Aggregate Idiosyncratic Tail Risk And Market Expected Return

After nearly three decades of development,the number and quality of listed companies in China's A-share market have been greatly improved.However,tail risk of the A-share market are not uncommon,such as the financial crisis in 2008 and the sharp rise and fall of the stock market in 2015.Many empirical studies also show that China's stock market has the characteristics of “peak” and “thick tail”.So now there is a widespread belief that the tail of the stock return is wider than that of normal distribution assumption,and the frequency of tail events is higher than predicted by the normal distribution,that is it's not accurate to simply rely on conditional variance and standard deviation to measure risk,the probability of tail risk of stock return is higher than that of normal distribution.In this case,it is of great significance to find a more accurate tail risk measurement method in order to prevent tail risk from causing huge losses to the financial market.William Sharpe(1964),an American economist,put forward the CAPM model.He believed that only market risk could be priced,while idiosyncratic risk(also known as non-systematic risk)could be dispersed,so they could not be priced.However,Merton(1987)believed that the portfolio could not fully disperse the nonsystematic risk in the imperfect market.In this case,the investors would ask for risk compensation for the idiosyncratic risk they took,and the idiosyncratic risk might also be priced.In the subsequent studies on idiosyncratic risk,most studies at home and abroad generally use idiosyncratic volatility to measure idiosyncratic risk,and find that there is a positive or negative correlation between idiosyncratic volatility and expected return.These results show that idiosyncratic risk can be priced.However,idiosyncratic volatility only reflects the average volatility of idiosyncratic risk,and this index cannot reflect the extreme volatility of the idiosyncratic risk.Therefore,it is necessary to improve the measurement method of idiosyncratic risk and further explore the hidden information in idiosyncratic risk.In this paper,in order to measure aggregate the extreme volatility of the idiosyncratic risk,the concept of Aggregate Idiosyncratic Tail Risk is raised for the first time,and this paper adopts two methods to measure the index.The two methods have different idiosyncratic information sources.The first one is from the factor model rolling regression to get the residual error sequence,the second one is from the excess returns of stocks.After obtaining the idiosyncratic information,aggregate idiosyncratic tail risk is the kurtosis value of the idiosyncratic information on the cross section.In comparison,method 2 is more advantageous because it can calculate the aggregate idiosyncratic tail risk at any time point without complex model estimation.In order to further analyze the distribution characteristics of residual error and excess return rate on the cross section,this paper also takes the mean of residual error and excess return rate on the cross section as the center and divides the cross section distribution into the left side and the right side,so as to calculate the aggregate idiosyncratic tail risk on the left and right side.In this paper,the research focus is on the relationship between aggregate idiosyncratic tail risk and the market expected return.In the framework of the whole samples,the paper studies the relationship,and makes a series of the robustness tests.This article also in the framework of sub-sample,taking into account the different market conditions(bull market and bear market)and different markets(the Shanghai,Shenzhen,the Growth Enterprises Market),researches the difference of relationship.This paper takes China's A-share market as the research sample,with the sample interval from 2001 to 2017,sample frequency for the day.Through empirical research,this paper draws the following conclusions:First,in general,both the aggregate idiosyncratic tail risk on the left and right side and the market expected return have a negative relationship,that is,the greater the aggregate idiosyncratic tail risk,the smaller the market expected return.Second,the aggregate idiosyncratic tail risk on the left and right side in different market conditions have different performance.In bear market,the aggregate idiosyncratic tail risk on the right side has a negative relationship in the market expected return;In bull market,the aggregate idiosyncratic tail risk on the left side is significantly negatively related to the market expected return.This difference may be explained by investors' preference for lottery-like assets and overconfidence.Third,there are differences in the performance mechanism of aggregate idiosyncratic tail risks among Shanghai A-share,Shenzhen A-share and GEM.In each sub-market,the aggregate idiosyncratic tail risk calculated by method 1 has a significant negative impact on the expected return of Shenzhen A-share market and GEM market,but has no impact on the expected return of Shanghai A-share market.The aggregate idiosyncratic tail risk calculated by method 2 has significant explanatory power for the expected returns of the three sub-markets,that is,the higher the aggregate idiosyncratic tail risk,the lower the expected return of the market.In addition,the paper studies the joint influence of three sub-markets' aggregate idiosyncratic tail risk on the expected return of China's A-share market,three differences are found:(1)when using the aggregate idiosyncratic tail risk calculated by method 1 to predict the expected return of the China's A-share market,only aggregate idiosyncratic tail risk of the Shenzhen A-share market is significantly negative.(2)when the aggregate idiosyncratic tail risk calculated by method 2 is used to predict the expected return of the China's A-share market,only the aggregate idiosyncratic tail risk of the GEM market is significantly negative.(3)the combined explanatory power of the three sub-markets on aggregate idiosyncratic tail risk is stronger than that of the China's A-share market.The innovation of this paper is that the concept of aggregate idiosyncratic tail risk is proposed for the first time,and two different measurement methods are given,one is the factor model method based on time series data,the other is the model-free method based on cross-sectional data.The second method has particular computational advantages,requiring only the data of the excess rate of return on the cross section.