Conditional OLS minimum variance hedge ratios

The paper presents a new methodology to estimate time dependent minimum variance hedge ratios. The so‐called conditional OLS hedge ratio modifies the static OLS approach to incorporate conditioning information. The ability of the conditional OLS hedge ratio to minimize the risk of a hedged portfolio is compared to conventional static and dynamic approaches, such as the naïve hedge, the roll‐over OLS hedge, and the bivariate GARCH(1,1) model. The paper concludes that, both in‐sample and out‐of‐sample, the conditional OLS hedge ratio reduces the basis risk of an equity portfolio better than the alternatives conventionally used in risk management. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:945–964, 2004     

Optimal futures hedging for energy commodities: An application of the GAS model

This paper applies generalized autoregressive score-driven (GAS) models to futures hedging of crude oil and natural gas. For both commodities, the GAS framework captures the marginal distributions of spot and futures returns and corresponding dynamic copula correlations. We compare within-sample and out-of-sample hedging effectiveness of GAS models against constant ordinary least square (OLS) strategy and time-varying copula-based GARCH models in terms of volatility reduction and Value at Risk reduction. We show that the constant OLS hedge ratio is not inherently inferior to the time-varying alternatives. Nonetheless, GAS models tend to exhibit better hedging effectiveness than other strategies, particularly for natural gas.     

A further note on the optimality of the OLS hedge strategy

This note considers the hedging effectiveness of a dynamic hedge strategy as compared to the conventional OLS strategy. The conditions for the superiority of the OLS strategy are identified. It is argued that these conditions are frequently satisfied and therefore one expects to find the dominance of the OLS strategy over any dynamic strategy in the empirical work. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:308–311, 2008     

Optimal hedging with a regime‐switching time‐varying correlation GARCH model

The authors develop a Markov regime‐switching time‐varying correlation generalized autoregressive conditional heteroscedasticity (RS‐TVC GARCH) model for estimating optimal hedge ratios. The RS‐TVC nests within it both the time‐varying correlation GARCH (TVC) and the constant correlation GARCH (CC). Point estimates based on the Nikkei 225 and the Hang Seng index futures data show that the RS‐TVC outperforms the CC and the TVC both in‐ and out‐of‐sample in terms of variance reduction. Based on H. White's (2000) reality check, the null hypothesis of no improvement of the RS‐TVC over the TVC is rejected for the Nikkei 225 index contract but is not rejected for the Hang Seng index contract. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:495–516, 2007     

A random coefficient autoregressive Markov regime switching model for dynamic futures hedging

The random coefficient autoregressive Markov regime switching model (RCARRS) for estimating optimal hedge ratios, which generalizes the random coefficient autoregressive (RCAR) and Markov regime switching (MRS) models, is introduced. RCARRS, RCAR, MRS, BEKK‐GARCH, CC‐GARCH, and OLS are compared with the use of aluminum and lead futures data. RCARRS outperforms all models out‐of‐sample for lead and is second only to BEKK‐GARCH for aluminum in terms of variancereduction point estimates. White's data‐snooping reality check null hypothesis of no superiority is rejected for BEKK‐GARCH and RCARRS for aluminum, but not for lead. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:103–129, 2006     

A Markov regime switching approach for hedging stock indices

In this paper we describe a new approach for determining time‐varying minimum variance hedge ratio in stock index futures markets by using Markov Regime Switching (MRS) models. The rationale behind the use of these models stems from the fact that the dynamic relationship between spot and futures returns may be characterized by regime shifts, which, in turn, suggests that by allowing the hedge ratio to be dependent upon the “state of the market,” one may obtain more efficient hedge ratios and hence, superior hedging performance compared to other methods in the literature. The performance of the MRS hedge ratios is compared to that of alternative models such as GARCH, Error Correction and OLS in the FTSE 100 and S&P 500 markets. In and out‐of‐sample tests indicate that MRS hedge ratios outperform the other models in reducing portfolio risk in the FTSE 100 market. In the S&P 500 market the MRS model outperforms the other hedging strategies only within sample. Overall, the results indicate that by using MRS models market agents may be able to increase the performance of their hedges, measured in terms of variance reduction and increase in their utility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:649–674, 2004     

The Asymmetric Commodity Inventory Effect on the Optimal Hedge Ratio

Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This study illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modeling the variance–covariance dynamics. We show by in‐sample and out‐of‐sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK–GARCH model outperforms the symmetric BEKK, static (OLS), or naïve models. Robustness checks on a set of commodities and by an alternative mean‐variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.     

Optimal hedge ratios in the presence of common jumps

This study derives optimal hedge ratios with infrequent extreme news events modeled as common jumps in foreign currency spot and futures rates. A dynamic hedging strategy based on a bivariate GARCH model augmented with a common jump component is proposed to manage currency risk. We find significant common jump components in the British pound spot and futures rates. The out‐of‐sample hedging exercises show that optimal hedge ratios which incorporate information from common jump dynamics substantially reduce daily and weekly portfolio risk. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:801–807, 2010     

Hedging performance of multiscale hedge ratios

In this study, the wavelet multiscale model is applied to selected assets to hedge time-dependent exposure of an agent with a preference for a certain hedging horizon. Based on the in-sample and out-of-sample portfolio variances, the wavelet-based generalized autoregressive conditional heteroskedasticity (GARCH) model produces the lowest variances. From a utility standpoint, wavelet networks combined with GARCH have the highest utility. Finally, the wavelet-GARCH model has the lowest minimum capital risk requirements. Overall, the wavelet GARCH and wavelet networks offer improvements over traditional hedging models.     

