Hedging effectiveness of stock index futures

1 Introduction This paper is concerned with the use of stock indices futures to hedge the return on portfolios. This topic has received considerable attention in the literature, which will be briefly summarised in section 2 of the paper. First of all it is desirable to consider the nature of hedging. The main aim of hedging is assumed to be the minimisation of the variance of the return on the portfolio 1 though for sake of completion we also quote the effect on the mean return 2. The portfolios we consider are represented by investment companies quoted on the London Stock Exchange where the major part of the assets consist of shares held in other companies 3. Each company will hold a wide range of shares in its portfolio, which is controlled by professional managers so that it would be expected that the portfolios are efficiently managed. Hence our hedging strategy is to offset the holdings in these investment companies by selling futures in an appropriate stock index, the choice being the FTSE 100 or FTSE 259 index future traded on LIFFE. We define the return as log(P t /P t-1) and for a hedged portfolio the related variance is defined as: Var p = σ S ² + h²σ F ²-2hcovar(S,F) (1) Where the subscripts S and F refer to the cash market and futures securities respectively and h the hedge ratio. It should be noted that if the returns on the spot and futures assets are perfectly correlated, then the variance of the portfolio equals zero. However such perfect correlation does not exist and thus there is another form of risk called basis risk existing because the gap between the price of the cash market asset and that of the futures will vary. Minimising (1) with respect to h produces the minimum variance hedge ratio: h = Covar(S,F)/σ F ² (2) If the standard assumptions of the classical linear regression model hold, then regression of the return on the portfolio on the return on the futures index will produce the best linear unbiased estimator of h of the hedge ratio (MVHR). The structure of the paper is as follows. In section 2 we survey a number of the more relevant references and in section 3 indicate the nature of the data. In section 4 we discuss more fully the methodology adopted and in section 5 present the empirical …