An empirical analysis of dynamic multiscale hedging using wavelet decomposition

Abstract

This study investigates the hedging effectiveness of a dynamic moving‐window OLS hedging model, formed using wavelet decomposed time‐series. The wavelet transform is applied to calculate the appropriate dynamic minimum‐variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dynamic multiscale hedging strategy is then tested, both in‐ and out‐of‐sample, using standard variance reduction and expanded to include a downside risk metric, the scale‐dependent Value‐at‐Risk. Measured using variance reduction, the effectiveness converges to one at longer scales, while a measure of VaR reduction indicates a portion of residual risk remains at all scales. Analysis of the hedge portfolio distributions indicate that this unhedged tail risk is related to excess portfolio kurtosis found at all scales.

Does gold glitter in the long-run? Gold as a hedge and safe haven across time and investment horizon

“…Simultaneously hedging a portfolio of industrial metals using futures contracts, Fernandez (2008) accounts for heterogeneous hedging horizons using wavelets. Conlon and Cotter (2012) use wavelet multiscaling to show that the optimal futures hedge ratio is simultaneously time and frequency dependent. In this paper, we use the continuous wavelet transform to examine the potential for gold to simultaneously act as a hedge and safe haven at both short and long investment horizons.…”

Time Scale Analysis of Interest Rate Spreads and Output Using Wavelets

“…As a result wavelet analysis can be used to look for (highly localized) patterns, possibly only at certain scales, and to reveal potentially interesting structure, like characteristic scales, in the data. (It is worth noting that methods have been developed to account for the time-varying nature of the second moment at different scales [38].) Among the several types of wavelet families available such as, Morlet, Mexican hat, Haar, Daubechies, etc., we choose to employ a widely used wavelet such as the Morlet wavelet, (The Morlet wavelet, consisting of a plane wave modulated by a Gaussian, has optimal joint time frequency concentration as it attains the minimum possible uncertainty of the corresponding Heisenberg box.)…”

Optimal conditional hedge ratio: A simple shrinkage estimation approach

“…Time-varying hedge ratios are usually referred to as conditional hedge ratios in the literature since the estimated hedge ratios are conditioned on the data set available for the previous time period. Recently, more sophisticated and flexible models are used to improve hedging effectiveness; for example, a random coefficient autoregressive Markov regime switching model (Lee et al, 2006), a copula-based generalized autoregressive conditional heteroskedasticity (GARCH) model (Hsu et al, 2008), a wavelet-based model (Conlon and Cotter, 2012), a Markov regime-switching autoregressive moving-average (ARMA) model (Chen and Tsay, 2011), a higherorder moment model (Brooks et al, 2012), a stochastic volatility model (Liu et al, 2014), and a functional coefficient model (Fan et al, 2015). However, the out-of-sample performances of most of these models are very similar to or dominated by a simple constant (unconditional) hedging strategy obtained by the ordinary least squares (OLS) estimate for the slope parameter in the linear regression of spot returns on futures returns.…”