CVaR And The Cross Section Of Asset Returns

In the development process of financial market,people have been trying to explore the determinants of asset returns through various ways,trying to explain assets renturns by various means and variables,that is,asset pricing we often talk about.In this,the most important thing is the relationship between risk and returns.The financial crisis that happened again and again in history has made people realize that the tail risk has a huge impact on the operation of the financial market.Bali et al.(2014)found that there is a significant negative relationship between the idiosyncratic tail risk and the expected return of stock in the process of studying the tail risk of the US stock market.Based on previous studies,this paper proposes a new method to measure the idiosyncratic tail risk,and split it into the left tail and the right tail,respectively,namely the total excess loss CVaR~-of the left tail and the total excess return CVaR~+of the right taile.So,this paper is to study whether CVaR,as a idiosyncratic tail risk with lower partial moment,has a significant pricing effect in the Chinese stock market.If so,what is the direction of its pricing?Taking China's A share market data from January 1,1995 to November 30,2016as the research object,we verify the pricing effect of idiosyncratic tail risk with lower partial moment in Chinese stock market.First,the stocks are grouped according to CVaR,and then,the average return and CVaR of each group are calculated to preliminarily judge the correlation between stock returns and CVaR.Secondly,the variables which are commonly related to stock returns in other literatures are selected as control variables.Cross section valification is carried out by bivariate portfolio-level analysis and Fama-MacBeth method,which further proves CVaR's impact on stock's expected return.Finally,we build idiosyncratic tail risk factor HCVaRL with CVaR,and add it to Fama-French three factors model to verify the pricing power of CVaR in time series,that is,the additional pricing power.Through a series of empirical studies,we found that:(1)The correlation between left tail total excess loss CVaR~-and expected stock returns is significant negative,which is different from the negative correlation between idiosyncratic volatility and stock returns.It indicates that stocks perform poorly in the past(CVaR~-high)would also have bad performance in the future(low return).(2)There is a significant negative correlation between the total excess return CVaR~+of the right tail and the cross-section stock returns,which remains robust after controlling other predictive variables.In addition,different from the U.S.market,both the CVaR~+and IVOL effects appear to independently coexist in the Chinese stock markets,which verifies the conclusion about the coexistence of extreme positive returns and idiosyncratic volatility effect in the Nartea et al.(2016),and supports the evidence of a preference among investors for stocks with lottery-like features as the Bali et al.(2011)and Nartea et al.(2016).(3)In the time series pricing test,after add the left tail risk factor HCVaR~-L into Fama-French three factor model,the average explanatory power of the model has improved,indicates that CVaR~-can capture the time variation of returns to a certain extent,that is,the pricing function of CVaR is effective.(4)According to the analysis of CVaR~-and CVaR~+,we found that there is a significant negative correlation between CVaR and expected stock returns,and this relation is different from the anomalous idiosyncratic volatility effect,nor explained by the standard three factors.Therefore,we propose that the lower partial moment idiosyncratic tail risk puzzle exists in Chinese stock market,also known as"CVaR anomaly".This paper proposed a new method to measure the idiosyncratic tail risk of lower partial moment,and found its negative pricing power to China A shares,proposed"CVaR anomaly",to further enrich the studies about idiosyncratic tail risk in our country.