Can Realized Higher-order Moments Predict Chinese Commodity Futures Return?

From the first day of the birth of financial markets,price,a property of asset,which reveals information,has become a secret that various market participants want to study and master.Markowitz(1952)used the mean to represent the expected return of asset and the variance to represent the risk,he built a mean-variance framework.and assumed that asset price follows a normal distribution.It is the first time that mathematical method was used to solve the mystery of asset price.Subsequent classic models of asset pricing,such as the CAPM model and the Fama-French three factors model,were all established under this framework.In real financial markets,the distribution of asset price is asymmetrical with higher peak and thick tail.This phenomenon challenges the rationality of the pricing model under the mean-variance framework.Many domestic and foreign scholars focus on the pricing role of third-order moment skewness and fourth-order moment kurtosis,the research covers the stock markets of various developed and emerging countries,but there has been no consistent conclusion on the pricing role of skewness and kurtosis.Less research about the predicting ability of skewness and kurtosis on other types of asset can be found.This article's research is based on the data of Chinese commodity futures market,discussing whether the higher-order moments can predict asset return on commodity futures with hedging function.and no short selling restriction.This article summarizes the calculation methods of skewness and kurtosis,puts forward three major theories of the relationship between skewness and return:investor preference theory,cumulative prospect theory,and selective hedging theory.theoretically explaining the negative correlation between skewness and rate of return.Then,the article screens the data of Chinese commodity futures,removing inactive futures varieties.Finally,22 types of futures are selected as research objects for empirical research.The research of this article starts from two dimensions.The first dimension is the empirical study of the prediction ability of higher-order moments to futures return under the perspective of high-frequency data.Based on the method proposed by Amaya et al.(2015)about using high-frequency minute data to construct intraday higher-order moments,the article uses 5-minute price data of the commodity futures' continuous main contract to calculate intraday volatility,skewness and kurtosis for generating a weekly higher-order moments.First,this article uses the portfolio grouping analysis method to divide futures into five portfolios separately based on the ranking of realized volatility,skewness and kurtosis,and observes whether there is a monotonous trend in the return from the lowest higher-order moments portfolio to highest higher-order moments portfolio to judge the relationship between the higher-order moments and futures return.The research finds that there is no obvious correlation between the realized volatility and the rate of return,but there is a significant negative correlation between the realized skewness and the rate of return,there is also a significant negative correlation between the realized kurtosis and the rate of return.By constructing five pure long strategies and a long-short strategy,these conclusions are further verified.Then,the article proves that the negative correlation between skewness or kurtosis and futures return is not limited to specific futures.And the benchmark pricing model constructed by roll return,momentum factor and inventory factor is regressed on each portfolio.By observing the change of the intercept term,it is proved that the skewness and kurtosis have an explanatory power independent of the benchmark model.Next,in order to further test the predictive ability of higher-order moments factors,the article uses Fama-Macbeth two-step regression method for further analysis.The regression results show that there is a negative correlation between skewness and the rate of return,a negative correlation between kurtosis and the rate of return.Similarly,it proves that volatility can't predict the return of futures.Finally,by constructing the efficient frontier of Markowitz,it shows that the skewness and kurtosis portfolio can increase the value for diversified investors,and the skewness and kurtosis portfolio are effective under three different risk conditions.The second dimension is empirically testing the prediction ability of higher-order moments from the perspective of low-frequency data.this article uses Fernandez et al.(2018)'s method of using daily price data of every 12 months to construct monthly higher-order moments through rolling windows.it is confirmed that changes in time frequency will not change the correlation between realized higher-order moments and return of commodity futures.However,the stability of realized higher-order moments' predictive power in low-frequency perspective is weaker than that in high-frequency perspective.The innovations of this article are as follows: Firstly,in the stock market,the higher-order moments have been researched by many scholars,but no unified conclusion has been obtained.In the futures market of emerging countries,the predictive power of the higher-order moments is still to be studied,this article fills this gap.Secondly,this article takes a step forward by using the weekly higher-order moment data based on the intraday high-frequency data,which contains more information about the distribution of return rate.,comparing with former research of higher-order moments pricing which is based on the low-frequency data.Thirdly,considering the time-varying characteristics of higher-order moments,this article uses the method of quantitative analysis to construct the pure long strategy and the long-short strategy,and compares the performance of each strategy,further confirming the pricing role of higher-order moments,and eliminates the specificity of predictive power by calculating the probability of futures falling into extreme portfolio.Fourthly,the Fama-Macbeth two-step regression method is used in this article,which contains multiple regression on time series and cross-section,reducing the estimation error caused by too few cross-sections,and eliminating the influence of cross-section correlation of residual error on standard error.