Do Jumps Contribute To The Dynamics Of The Equity Premium?

The volatility of asset returns is not always continuous and smooth.A large number of facts show that there is discrete large volatility.The discrete large volatility is called jump.Jumps have been widely studied both in parametric and non-parametric methods.The nature and characteristics of jumps have been comprehensively recognized.Jumps will change the higher moments of asset returns distribution when jumps exist in equity returns.If investors have higher moments preference,they will require additional premium to bear the risk of higher moments.Intuitively,jumps will indirectly affect equity premium through the higher moments of equity returns.This paper mainly discusses the impact of jumps on asset premium and test this intuition.This paper investigates whether risks associated with time-varying arrival of jumps and their effect on the dynamics of higher moments of returns are priced in the conditional mean of daily market excess returns.Using the ARVI-GARCH-Jump model with the mean equation containing the higher moments of asset returns and applying the sign restriction to the higher moments of returns according to the preference theory,this paper makes an empirical study on the daily data of Shanghai Stock Exchange Index from January 2005 to June 2018 and find that the variance risk and skewness risk are significantly priced in equity premium,but the kurtosis price is not significant.The significantly priced variance risk and skewness risk indirectly prove that the jump risk is significantly priced in equity premium.We also find the same robust result in alternative equity premium specifications and alternative specifications of dynamics.Since both jumps and the GARCH volatility enter our parameterizations of the conditional higher moments,we focus these two contributions to equity premium and isolate their net effects.We calculate the contribution of jump risk to equity premium and find that with one more jump in a year,the equity premium will increase by 0.0226%.Arrival of jumps is about 157 times per year,which implies the equity premium resulted from jump risk is about 3.54%per year.The jump risk indicates such character that the arrival of jumps shows high frequency,but the contribution of single jump to equity premium is very small.We also investigate the impact of GARCH volatility on equity premium.During the relatively calm period(low volatility),a negative relationship between conditional variance and returns occurs in this situation.In contrast,the relationship between conditional variance and returns become positive during the volatile period(high volatility).Among the contribution of higher moments risk to equity premium,variance risk contributes about 5.25%per year,skewness risk contributes about 6.78%per year.Skewness premium is slightly higher than variance premium.This phenomenon stems from the low average volatility caused by the "short bull long bear" characteristic of Shanghai stock exchange composite index.According to the estimation results of the model,the summary statistics of conditional higher moments are highly similar to the variance and skewness of the excess returns.The conditional jump risk and conditional variance are also highly consistent with the trend of the Shanghai Stock Exchange Index,which shows the model captures the distribution characteristics of the excess returns very well.At last,our results show that it is possible to identify jump risk and its contribution to the market risk-return tradeoff using equity data only.