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     

Futures Hedging Under Disappointment Aversion

This article considers optimal futures hedging decisions when the hedger is disappointment‐averse (Gul, 1991). When the futures contract is a perfect hedge instrument, a disappointment‐averse hedger always holds a position closer to the full hedge than a nondisappointment‐averse hedger. In the presence of basis risk, the optimal futures position is either a partial hedge or a full hedge. Neither Texas hedge nor overhedge could be optimal. The effects of different degrees of disappointment aversion on futures trading are also analyzed. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1029–1042, 2001     

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     

Risk aversion,disappointment aversion,and futures hedging

This article examines the effect of disappointment aversion on futures hedging. We incorporated a constant‐absolute‐risk‐aversion (CARA) utility function into the disappointment‐aversion framework of Gul (1991). It is shown that a more disappointment‐averse hedger will choose an optimal futures position closer to the minimum‐variance hedge than will a less‐disappointment‐averse hedger. The effect of disappointment aversion is stronger when the hedger is less risk averse. A small disappointment aversion will cause a near‐risk neutral hedger to take a drastically different position. In addition, a more‐risk‐averse or disappointment‐averse hedger will have a lower reference point. Numerical results indicate that the reference point of a disappointment‐averse hedger tends to be lower than that of a conventional loss‐averse hedger. Consequently, the disappointment‐averse hedger will act more conservatively, not exploiting profitable opportunities as much as the conventional loss averse hedger will. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:123–141, 2002     

A Note on Loss Aversion and Futures Hedging

This note examines the effect of loss aversion on the futures trading behavior of a short hedger. Using a modified constant‐absolute‐risk‐aversion utility function, I show that loss aversion has no effect in an unbiased futures market. It has different, predictable impacts when the futures market is in backwardation or contango. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21: 681–692, 2001     

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     

The incremental value of a futures hedge using realized volatility

A number of prior studies have developed a variety of multivariate volatility models to describe the joint distribution of spot and futures, and have applied the results to form the optimal futures hedge. In this study, the authors propose a new class of multivariate volatility models encompassing realized volatility (RV) estimates to estimate the risk‐minimizing hedge ratio, and compare the hedging performance of the proposed models with those generated by return‐based models. In an out‐of‐sample context with a daily rebalancing approach, based on an extensive set of statistical and economic performance measures, the empirical results show that improvement can be substantial when switching from daily to intraday. This essentially comes from the advantage that the intraday‐based RV potentially can provide more accurate daily covariance matrix estimates than RV utilizing daily prices. Finally, this study also analyzes the effect of hedge horizon on hedge ratio and hedging effectiveness for both the in‐sample and the out‐of‐sample data. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:874–896, 2010     

Information transmission in electronic versus open‐outcry trading systems: An analysis of U.S. equity index futures markets

In this article the intraday price discovery process between regular index futures (floor trading) and E‐mini index futures (electronic trading) in the S&P 500 and Nasdaq 100 index futures markets is examined, using intraday data from the introduction of the E‐mini index futures to 2001. Using both information shares (Hasbrouck, J., 1995) and common long‐memory factor weights (Gonzalo, J., & Granger, C. W. J., 1995) techniques, we find that both E‐mini index futures and regular index futures contribute to the price discovery process. However, since September 1998, the contribution made by E‐mini index futures has been greater than that provided by regular index futures. Based on regression analysis, we have also found direct empirical evidence to support the hypothesis that the joint effects of operational efficiency and relative liquidity determine the greater contribution made towards price discovery by electronic trading relative to open‐outcry trading over time. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25: 679–715, 2005     

Illiquidity transmission from spot to futures markets

We develop a model of illiquidity transmission from spot to futures markets that formalizes the derivative hedge theory of Cho and Engle (1999). The model shows that spot market illiquidity does not translate one to one to the futures market but, rather, interacts with price risk, liquidity risk, and the risk aversion of the market maker. The model's predictions are tested empirically with data from the stock market and markets for single-stock futures and index futures. The results support our model and show that the derivative hedge theory provides an explanation for the liquidity link between spot and futures markets.     

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     

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     

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     

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     

Risk management with options and futures under liquidity risk

Futures hedging creates liquidity risk through marking to market. Liquidity risk matters if interim losses on a futures position have to be financed at a markup over the risk‐free rate. This study analyzes the optimal risk management and production decisions of a firm facing joint price and liquidity risk. It provides a rationale for the use of options on futures in imperfect capital markets. If liquidity risk materializes, the firm sells options on futures in order to partly cover this liquidity need. It is shown that liquidity risk reduces the optimal hedge ratio and that options are not normally used before a liquidity need actually arises. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:297–318, 2009     

Pricing efficiency of the S&P 500 index market: Evidence from the Standard & Poor's Depositary Receipts

Standard & Poor's Depositary Receipts (SPDRs) are exchange traded securities representing a portfolio of S&P 500 stocks. They allow investors to track the spot portfolio and better engage in index arbitrage. We tested the impact of the introduction of SPDRs on the efficiency of the S&P 500 index market. Ex‐post pricing efficiency and ex‐ante arbitrage profit between SPDRs and futures were also examined. We found an improved efficiency in the S&P 500 index market after the start of SPDRs trading. Specifically, the frequency and length of lower boundary violations have declined since SPDRs began trading. This result is consistent with the hypothesis that SPDRs facilitate short arbitrage by simplifying the process of shorting the cash index against futures. Tests of pricing efficiency comparing SPDRs and futures suggested that index arbitrage using SPDRs as a substitute for program trading in general results in losses. Although short arbitrages earn a small profit on average, gains are statistically insignificant. A trade‐by‐trade investigation showed that prices are instantaneously corrected after the presence of mispricing signals, introducing substantial risk in arbitraging. Evidence in general supported pricing efficiency between SPDRs and the S&P 500 index futures—both ex‐post and ex‐ante. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:877–900, 2002     

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     

Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003     

The Demand for Hedging with Futures and Options

The optimal hedging portfolio is shown to include both futures and options under a variety of circumstances when the marginal cost of hedging is nonzero. Futures and options are treated as substitute goods, and the properties of the resulting hedging demand system are explained. The overall optimal hedge ratio is shown to increase when the marginal cost of trading options is reduced. The overall optimal hedge ratio is shown to decrease when the marginal cost of trading futures is decreased. One implication is that hedging demand can be stimulated by a reduction in the perceived cost of trading options through the education of hedgers about options and the initiation of programs such as the Dairy Options Pilot Program. The demand approach is applied to estimate optimal hedge ratios for dairy producers hedging corn inputs in five regions of Pennsylvania. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:693–712, 2001     

Production and hedging under Knightian uncertainty

This article introduces Knightian uncertainty into the production and futures hedging framework. The firm has imprecise information about the probability density function of spot or futures prices in the future. Decision‐making under such scenario follows the “max‐min” principle. It is shown that inertia in hedging behavior prevails under Knightian uncertainty. In a forward market, there is a region for the current forward price within which full hedge is the optimal hedging policy. This result may help explain why the one‐to‐one hedge ratio is commonly observed. Also inertia increases as the ambiguity with the probability density function increases. When hedging on futures markets with basis risk, inertia is established at the regression hedge ratio. Moreover, if only the futures price is subject to Knightian uncertainty, the utility function has no bearing on the possibility of inertia. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 397–404, 2000