Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement

Abstract

This study presents a model to select the optimal hedge ratios of a portfolio composed of an arbitrary number of commodities. In particular, returns dependency and heterogeneous investment horizons are accounted for by copulas and wavelets, respectively. A portfolio of London Metal Exchange metals is analyzed for the period July 1993-December 2005, and it is concluded that neglecting cross correlations leads to biased estimates of the optimal hedge ratios and the degree of hedge effectiveness. Furthermore, when compared with a multivariate-GARCH specification, our methodology yields higher hedge effectiveness for the raw returns and their short-term components. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:182-207, 2008 Financial support from SOC 06/01-2 Grant (Research Division of the University of Chile) and from an institutional grant of the Hewlett Foundation to CEA is greatly acknowledged. All remaining errors are the author's. INTRODUCTIONThe determination of the optimal hedge ratio is an issue of both practical and theoretical interests as it impacts hedging effectiveness. Recent contributions to the literature on heterogeneous investors and the selection of an optimal hedge ratio have focused on a single commodity in isolation (e.g., In & Kim, 2006a, 2006bLien & Shrestha, 2007). This study presents a generalization of such an approach, in which the selection of optimal hedge ratios is considered for a portfolio composed of several net positions in commodities (i.e., cash position minus a proportion of a futures contract). In particular, an analytical expression is obtained for an optimal vector of hedge ratios and a measure of the degree hedge effectiveness (HE) for such a portfolio. Toward that end, wavelet and copula analysis is used to accommodate for the existence of heterogeneous investors and asset returns dependency, respectively. The empirical application used in this study considers a portfolio composed of cash and futures positions on London Metal Exchange (LME) metals for the sample period July 1993-December 2005. The portfolio choice is based on the grounds of data availability on cash and futures prices at a high frequency. Indeed, wavelet analysis is a computationally intensive statistical tool, which requires long time series (e.g., Gençay, Whitcher, & Selçuk, 2002;Percival & Walden, 2000). In contrast, given that the LME data have been analyzed earlier (e.g., McMillan, 2005), our conclusions can be contrasted with those of previous studies.The simulations we carry out to characterize the distribution functions of the hedge ratios and the degree of HE are performed under two scenarios: with and without accounting for the cross correlations of returns on cash and futures contracts. As mentioned above, dependency is handled by copula analysis, a statistical tool that has recently gained ground in the finance field to extract the dependence structure from the joint probability distribution function of a set of random variables (e.g., Cherubini, Luciano, & Vecchiato, 2004).Indeed, earlier at...

Commodity futures hedging, risk aversion and the hedging horizon

“…In the cases of cotton, corn and crude oil correlation is found to increase at longer time horizons, in keeping with findings for other assets in previous studies (Fernandez, 2008;Lien & Shrestha, 2007;In & Kim, 2006). Coffee is the exception here, with maximum correlation found at intermediate horizon, perhaps explained by difficulties in coffee storage over longer horizons.…”

“…In contrast to previous findings, (Fernandez (2008) and references therein), the maximal hedge ratio is found at intermediate horizon for certain assets, (coffee, corn and crude oil). However, the underlying data examined here is of a much longer horizon, (monthly rather than daily in previous studies), contributing additional insight from the perspective of longer-term hedgers.…”

“…28 While previous studies have applied a minimum-variance hedging approach and measured performance using mean-variance utility, (Alizadeh et al, 2008;Fernandez, 2008;In & Kim, 2006), we provide a consistent view by applying the same hedging preferences to find both the optimal mean variance hedge ratio and measure associated performance.…”

“…Further details on the application of wavelets to financial research can be found in Gençay et al (2001). 7 Further, Fernandez (2008) and Lien & Shrestha (2007) applied wavelet decomposition to minimumvariance futures hedging, demonstrating improved hedging performance for investors with long time horizons.…”

An Empirical Analysis of Dynamic Multiscale Hedging Using Wavelet Decomposition

“…Comparison to the error-correction hedge ratio revealed an outperformance for short time-horizons, while for long time-horizons, the optimal multiscale wavelet ratio was found to dominate, with similar results found both in-and out-of-sample. The optimal hedge ratios for a portfolio of commodities was found, Fernandez (2008), using copulas to measure the asset returns dependency and wavelets to account for hedging horizon. Improved hedging effectiveness was found for the portfolio of commodities compared to a single position, with additional benefits at longer scales.…”