Optimal hedging with higher moments

This study proposes a utility‐based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out‐of‐sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out‐of‐sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:909–944, 2012     

The Cross‐Currency Hedging Performance of Implied Versus Statistical Forecasting Models

This article examines the ability of several models to generate optimal hedge ratios. Statistical models employed include univariate and multivariate generalized autoregressive conditionally heteroscedastic (GARCH) models, and exponentially weighted and simple moving averages. The variances of the hedged portfolios derived using these hedge ratios are compared with those based on market expectations implied by the prices of traded options. One‐month and three‐month hedging horizons are considered for four currency pairs. Overall, it has been found that an exponentially weighted moving‐average model leads to lower portfolio variances than any of the GARCH‐based, implied or time‐invariant approaches. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1043–1069, 2001     

The performance of event study approaches using daily commodity futures returns

Simulations are conducted to assess the inferential accuracy of statistical event study approaches using daily futures returns. Methods examined include constant mean return models and several regression models—OLS, GARCH(1,1), and a GARCH(1,1) model having an error term with a Student's t distribution. The simulations address four of the most commonly analyzed agricultural futures commodities—corn, soybeans, live cattle, and hogs. In terms of the size of the test statistics, constant mean return models with short normal periods perform poorly, leading to unacceptably high rejection rates of the null hypothesis. Test statistics from constant mean return models with longer normal periods, OLS, and GARCH specifications provide rejection rates largely consistent with those of a unit normal distribution. Test statistics from all models are powerful enough to detect abnormal performance levels below those that would trigger limit locks. At small levels of abnormal performance the GARCH(1,1) model with a t distribution was consistently the most powerful model. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:533–555, 2004     

The effects of structural breaks and long memory on currency hedging

Empirical evidence suggests that unconditional variance of exchange rate return series is subject to occasional structural breaks that may induce spurious phenomenon of high persistence and long memory of volatility processes. In this study, we investigate the effects of such breaks on estimated risk-minimizing hedge strategies (ratios) and their performance in currency markets. Using bivariate GARCH (BGARCH) and fractionally integrated GARCH models, we estimate the hedge ratios for six foreign currencies in the full sample with and without controlling for breaks and each subsample of different unconditional variance regimes identified by a modified version of the Inclan C, and Tiao GC (1994) algorithm. Our findings suggest that daily currency risk can be better hedged with currency futures when controlling for unconditional variance breaks in the BGARCH model. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:607–632, 2010     

A simplified approach to modeling the co‐movement of asset returns

The authors propose a simplified multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model (the S‐GARCH model), which involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The proposed model is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. The S‐GARCH model is used to estimate the minimum‐variance hedge ratio for the FTSE (Financial Times and the London Stock Exchange) 100 Index portfolio, hedged using index futures, and compared to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, it was found that the S‐GARCH model performs at least as well as the other models that were considered, and in some cases it was better. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:575–598, 2007     

An empirical analysis of dynamic multiscale hedging using wavelet decomposition

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.     

Dynamic hedging with futures: A copula‐based GARCH model

In a number of earlier studies it has been demonstrated that the traditional regression‐based static approach is inappropriate for hedging with futures, with the result that a variety of alternative dynamic hedging strategies have emerged. In this study the authors propose a class of new copula‐based GARCH models for the estimation of the optimal hedge ratio and compare their effectiveness with that of other hedging models, including the conventional static, the constant conditional correlation (CCC) GARCH, and the dynamic conditional correlation (DCC) GARCH models. With regard to the reduction of variance in the returns of hedged portfolios, the empirical results show that in both the in‐sample and out‐of‐sample tests, with full flexibility in the distribution specifications, the copula‐based GARCH models perform more effectively than other dynamic hedging models. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1095–1116, 2008     

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

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     

Asymmetric covariance in spot‐futures markets

This article studies how the spot‐futures conditional covariance matrix responds to positive and negative innovations. The main results of the article are achieved by obtaining the Volatility Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures, extending Lin (1997) findings for symmetric GARCH models. This theoretical result is general and can be applied to analyze covariance dynamics in any financial system. After testing how multivariate GARCH models clean up volatility asymmetries, the Asymmetric VIRF is computed for the Spanish stock index IBEX‐35 and its futures contract. The empirical results indicate that the spot‐futures variance system is more sensitive to negative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Additionally, evidence is obtained showing that optimal hedge ratios are insensitive to the well‐known asymmetric volatility behavior in stock markets. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1019–1046, 2003     

Optimal Futures Hedging Under Multichain Markov Regime Switching

Most of the existing Markov regime switching GARCH‐hedging models assume a common switching dynamic for spot and futures returns. In this study, we release this assumption and suggest a multichain Markov regime switching GARCH (MCSG) model for estimating state‐dependent time‐varying minimum variance hedge ratios. Empirical results from commodity futures hedging show that MCSG creates hedging gains, compared with single‐state‐variable regime‐switching GARCH models. Moreover, we find an average of 24% cross‐regime probability, indicating the importance of modeling cross‐regime dynamic in developing optimal futures hedging strategies. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:173–202, 2014     

A copula‐based regime‐switching GARCH model for optimal futures hedging

The article develops a regime‐switching Gumbel–Clayton (RSGC) copula GARCH model for optimal futures hedging. There are three major contributions of RSGC. First, the dependence of spot and futures return series in RSGC is modeled using switching copula instead of assuming bivariate normality. Second, RSGC adopts an independent switching Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process to avoid the path‐dependency problem. Third, based on the assumption of independent switching, a formula is derived for calculating the minimum variance hedge ratio. Empirical investigation in agricultural commodity markets reveals that RSGC provides good out‐of‐sample hedging effectiveness, illustrating importance of modeling regime shift and asymmetric dependence for futures hedging. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:946–972, 2009