Detrended minimum-variance hedge ratio: A new method for hedge ratio at different time scales

Abstract

In this paper, based on the detrended fluctuation analysis (DFA) method and the detrended cross-correlation analysis (DCCA) method, we propose an improved method of minimum-variance (MV) hedge ratio, i.e., the detrended minimum-variance (D-MV) hedge ratio, which can measure the hedge ratio at different time scales. The proposed D-MV hedge ratio is defined as the detrended covariance function between spot and futures returns divided by the detrended variance function of futures returns. Through the simulated and empirical analysis, we find that (i) the outcomes of the hedge ratio and the corresponding hedging effectiveness for the D-MV hedge ratio are diverse at different time scales, which can meet needs of various hedging participants with different hedging horizons; (ii) our proposed D-MV hedge ratio has a better hedging performance and a greater potential to determine the hedge ratio because its results of hedging effectiveness at most of time scales are better than those of the traditional MV hedge ratio; and (iii) as for the method of D-MV hedge ratio for different polynomial orders m in the fitting procedure, the D-MV-1 hedge ratio (i.e., the linear polynomial in the fitting procedure) has the best hedging capability for determining the hedge ratio.