Optimal hedge ratio estimation and hedge effectiveness with multivariate skew distributions

Abstract

This article proposes to use the three multivariate skew distributions (generalized hyperbolic distribution, multivariate skew normal distribution, and multivariate skew Student-t distribution) for estimating the 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 (RHRE). Three portfolios of spot and futures series are formed for empirical analysis. The outcomes confirm that the three multivariate skew distributions are more helpful in deciding the minimum variance hedge ratio, especially the generalized hyperbolic distribution, than the symmetrical normal and Student-t distributions. This outperformance is significant especially at critical market moments and it is indicated by three hedge effectiveness measures. This advantage is held without the cost of lowering portfolio return. In addition, there is speculation possibility existing in the portfolio hedged by the traditional optimal hedge ratio and this potential can be detected especially by RHRE.