Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge.

Six different commodities are examined using daily data over two futures contract periods. Cash and futures prices for all six commodities are found to be well described as martingales with near-integrated GARCH innovations. Bivariate GARCH models of cash and futures prices are estimated for the same six commodities. The optimal hedge ratio (OHR) is then calculated as a ratio of the conditional covariance between cash and futures to the conditional variance of futures. The estimated OHRs reveal that the standard assumption of a time-invariant OHR is inappropriate. For each commodity the estimated OHR path appears non-stationary, which has important implications for hedging strategies. Copyright 1991 by John Wiley & Sons, Ltd.