A note on estimating the minimum extended Gini hedge ratio

The extended Gini coefficient, Γ, is a measure of dispersion with strong theoretical merit for use in futures hedging. Yitzhaki (1982, 1983) provides conditions under which a two‐parameter framework using the mean and Γ of portfolio returns yields an efficient set consistent with second‐order stochastic dominance. Unlike mean‐variance theory, the mean‐Γ framework requires no particular return distribution or utility function to yield this conclusion. However, Γ must be computed iteratively making it less convenient to use than variance. Shalit (1995) offers a solution to the computation problem by suggesting an instrumental variables (IV) slope estimator, β-super-I-super-V, as the basis for the minimum extended Gini hedge ratio where the instruments are based on the empirical distribution function (edf) of futures prices. However, the validity of employing the IV slope coefficient as the basis for the minimum extended Gini hedge ratio requires the questionable assumption that the rankings of futures prices to be the same as those for the profits of the hedged portfolio. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19:101–113, 1999