Estimating the optimal hedge ratio of energy commodities

Abstract

Introduction: Price fluctuation is one of the most important features of the energy market that leads to price risk and economic instability. In the financial market, one of the best uses of derivative securities is in hedging. The most common way of hedging in the investment is through appropriate derivative instruments. They include options, swaps, futures and forward contracts. Even though there are many criteria used in the derivation of the optimal hedge ratio, the minimum-variance (MV) hedge ratio considered by Johnson (1960) has been one of the most popular choices. The basic concept of the minimum variance hedging risk lies in the combination of investments in the spot and future markets in order to reduce value fluctuations. Thus, the optimal number of futures contracts that a person must hold to hedge against the risk of price fluctuation in the underlying assets can be obtained by calculating the optimal ratio of hedging risk. The literature shows that researchers mainly use future contracts to minimize the risk of price fluctuation in the spot market. Accordingly, in these studies, various econometric methods have been used to calculate the optimal hedging risk ratio. Also, in order to introduce the best hedging risk model, the performances of different models have been compared. The evaluation of hedging performance is based on the percentage reduction in spot variance compared to portfolio variance. Then, the purpose of this study is to choose an optimal model with the highest degree of hedging risk for the selected commodity. Methodology: Several techniques have been proposed in the literature to estimate the hedge ratio with index futures contracts.  Many practitioners and academicians have sought to solve the problem of how to calculate the optimal hedge ratio accurately. To achieve the goal, we compare the estimates of the hedge ratio from the ordinary least squares methods (OLS), autoregressive model (VAR/VECM), autoregressive conditional heteroscedasticity (ARCH/ GARCH) and copula. Also, to determine the changes in the optimal hedging risk ratio, we use the weekly time series of spot and future contract prices for crude oil and natural gas during the five-year period of 2013-2018. In the next step, the rolling window regression technique will be used to compare the performances of the studied models and select an efficient hedging risk model. The results of the weights for future by each of the four above-mentioned models will be used for hedging the spot prices of the two examined commodities. The obtained hedge ratios are applied on the real data in the following 20 weeks. Thus, the ability to reduce risk in every method is measured and compared during the specified period. Results and Discussion: All the models are able to offer a significate reduction in the portfolio. The conventional approach to estimating the MV hedge ratio involves the regression of the changes in spot prices on the changes in future prices using the OLS technique. As we found, the minimum variance hedge ratio by the OLS method was 62% for crude oil and 37% for natural gas. However, for the OLS technique to be valid and efficient, the assumptions associated with the OLS regression must be satisfied. Thus, we use an autoregressive model (VAR/VECM). The optimal hedging risk ratio obtained from the VECM model is 98% for crude oil and 86% for natural gas. However, the OLS and VAR methods only capture the influence of two risk factors on stock returns in the mean on average but are not sufficient to capture the dependence structure in higher moments or tail dependence. The volatility clustering phenomenon and the existence of ARCH effects demonstrate that hedge funds volatility varies over time. Then, we use the conditional autoregressive model (GARCH). Furthermore, we utilize the copula method to capture the general dependence structure between the futures and spot prices. The copula method has been used for multivariate statistical modelling owing to its edibility and convenience to describe its ability to capture the nonlinear relationship of random variables. The copula approach allows us to model the marginal distributions of individual random variables and their dependence structure separately. Our finding show copula serves normally to hedge crude oil and natural gas at the rate of 98% and 93% respectively. These rates are the models for crude oil and natural gas copula at 98% and 94% respectively. In this paper, the efficiency of different models of the rolling window regression technique are compared. This section is the core of the research. The results of the effectiveness of the optimal hedging rates of the crude oil and natural gas market show that copula functions in both markets have been in better conditions than the other models. Thus, the result of the research indicates the high efficiency of the copula functions approach to calculate hedging risk rates. Conclusion: The results show that modeling the relationship between the current and future prices in the form of copula functions is more efficient.