اثر نامتقارن اصول بر فرابورس معاملات آتی پویا : شواهد تجربی از بازار کالا

The dynamic minimum variance hedge ratios (MVHRs) have been commonly estimated using the Bivariate GARCH model that overlooks the basis effect on the time-varying variance–covariance of spot and futures returns. This paper proposes an alternative specification of the BGARCH model in which the effect is incorporated for estimating MVHRs. Empirical investigation in commodity markets suggests that the basis effect is asymmetric, i.e., the positive basis has greater impact than the negative basis on the variance and covariance structure. Both in-sample and out-of-sample comparisons of the MVHR performance reveal that the model with the asymmetric effect provides greater risk reduction than the conventional models, illustrating importance of the asymmetric effect when modeling the joint dynamics of spot and futures returns and hence estimating hedging strategies.

Minimum variance hedge ratio (MVHR), i.e., the ratio of futures contracts to a specific spot position that minimizes variance of the hedged portfolio returns, has been broadly used as a futures hedging strategy. Following Johnson, 1960 and Stein, 1961, the MVHR is calculated as the ratio of covariance between spot and futures returns to variance of futures returns. Early research utilizes regression models to estimate time-invariant MVHRs. More recently, Bivariate GARCH (BGARCH) models have been commonly adopted to estimate time-varying variance and covariance and subsequently generate dynamic MVHRs. It is often found that the dynamic MVHRs outperform those estimated from the regression models (Castelino, 1990, Baillie and Myers, 1991, Kroner and Sultan, 1993, Park and Switzer, 1995, Brooks et al., 2002 and Lien et al., 2002, among many others). However, much of this research overlooks the effect of basis (difference between spot and futures prices) on the variance-covariance structure when estimating the dynamic MVHRs. Importance of incorporating the changes in the basis into hedging decision dates back to Working, 1953a, Working, 1953b and Working, 1961). Most research focuses on the effect of basis on the level of spot and futures price movements in the models where MVHRs are estimated (Kroner and Sultan (1993), Lien, 1996), Lien and Tse, 1999 and Lien et al., 2002). The effect of basis on the variance-covariance structure is however mostly overlooked.1Ng and Pirrong, 1994, Lee, 1994 and Zhong et al., 2004 find that spot and futures prices become more volatile and less correlated as basis gets larger, suggesting that the MVHR should be altered as the basis changes. The models that ignore this effect of basis prescribe that the MVHR remain the same regardless of the changes in the basis. This “constant” MVHR may create over-hedged positions when the basis decreases and under-hedged positions when the basis increases, raising serious concerns regarding risk reduction ability of the conventional hedging models. In this paper, we propose an alternative specification of BGARCH model in which the basis effect is incorporated. We decompose basis into positive and negative bases and introduce them into the conditional variance and covariance equations of BGARCH model to investigate a potential asymmetric basis effect on the conditional variances and covariance of spot and futures returns and its consequences in dynamic hedging strategies. Examining commodity markets, the conditional variances are positively (negatively) related to the positive (negative) lagged basis, suggesting a V-shape relationship between the variance and the basis.2 In addition, the marginal effects when the basis is positive are greater than those when the basis is negative, indicating that the V-shape relationship is asymmetric.3 The asymmetric effect on the time-varying correlation between the two markets is also observed. Larger basis in the absolute term tends to reduce market co-movements more. We then calculate the MVHR based on the estimates of the conditional variance and covariance from our model and compare it with the MVHRs estimated from the BGARCH models where only symmetric effect is incorporated or the effect is totally ignored. Both in-sample and out-of-sample comparisons indicate that the model incorporating the asymmetric effect of basis into the hedging decision leads to a greater risk reduction than the conventional models. To capture the economic significance of different hedging strategies, we evaluate how much a hedger’s expected utility would increase if one strategy were used over others after taking into account transaction costs for rebalancing the hedging positions when there is benefit to do so, i.e., when the potential expected utility gains offset the transaction costs. We find that the expected utility increases significantly using the strategy from the asymmetric model over that from the symmetric model. Thus, we conclude that separating the effect of positive and negative bases on the market volatility and the correlation between the two markets not only provides better descriptions of the joint dynamic behavior of the commodity prices, but also plays an important role in determining the dynamic hedging strategies. The remainder of the paper is organized as follows. Section 2 discusses the model specifications. Section 3 discusses the data and preliminary diagnostic tests on the data. The model estimation results are provided in Section 4. The asymmetric effects of basis on the dynamic hedging strategy as well as on the risk reduction are analyzed in Section 5. Section 6 provides the conclusions of the paper.

This paper examines the asymmetric effect of basis on the time-varying variance and correlation of spot and futures returns and its consequence in dynamic futures hedging strategies in commodity markets. Incorporating the decomposed basis into the BGARCH model commonly used to estimate the dynamic MVHRs, we find that the positive basis has greater impact than the negative basis. We then compare hedging performances of the MVHRs from three distinct BGARCH model specifications: (1) incorporating the asymmetric effect of basis on the conditional variances and correlation, (2) replacing the asymmetric effect with the symmetric effects, and (3) ignoring the basis effect completely. The in-sample and out-of-sample results both reveal that incorporating the asymmetry basis effect into the hedging decision leads to a better risk reduction. After taking into account transaction costs, evidence still suggests that the dynamic hedging strategy generated from the asymmetric model outperforms the conventional strategies. Thus, we conclude that separating the effect of positive and negative bases on the time-varying variance-covariance in spot and futures markets not only provides better descriptions of the joint dynamic behaviors of commodity prices, but also plays an important role in determining optimal hedging strategies.