Crude oil hedging strategies using dynamic multivariate GARCH
Introduction
As the structure of world industries changed in the 1970s, the expansion of the oil market has continually grown to have now become the world's biggest commodity market. This market has developed from a primarily physical product activity into a sophisticated financial market. Over the last decade, crude oil markets have matured greatly, and their range and depth could allow a wide range of participants, such as crude oil producers, crude oil physical traders, and refining and oil companies, to hedge oil price risk. Risk in the crude oil commodity market is likely to occur due to unexpected jumps in global oil demand, a decrease in the capacity of crude oil production and refinery capacity, petroleum reserve policy, OPEC spare capacity and policy, major regional and global economic crises risk (including sovereign debt risk, counter-party risk, liquidity risk, and solvency risk), and geopolitical risks.
A futures contract is an agreement between two parties to buy and sell a given amount of a commodity at an agreed upon certain date in the future, at an agreed upon price, and at a given location. Furthermore, a futures contract is the instrument primarily designed to minimize one's exposure to unwanted risk. Futures traders are traditionally placed in one of two groups, namely hedgers and speculators. Hedgers typically include producers and consumers of a commodity, or the owners of an asset, who have an interest in the underlying asset, and are attempting to offset exposure to price fluctuations in some opposite position in another market. Unlike hedgers, speculators do not intend to minimize risk but rather to make a profit from the inherently risky nature of the commodity market by predicting market movements. Hedgers want to minimize risk, regardless of what they are investing in, while speculators want to increase their risk and thereby maximize profits.
Conceptually, hedging through trading futures contracts is a procedure used to restrain or reduce the risk of unfavorable price changes because cash and futures prices for the same commodity tend to move together. Therefore, changes in the value of a cash position are offset by changes in the value of an opposite futures position. In addition, futures contracts are favored as a hedging tool because of their liquidity, speed and lower transaction costs.
Among the industries and firms that are more likely to use a hedging strategy is the oil and gas industry. Firms will hedge only if they expect that an unfavorable event will arise. Knill et al. (2006) suggested that if an oil and gas company uses futures contracts to hedge risk, they hedge only the downside risk. When an industry perspective is good (bad), it will scale down (up) on the futures usage, thereby pushing futures prices higher (lower). Hedging by the crude oil producers normally involves selling the commodity futures because producers or refiners use futures contracts to lock the futures selling prices or a price floor. Thus, they tend to take short positions in futures. At the same time, energy traders, investors or fuel oil users focusing to lock in a futures purchase price or price ceiling tend to long positions in futures. Daniel (2001) shows that hedging strategies can substantially reduce oil price volatility without significantly reducing returns, and with the added benefit of greater predictability and certainty.
Theoretically, issues in hedging involve the determination of the optimal hedge ratio (OHR). One of the most widely-used hedging strategies is based on the minimization of the variance of the portfolio, the so-called minimum-variance hedge ratio (see Chen et al. (2003) for a review of the futures hedge ratio, and Lien and Tse (2002) for some recent developments in futures hedging). With the minimum-variance criterion, risk management requires determination of the OHR (the optimal amount of futures bought or sold expressed as a proportion of the cash position). In order to estimate such a ratio, early research simply used the slope of the classical linear regression model of cash on the futures price, which assumed a time-invariant hedge ratio (see, for example, Ederington, 1979, Figlewski, 1985, Myers and Thompson, 1989).
However, it is now widely agreed that financial asset returns volatility, covariances and correlations are time-varying with persistent dynamics, and rely on techniques such as conditional volatility (CV) and stochastic volatility (SV) models. Baillie and Myers (1991) claim that, if the joint distribution of cash prices and futures prices changes over time, estimating a constant hedge ratio may not be appropriate. In this paper, alternative multivariate conditional volatility models are used to investigate the time-varying optimal hedge ratio and optimal portfolio weights, and the performance of these hedge ratios is compared in terms of risk reduction.
The widely-used ARCH and GARCH models appear to be ideal for estimating time-varying OHRs, and a number of applications have concluded that such ratios seem to display considerable variability over time (see, for example, Cecchetti et al., 1988, Baillie and Myers, 1991, Myers, 1991, Kroner and Sultan, 1993). Typically, the hedging model is constructed for a decision maker who allocates wealth between a risk-free asset and two risky assets, namely the physical commodity and the corresponding futures. OHR is defined as , where st and ft are spot price and futures price, respectively, and Ft − 1 is the information set. Therefore, OHRt can be calculated given the knowledge of the time-dependent covariance matrix for cash and futures prices, which can be estimated using multivariate GARCH models.
