Hedging (Co)Variance Risk with Variance Swaps

Abstract

In this paper we measure the impact of variance and covariance risks in financial markets. In an asset allocation framework with stochastic (co)variances, we consider the possibility to invest not only in the risky assets but also in the variance swaps associated that are non redundant derivatives which span the volatility as well as the co-volatility risks. We provide explicit solutions for the portfolio optimization problem in both the incomplete and completed market cases. We use the ratio between the initial wealths leading to the same expected utility in the two market cases as a criterion in order to measure the impact of (co)variance risk. Using real data on major indexes and this criterion, we find that the impact of (co)variance risk on the optimal strategy is huge. We especially discuss the sensitivity of the criterion proposed to measure (co)variance risk with respect to the volatility of volatility parameter and it is found to be huge. This is consistent with the single asset empirical literature and the fast development of variance and covariance-based derivative products.

Keywords: Wishart Affine Stochastic Correlation model, complete and incomplete markets, variance swaps, optimal portfolio choice with derivatives

JEL Classification: G11, G12