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     

Estimation and hedging effectiveness of time‐varying hedge ratio: Flexible bivariate garch approaches

Bollerslev's ( 1990 , Review of Economics and Statistics, 52, 5–59) constant conditional correlation and Engle's (2002, Journal of Business & Economic Statistics, 20, 339–350) dynamic conditional correlation (DCC) bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models are usually used to estimate time‐varying hedge ratios. In this study, we extend the above model to more flexible ones to analyze the behavior of the optimal conditional hedge ratio based on two (BGARCH) models: (i) adopting more flexible bivariate density functions such as a bivariate skewed‐t density function; (ii) considering asymmetric individual conditional variance equations; and (iii) incorporating asymmetry in the conditional correlation equation for the DCC‐based model. Hedging performance in terms of variance reduction and also value at risk and expected shortfall of the hedged portfolio are also conducted. Using daily data of the spot and futures returns of corn and soybeans we find asymmetric and flexible density specifications help increase the goodness‐of‐fit of the estimated models, but do not guarantee higher hedging performance. We also find that there is an inverse relationship between the variance of hedge ratios and hedging effectiveness. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:71–99, 2010     

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 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.     

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     

An empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short‐ and long‐run hedge ratios

This article analyzes the effects of the length of hedging horizon on the optimal hedge ratio and hedging effectiveness using 9 different hedging horizons and 25 different commodities. We discuss the concept of short‐ and long‐run hedge ratios and propose a technique to simultaneously estimate them. The empirical results indicate that the short‐run hedge ratios are significantly less than 1 and increase with the length of hedging horizon. We also find that hedging effectiveness increases with the length of hedging horizon. However, the long‐run hedge ratio is found to be close to the naïve hedge ratio of unity. This implies that, if the hedging horizon is long, then the naïve hedge ratio is close to the optimum hedge ratio. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:359–386, 2004     

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     

Fractional cointegration and futures hedging

This article examines the performance of various hedge ratios estimated from different econometric models: The FIEC model is introduced as a new model for estimating the hedge ratio. Utilized in this study are NSA futures data, along with the ARFIMA-GARCH approach, the EC model, and the VAR model. Our analysis identifies the prevalence of a fractional cointegration relationship. The effects of incorporating such a relationship into futures hedging are investigated, as is the relative performance of various models with respect to different hedge horizons. Findings include: (i) Incorporation of conditional heteroskedasticity improves hedging performance; (ii) the hedge ratio of the EC model is consistently larger than that of the FIEC model, with the EC providing better post-sample hedging performance in the return–risk context; (iii) the EC hedging strategy (for longer hedge horizons of ten days or more) incorporating conditional heteroskedasticty is the dominant strategy; (iv) incorporating the fractional cointegration relationship does not improve the hedging performance over the EC model; (v) the conventional regression method provides the worst hedging outcomes for hedge horizons of five days or more. Whether these results (based on the NSA index) can be generalized to other cases is proposed as a topic for further research. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 457–474, 1999     

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     

Robust estimation of the optimal hedge ratio

When using derivative instruments such as futures to hedge a portfolio of risky assets, the primary objective is to estimate the optimal hedge ratio (OHR). When agents have mean‐variance utility and the futures price follows a martingale, the OHR is equivalent to the minimum variance hedge ratio,which can be estimated by regressing the spot market return on the futures market return using ordinary least squares. To accommodate time‐varying volatility in asset returns, estimators based on rolling windows, GARCH, or EWMA models are commonly employed. However, all of these approaches are based on the sample variance and covariance estimators of returns, which, while consistent irrespective of the underlying distribution of the data, are not in general efficient. In particular, when the distribution of the data is leptokurtic, as is commonly found for short horizon asset returns, these estimators will attach too much weight to extreme observations. This article proposes an alternative to the standard approach to the estimation of the OHR that is robust to the leptokurtosis of returns. We use the robust OHR to construct a dynamic hedging strategy for daily returns on the FTSE100 index using index futures. We estimate the robust OHR using both the rolling window approach and the EWMA approach, and compare our results to those based on the standard rolling window and EWMA estimators. It is shown that the robust OHR yields a hedged portfolio variance that is marginally lower than that based on the standard estimator. Moreover, the variance of the robust OHR is as much as 70% lower than the variance of the standard OHR, substantially reducing the transaction costs that are associated with dynamic hedging strategies. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:799–816, 2003     

A novel risk management framework for natural gas markets

This paper examines dynamic hedges in the natural gas futures markets for different horizons and explores the gains from devising risk management strategies. Despite the substantial progress made in developing hedging models, forecast combinations have not been explored. We fill this gap by proposing a framework for combining hedge-ratio predictions. Composite hedge ratios lead to significant reduction in portfolio risk, whether spot prices are partially predictable or not. We offer insights on hedging effectiveness across seasons, backwardation-contango conditions and the asymmetric profiles of long-short hedgers. We conclude that forecast combinations better reconcile realized performance with the hedging process, mitigating model instability.     

