Estimating Optimal Hedge Ratio and Hedge Effectiveness Via Fitting the Multivariate Skewed Distributions

Abstract

This paper presents the use of three multivariate skew distributions (Generalized Hyperbolic distribution, multivariate skew normal distribution, and multivariate skew t distribution) for estimating minimum variance hedge ratio in a dynamic setting. Three criteria for measuring hedge effectiveness are employed: Hedging Instrument Effectiveness, Overall Hedge Effectiveness, and Relative-to-Optimal Hedge Ratio Effectiveness. The empirical analysis outcomes confirm that the three multivariate skew distributions are useful in deciding the optimal hedge ratio especially at the critical market moments because they consider both hedge and speculation. This advantage is held without the price of lower portfolio return. The traditional minimum variance hedge ratio can function as an effective hedge but only at most keep the portfolio variance level at its minimum.

Keywords: multivariate skew normal distribution, multivariate skew T distribution, generalized hyperbolic distribution, hedge effectiveness, dynamic optimal hedge ratio

JEL Classification: G11, C13