Hedging Long-Term Exposures of a Well-Diversified Portfolio with Short-Term Stock Index Futures Contracts

It is difficult for passive portfolio strategy to manage the long-term exposure of a well-diversified portfolio because stock index futures contracts have a finite life limited by their maturity. In this paper, we investigate the problem of the rollover hedge strategy for the long-term exposure of a well-diversified portfolio. First, we consider the rollover hedge strategy for the well-diversified portfolio when the portfolio is not adjusted during the period. In order to obtain the optimal solution of the proposed model, the auxiliary models are constructed using the equivalent transformation technique. Moreover, dynamic programming is employed to derive the optimal positions of stock index futures contracts for the long-term exposure of the well-diversified portfolio. In addition, we extend the result to the case of the rollover hedge strategy with transaction costs and derive the optimal number of stock index futures contracts.