n optimal hedge ratio is usually defined as the proportion of a cash position A that should be covered with an opposite position on a futures market. Under certain simplifying assumptions discussed below, optimal hedge ratios can be characterized by a simple rule: set the hedge ratio equal to the ratio of the covariance between cash and futures prices to the variance of the futures price (see Anderson and Danthine (1981) and Benninga, Eldor, and Zilcha (1984)). The conventional approach to implementing this rule is to regress historical cash prices, price changes, or returns on futures prices, price changes, or returns. The resulting slope coefficient is then used as the estimated optimal hedge ratio (see Ederington, (1979) and Kahl (1983)).
There are two problems with the conventional regression approach to optimal hedge ratio estimation. First, it generally fails to take proper account of all of the relevant conditioning information available to hedgers when they make their hedging decision (see Myers and Thompson (1989)). Second, it implicitly assumes that the covariance matrix of cash and futures prices, and hence optimal hedge ratios, are constant over time. There is evidence, however, that commodity price volatility changes as markets move through cycles of high and low uncertainty about future economic conditions (see Anderson (1985) and Fackler (1986)). For example, there was a clear jump in commodity price volatility during the boom of 1973, and during the recent 1988 drought. This suggests that the conditional covariance matrix of cash and futures prices, and hence optimal hedge ratios, may vary substantially over time. A recent article by Cecchetti, Cumby, and Figlewski (1988) estimates time-varying optimal hedge ratios for Treasury bonds using the autoregressive conditional heteroscedastic (ARCH) framework of Engle (1982). They find substantial fluctuations in the time path of optimal hedge ratios.
This article outlines and compares two approaches for estimating time-varying optimal hedge ratios on futures markets. Both methods take account of relevant conditioning information but they differ in their degree of sophistication and ease of estimation. The first method involves calculating moving sample variances and covariances of past prediction errors for cash and futures prices. This method is simple and easy to apply, but is also ad hoc and imposes questionable restrictions on the time pattern of commodity price volatility. The second method is the general-