Hedging and Value at Risk

Abstract

In this paper, we show that although minimum-variance hedging unambiguously reduces the standard deviation of portfolio returns, it tends to increase portfolio kurtosis and consequently the effectiveness of hedging in terms of a more general measure of risk such as VaR is uncertain. We compare the reduction in standard deviation with the reduction in 99% VaR for thirteen cross-hedged currency portfolios using both in-sample and out-of-sample approaches. We find that minimum-variance hedging reduces standard deviation considerably more than it reduces VaR. Indeed, for some portfolios, the out-of-sample reduction in VaR is negligible. As an alternative, we propose a minimum-VaR hedging strategy that minimises the historical simulation VaR of the hedge portfolio. Minimum-VaR hedge ratios are found to be significantly lower than minimum-variance hedge ratios. The minimum-VaR hedging strategy offers a significant improvement over the minimum-variance hedging strategy in terms of VaR. Moreover, in many cases, it actually yields a larger out-of-sample reduction in standard deviation also.