The Idiosyncratic Volatility Puzzle Based On Quantile Regression

According to the classical asset pricing model,non-systemic risk can be completely offset by the diversification of investors.However,the real stock market is inefficient,which will make it impossible for most investors to carry out diversified investments.Therefore,investors will always bear the risk associated with the company’s own characteristics,that is,the idiosyncratic risk that will also ask for appropriate risk compensation.But in empirical study,Ang et al.(2006)first discovered that there was a significant negative correlation between idiosyncratic volatilities and cross-sectional return in the US stock market.But so far no one theory can make a good explanation to the negative relationship,which was called "idiosyncratic volatility puzzle".There are still disputes about the existence of "idiosyncratic volatility puzzle"in the domestic and foreign stock markets.In this paper,we employ two models to estimate expected idiosyncratic volatilities.And then we use the quantile regression method for the first time to estimate relation between idiosyncratic volatilities and cross-sectional returns of the Chinese stock market.We selected all the stocks of Shanghai and Shenzhen A shares from 2000 to 2015 as the research object.We used the Fama-French three-factor model as the mean equation,and then adopted the standard deviation of traditional OLS regression residual and the EGARCH(1,1)model to estimate idiosyncratic volatilities.After the idiosyncratic volatilities were estimated,we used the Fama-MacBeth cross-sectional regression and the quantile regression method to study the relationship between the idiosyncratic volatilities and the expected return on the stock.The results show that,both the OLS regression model and the EGARCH(1,1)model have no effect on the relationship between idiosyncratic volatilities and expected returns of the stocks.In the cross-sectional regression,there is no significant negative correlation between the idiosyncratic volatilities and the expected returns.However,in the quantile regression,there is a negative correlation between them at the low quantiles,while there is a significant positive correlation at the high quantiles.With the quantiles changing,the relation between idiosyncratic volatilities and expected returns is dynamic.Since the negative correlation between the idiosyncratic volatilities and the expected returns is not significant,we further choose the expected idiosyncratic volatilities as the explanatory variable to examine the relationship between them.The results show that the expected idiosyncratic volatilities are significantly positive correlated with the expected returns in the cross-sectional regression,but in the quantile regression,the result is basically same with the idiosyncratic volatilities,which clearly demonstrates the existence of idiosyncratic volatility puzzle.