A Study On The Optimal Hedging Ratio Of Stock Index Futures Based On A Simple Shrinkage Estimation

On April 16,2010,China officially launched the first stock index futures contract ——Shanghai and Shenzhen 300 stock index futures,which opened a new chapter in China's financial futures trading.Five years later,CSI 500 stock index futures and SSE 50 stock index futures were listed and traded one after another,which ended the history of single stock index futures trading in China and provided investors with diversified index investment tools.The stock index futures play an important role in risk management,price discovery and asset allocation.Hedging as a means of risk aversion has been widely studied by scholars at home and abroad.The successive introduction of domestic stock index futures also provides a certain space for hedgers to operate.In addition,in recent years,changes in the domestic and foreign economic environment have also made investors face more and more diversified and complex risks.Since 2018,the trade frictions between the United States and China have greatly shaken their respective financial markets,and the risk management needs of domestic real enterprises and investors have also increased significantly.Therefore,under such a background,it is of practical significance to study how to better use stock index futures for hedging.The key problem of hedging is to determine the optimal hedging ratio.At present,the research models of optimal hedging ratio can be divided into two categories: static hedging models and dynamic hedging models.Static models mainly include the ordinary least squares model(OLS),the bivariate vector autoregressive model(BVAR),the vector error correction model(VECM)and so on.The common point of these models is that the optimal hedging ratio obtained does not change with time.Although the static model is simple and easy to implement,it can not solve the problems of autocorrelation and heteroscedasticity commonly existing in financial time series.Therefore,scholars begin to use GARCH and other dynamic models for relevant research,but in the field of the empirical research,different scholars still have controversies about which kind of model can get better hedging performance,that is,the study found that dynamic models are not always better than static models.In addition,some foreign scholars have found that the volatility of the optimal hedging ratio estimated by dynamic model is inversely correlated with the performance of out-of-sample hedging,and they have tried to improve the performance of the model by reducing the volatility of the optimal hedging ratio.The empirical research of foreign stock index futures have achieved good results.The domestic literature on this aspect of correlation research and empirical research is relatively small,mainly focused on the comparison of various models of hedging performance.Therefore,in order to explore whether this reverse correlation also exists in China's stock index futures market,whether the hedging performance of the model can be improved by reducing the volatility of the optimal hedging ratio estimated by the dynamic model.In this paper,the convex combination of sample(conditional)covariance matrix estimated by dynamic DCC-GARCH model and static OLS model is used as a new estimation of conditional covariance matrix by using Kim and Park(2016)methods,which reduces the volatility of the optimal hedging ratio obtained by the model.The optimal hedging ratio estimated by this shrinkage estimation method has three advantages over the general dynamic model:(1)The optimal hedging ratio estimated by this method keeps the time-varying of the dynamic model,but at the same time it can reduce the volatility of the hedging ratio.(2)By choosing the time-varying shrinkage weights,the performance indicators of hedging,such as variance reduction,can be maximized to meet the actual needs of hedgers.(3)The calculation cost of this method is much smaller than many existing complex models,and it is very convenient to operate.The empirical part of this paper uses the spot and future data of Shanghai and Shenzhen 300,CSI 500 and SSE 50 stock indexes from January 11,2016 to December 28,2018 to test the effectiveness of this method.Under the framework of the minimum variance,the results show that the average value of the optimal hedging ratio obtained by this shrinkage estimation method is lower than that of DCC-GARCH model both inside and outside the sample,which means that the occupancy cost of funds is lower and the leverage risk of hedgers is lower.In addition,while effectively reducing the fluctuation of the estimated optimal hedging ratio,it can better maintain the time-varying and sustainability of DCC-GARCH model,and the hedging performance is also better than the traditional static OLS model and dynamic DCC-GARCH model.This paper will help enrich the empirical research on the correlation between the volatility of the optimal hedging ratio and the performance of hedging in the domestic futures market,provide some help for exploring the hedging model suitable for the stock index futures market in China,and provide some reference for investors with hedging demand in the domestic market.