A Study Of The Relationship Between Asymmetric Risk And Expected Stock Returns Based On Probability Density Function

The relationship between risk and return is one of the core issues of finance research and an important element of asset pricing.The economic importance of this is that the expected risk can predict the future excess return of an asset.Most of the traditional pricing theories are based on the "mean-variance" model and the CAPM model,and one of the prerequisites of the model is that the asset returns obey a symmetric normal distribution,but with the in-depth study,many scholars found that in the real financial market,especially in China,which is an emerging market with a late start,the returns of assets are not as high as they should be.However,as the research progresses,many scholars find that in real financial markets,especially in emerging markets like China,the distribution of asset returns is often asymmetric.Risk is reward,and if investors ignore this asymmetric risk,they will lose part of the excess return.In addition,almost all domestic and international research studies on asymmetric risk of returns use only skewness as a measure of asymmetric risk,but there is no uniform conclusion on how skewness or asymmetric risk affects stock returns.Thus,in order to better investigate how asymmetry risk in the Chinese stock market affects expected stock returns,this paper will construct a new measure of return asymmetry risk,investigate whether the new indicator can effectively predict excess stock returns,and compare it with the traditional asymmetry measure skewness at the same time to compare whether our newly constructed indicator is theoretically and economically meaningful.In this paper,we mainly refer to Jiang et al.(2018)to construct a new density function-based asymmetry metric,refer to Amaya et al.(2015)and Chen et al.(2018)to construct the actual skewness,and use simulated data and predictive regression models to compare the two asymmetry metrics.For the empirical analysis,the data sample period used in this paper is every 5-minute high-frequency data of the SSE and Shenzhen indices from January 2010 to December 2019,which are studied from both qualitative and quantitative analysis.For qualitative analysis,this paper examines the trend of the relationship between the future period excess return of stocks and two asymmetry measures,and finds that both indicators have a negative correlation with the future period excess return of stocks.For quantitative analysis,this paper tests the predictive power of the two metrics on the short-term and long-term stock excess returns through a predictive regression model,and the regression results show that for short-term excess returns,both metrics have significant predictive power,but for long-term excess returns,the actual skewness has stronger predictive power than our newly constructed metrics.Finally,this paper performs a robustness check on the empirical regression results,and the results show that the two asymmetry measures are robust to the predictive power of the future period excess return of stocks for different risk-free rates and different markets.The main contribution of this paper is to construct a new indicator to measure asymmetric risk of stock returns and use it to confirm that there is a negative correlation between asymmetric risk and expected stock returns,and thus the newly constructed indicator has implications for both asset pricing models and financial risk management.Although this paper theoretically demonstrates that the newly constructed indicator is a better measure of asymmetric risk than skewness in some cases,it is found in the empirical analysis that skewness performs better in predicting long-term stock returns due to the error in fitting the density function of stock returns.