In the literature, research has been conducted on the volatility of crude spot, forward and futures returns. Lanza et al. (2006) applied the constant conditional correlation (CCC) model of Bollerslev (1990) and the dynamic conditional correlation (DCC) model of Engle (2002) for West Texas Intermediate (WTI) oil forward and futures returns. Manera et al. (2006) used the CCC, the vector autoregressive moving average (VARMA-GARCH) model of Ling and McAleer (2003), the VARMA-Asymmetric GARCH model of McAleer et al. (2009), and the DCC to spot and forward return in the Tapis market. Chang et al., 2009a, Chang et al., 2009b estimated multivariate conditional volatility and examined volatility spillovers for the returns on spot, forward and futures returns for Brent, WTI, Dubai and Tapis to aid risk diversification in crude oil markets.
For estimated time-varying hedge ratios using multivariate conditional volatility models, Haigh and Holt (2002) modeled the time-varying hedge ratio among crude oil (WTI), heating oil and unleaded gasoline futures contracts of crack spread in decreasing price volatility for an energy trader with the BEKK model of Engle and Kroner (1995) and linear diagonal VEC model of Bollerslev et al. (1988), and accounted for volatility spillovers. Alizadeh et al. (2004) examined appropriate futures contracts, and investigated the effectiveness of hedging marine bunker price fluctuations in Rotterdam, Singapore and Houston using different crude oil and petroleum futures contracts traded on the New York Mercantile Exchange (NYMEX) and the International Petroleum Exchange (IPE) in London, using the VECM and BEKK models. Jalali-Naini and Kazemi-Manesh (2006) examined the hedge ratios using the weekly spot prices of WTI and futures prices of crude oil contracts one month to four months on NYMEX. The results from the BEKK model showed that the OHRs are time-varying for all contracts, and higher duration contracts had higher perceived risk, a higher OHR mean, and standard deviations.
Recently, Chang et al. (2010) estimated OHR and optimal portfolio weights of the crude oil portfolio using only the VARMA-GARCH model. However, they did not focus on the optimal portfolio weights and optimal hedging strategy based on a wide range of multivariate conditional volatility models, and did not compare their results in terms of risk reduction or hedge strategies. As WTI and Brent are major benchmarks in the world of international trading and the reference crudes for the USA and North Sea, respectively, the empirical results of this paper show different optimal portfolio weights, optimal hedging strategy and their explanation to aid in risk management in crude oil markets.
The purpose of the paper is three-fold. First, we estimate alternative multivariate conditional volatility models, namely CCC, VARMA-GARCH, DCC, BEKK and diagonal BEKK for the returns on spot and futures prices for Brent and WTI markets. Second, we calculate the optimal portfolio weights and OHRs from the conditional covariance matrices for effective optimal portfolio design and hedging strategies. Finally, we investigate and compare the performance of the OHRs from the estimated multivariate conditional volatility models by applying the hedging effectiveness index.
The structure of the remainder of the paper is as follows. Section 2 discusses the multivariate GARCH models to be estimated, and the derivation of the OHR and hedging effective index. Section 3 describes the data, descriptive statistics, unit root test and cointegration test statistics. Section 4 analyzes the empirical estimates from empirical modeling. Some concluding remarks are given in Section 5.
Section snippets
Multivariate conditional volatility models
This section presents the CCC model of Bollerslev (1990), VARMA-GARCH model of Ling and McAleer (2003), DCC model of Engle (2002), BEKK model of Engle and Kroner (1995) and Diagonal BEKK. The first two models assume constant conditional correlations, while the last two models accommodate dynamic conditional correlations.
Consider the CCC multivariate GARCH model of Bollerslev (1990):where yt = (y1t,..., ymt)′, ηt = (η1t,..., ηmt)′ is a sequence of independently
Data
Daily synchronous closing prices of spot and nearby futures contract (that is, the contract for which the maturity is closest to the current date) of crude oil prices from two major crude oil markets, namely Brent and WTI, are used in the empirical analysis. The 3132 price observations from 4 November 1997 to 4 November 2009 are obtained from the DataStream database. The returns of crude oil prices i of market j at time t in a continuous compound basis are calculated as rij, t = log(Pij, t/Pij, t − 1
Empirical results
An important task is to model the conditional mean and conditional variances of the returns series. Therefore, univariate ARMA-GARCH models are estimated, with the appropriate univariate conditional volatility model given as ARMA(1,1)-GARCH(1,1). These results are available upon request. All multivariate conditional volatility models in this paper are estimated using the RATS 6.2 econometric software package.
Table 4 presents the estimates for the CCC model, with p = q = r = s = 1. The two entries
Conclusion
This paper estimated several multivariate volatility models, namely CCC, VARMA-GARCH, DCC, BEKK and diagonal BEKK, for the crude oil spot and futures returns of two major benchmark international crude oil markets, namely Brent and WTI. The estimated conditional covariance matrices from these models were used to calculate the optimal portfolio weights and optimal hedge ratios, and to indicate crude oil hedge strategies. Moreover, in order to compare the ability of variance portfolio reduction
Acknowledgments
The authors are grateful to the three reviewers for helpful comments and suggestions. For financial support, the first author wishes to thank the National Science Council, Taiwan, the second author wishes to acknowledge the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science, and the third author is most grateful to the Faculty of Economics, Maejo University, Thailand.
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