Optimal hedging under nonlinear borrowing cost,progressive tax rates,and liquidity constraints

Empirical research using optimal hedge ratios usually suggests that producers should hedge much more than they do. In this study, a new theoretical model of hedging is derived. Optimal hedge and leverage ratios and their relationship with yield risk, price variability, basis risk, taxes, and financial risk are determined using alternative assumptions. The motivation to hedge is provided by progressive tax rates and cost of bankruptcy. An empirical example for a wheat and stocker‐steer producer is provided. Results show that there are many factors, often assumed away in the literature, that make farmers hedge little or not at all. Progressive tax rates provide an incentive for farmers to hedge in order to reduce their tax liabilities and increase their after‐tax income. Farmers will hedge when the cost of hedging is less than the benefits of hedging that come from reducing tax liabilities, liquidity costs, or bankruptcy costs. When tax‐loss carryback is allowed, hedging decreases as the amount of tax loss that can be carried back increases. Higher profitability makes benefits from futures trading negligible and hedging unattractive, since farmers move to higher income brackets with near constant marginal tax rates. Increasing basis risk or yield risk also reduce the incentive to hedge. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 375–396, 2000     

Estimating the optimal hedge ratio with focus information criterion

In recent years, the error‐correction model without lags has been used in estimating the minimum‐variance hedge ratio. This article proposes the use of the same error‐correction model, but with lags in spot and futures returns in estimating the hedge ratio. In choosing the lag structure, use of the Akaike information criterion (AIC) and recently proposed focus information criterion (FIC) by G. Claeskens and N. L. Hjort (2003) is suggested. The proposed methods are applied to 24 different futures contracts. Even though the FIC hedge ratio is expected to perform better in terms of mean‐squared error, the AIC hedge ratio is found to perform as well as the FIC and better than the simple hedge ratios in terms of hedging effectiveness. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1011– 1024, 2005     

Dealing with downside risk in a multi‐commodity setting: A case for a “Texas hedge”?

This study analyzes the problem of multi‐commodity hedging from the downside risk perspective. The lower partial moments (LPM₂)‐minimizing hedge ratios for the stylized hedging problem of a typical Texas panhandle feedlot operator are calculated and compared with hedge ratios implied by the conventional minimum‐variance (MV) criterion. A kernel copula is used to model the joint distributions of cash and futures prices for commodities included in the model. The results are consistent with the findings in the single‐commodity case in that the MV approach leads to over‐hedging relative to the LPM₂‐based hedge. An interesting and somewhat unexpected result is that minimization of a downside risk criterion in a multi‐commodity setting may lead to a “Texas hedge” (i.e. speculation) being an optimal strategy for at least one commodity. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:290–304, 2010     

Implied deterministic volatility functions: An empirical test for Euribor options

This study proposes the implied deterministic volatility function (IDVF) for the volatility as the function of moneyness and time in the Heath, Jarrow, and Morton (1992) model to price and hedge Euribor options across moneyness and maturities from 1 January 2003 to 31 December 2005. The IDVF models are extended to two‐ and three‐factor models, indicating that they are potential candidates for interest rate risk management. Based on the criteria of in‐sample fitting, prediction, and hedging, it is found that two‐factor IDVF models provide the best in‐sample and prediction performance, whereas three‐factor IDVF models yield the best results for hedging. Correctly specified multifactor models with the volatility as the function of moneyness and time can replace inappropriate onefactor models. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:319–347, 2009     

An empirical analysis of the relationship between hedge ratio and hedging horizon using wavelet analysis

In this article, optimal hedge ratios are estimated for different hedging horizons for 23 different futures contracts using wavelet analysis. The wavelet analysis is chosen to avoid the sample reduction problem faced by the conventional methods when applied to non‐overlapping return series. Hedging performance comparisons between the wavelet hedge ratio and error‐correction (EC) hedge ratio indicate that the latter performs better for more contracts for shorter hedging horizons. However, the performance of the wavelet hedge ratio improves with the increase in the length of the hedging horizon. This is true for both within‐sample and out‐of‐sample cases. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:127–150, 2007     

An examination of the effectiveness of static hedging in the presence of stochastic volatility

Toft and Xuan (1998) use simulation evidence to demonstrate that the static hedging method of Derman et al. (1995) performs inadequately when volatility is stochastic. Particularly, the greater the “volatility of volatility,” the poorer the static hedge. This article presents an alternative static hedging methodology, denoted the generalized static hedge, that appears to perform more reliably. Specifically, the value, delta, and vega of the static hedges closely approximate those values of the barrier option being hedged. Further, simulation evidence indicates that when volatility of volatility is large, the standard deviation of simulated cash flows from the generalized static hedge position is less than the standard deviation of simulated cash flows from previously defined static hedge positions. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:859–890, 2003     

Optimal partial hedging of options with small transaction costs

This study uses asymptotic analysis to derive optimal hedging strategies for option portfolios hedged using an imperfectly correlated hedging asset with small fixed and/or proportional transaction costs, obtaining explicit formulae in special cases. This is of use when it is impractical to hedge using the underlying asset itself. The hedging strategy holds a position in the hedging asset whose value lies between two bounds, which are independent of the hedging asset's current value. For low absolute correlation between hedging and hedged assets, highly risk‐averse investors and large portfolios, hedging strategies and option values differ significantly from their perfect market equivalents. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 31:855–897, 2011     

Futures hedging under mark‐to‐market risk

This article introduces mark‐to‐market risk into the conventional futures hedging framework. It is shown that a hedger concerned with maximum daily loss will considerably reduce his futures position when the risk is taken into account. In case of a moderate hedge horizon, the hedger will hedge approximately 80% of his spot position. The effect of mark‐to‐market risk decreases very slowly as the hedge horizon increases. If the hedger is concerned with average daily loss, the effect is minimal for a moderate hedge horizon. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:389–398, 2003