Stock Index Futures Hedging Under Tail Risk

In recent years, Investors have shown great interest in the issue of tail risk management. Investors with different risk preference and risk tolerance may be inclined to take risk under speculation motivation and expect to hedge the extreme risk which may cause significant influence on them, rather than the normal risk. As the launch of CSI 300 index future, hedging with stock index futures will be taken as an important approach to hedge the systematic risk in stock market. But, most hedging models in the previous literatures are specified to reduce the overall risk and don't take tail risk into account. Our empirical study finds that, although hedging based on minimum-variance can reduce the variance, meanwhile it may enhance the tail risk. Therefore, on the occasion of the launch of the first stock index future in China and under the background of the financial crisis, it is prospective and significant to take research on stock index future hedging with the purpose of tail risk management.It needs to first define proper measures for tail risk in order to establish effective hedging model. Expected shortfall (ES) and tail variance (TV) are proposed to measure tail risk according to previous theory of risk management. The paper considers nonparametric estimators of ES and TV and constructs the hedging effectiveness index based on ES and TV. Then, comprehensive hedging degree (CHD) is proposed to evaluate the hedging performance for tail risk. According to the hedging principles, the paper establishes the maximum-CHD hedging model with nonparametric method and grid search. The new model can provide an effective analysis framework for investors to hedge different tail risk appropriately according to their need. Empirical studies show that the maximum-CHD hedging model outperforms the minimum-variance hedging model and can offer different optimal hedge ratios for hedging different tail risk, being helpful to reduce hedging cost and achieve better hedging performance. Maximum-CHD hedging model, which can be regarded as the generalization of the hedging models under minimum-variance framework and risk-return tradeoff framework, expand the theoretical studies in hedging and has a broad application prospect.The new model has more theoretical connotations. Different from previous hedging models, maximum-CHD hedging model divides investors risk preference into two parts. One part is embodied in the choice of tail risk for hedging, which can be implemented in the model by determining the parameter a. The other part is represented by the tradeoff between ES and TV, which reflects investors preference in ES hedging and TV hedging. The tradeoff can be implemented in the model by adjusting the value of the parameterλ. The paper provides practical methods for determining the parametersαandλ. The hedging efficiency of market is also discussed in the maximum-CHD model by introduced market hedging inclination index, which reflects the market capacity in hedging ES and TV due to the features in stock index futures market and the stock market.Although consistent with the risk-return tradeoff framework, the modeling procedure by combining ES and TV to measure tail risk comprehensively has more general sense. In most hedging models, variance is taken to measure risk while expected return is used to measure yield. In practice, expected return can represent the scale of expected loss and has the function of risk measurement. So, the expected return or the expected loss should be taken as a measurement of risk. The traditional definition of risk, that risk means the uncertainty of future return, is overly concerned with the uncertainty and ignores the value of variable. In practice, people not only hope that the future is deterministic, but also expect the future can be determined at an ideal level. Violation against one of the two points should be taken as risk. So, both uncertainty and expected level mean risk. The paper reformulates the definition of risk as "the uncertainty of future return at a certain expected level". Under the new definition, risk-return tradeoff is equivalent to risk minimization. So is the ES-TV tradeoff as used in the new hedging model.In order to achieve good hedging performance, proper future contracts should be selected for hedging. Correlation between stock index futures and spots is an important factor influencing hedging performance and the basis for future contract selection. As an important part of the research on hedging for tail risk, the mixed copula model is established to study the tail dependence between stock index futures and spots. A practical procedure which can be carried out simply by computer is proposed to estimate the parameters. The empirical studies find that, future contracts which have strong lower tail dependence and weak upper tail dependence with the spot are suitable for short hedge, while future contracts which have weak lower tail dependence and strong upper tail dependence with the spot are suitable for long hedge. In the initial period of the stock index future market in China, investors can select the no.1 contract or the no.4 contract to implement short hedge to reduce the tail risk caused by price slump in the stock market.The paper constructs spot portfolio with bulk-holding stock and calculates the optimal hedging ratio for different tail risk using the simulated data of CSI 300 stock index future. The evaluation of hedging performance is also given. The empirical results can be taken as reference for hedging under tail risk with the new stock index future market.Finally, it is worthy to note that nonparametric method, grid search technique, copula selection approach via penalized likelihood and comprehensive evaluation method used in the paper are helpful to improve model performance. They are good attempts for the modeling of hedging.