Optimal conditional hedge ratio: A simple shrinkage estimation approach

A number of recent studies adopt bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models to estimate the optimal conditional hedge ratio. Since the optimal hedge ratio can be expressed by the ratio of variance of futures returns to the covariance of spot and futures, the BGARCH model is quite useful to estimate the conditional hedge ratio. However, it is well known that high variability of an estimated conditional hedge ratio results in lower hedge effectiveness. In this study, we consider a simple shrinkage method to deal with this inverse relationship between volatility of the conditional hedge ratio and hedging effectiveness. Our main idea is that the shrinkage version of the optimal hedge ratio can be obtained from a convex combination of unconditional sample covariance matrix and conditional covariance matrices of a conventional BGARCH model. Our empirical results show the usefulness of our proposed model.