The Empirical Minimum-Variance Hedge

Abstract

<p>Decision making under unknown true parameters (estimation risk) is discussed along with Bayes and parameter certainty equivalent (PCE) criteria. Bayes criterion provides the solution for optimal decision making under estimation risk in a manner consistent with expected utility maximization. The PCE method is not consistent with expected utility maximization, but is the approach commonly used.</p> <p>Bayes criterion is applied to solve for the minimum variance hedge ratio (MVH) in two scenarios based on the multivariate normal distribution. Simulations show that discrepancies between prior and sample parameters may lead to substantial differences between Bayesian and PCE MVHs. Such discrepancies also highlight the superiority of Bayes criterion over the PCE, in the sense that the PCE method cannot not yield decision rules that contain prior (or nonsample) along with sample information.</p>