grab the skewness and fat tail characteristics in the stock market returns, but also portray the abnormal yields both on the left and right tail. Finally, we take the capital asset pricing model (CAPM) as an example, showing the value of skewness in practice. We combine the CAPM model with the MSN distribution to study the skewness’ impact on the capital asset pricing, and the result shows that the classical CAPM model with normal distribution is limiting the true value of a. When regressing with the industry returns with a negative skewness, the conclusion is actually the overestimated industry true returns and the underestimated risk.In short, if not able to give full consideration to skewness and fat tail, it will most likely result in wrong konwledge about the true return and risk. In the skewed market, it has widespread theoretical and practical significance to select an appropriate skewed distribution to study the financial problems. It will be of great use in asset pricing, portfolio constructing, futures margin ratio setting, financial risk predicting and regulatory rule-making, etc.