انحراف کوتاه مدت و نسبت پرچین متغیر در زمان: شواهدی از بازار آتی کشاورزی

This paper investigates the hedging effectiveness of time-varying hedge ratios in the agricultural commodities futures markets using four different versions of the GARCH models. The GARCH models applied are the standard bivariate GARCH, the bivariate BEKK GARCH, the bivariate GARCH-X and the bivariate BEKK GARCH-X. Futures data for corn, coffee, wheat, sugar, soybeans, live cattle and hogs are applied. Comparison of the hedging effectiveness is done for the within sample period (1980–2004), and two out-of-sample periods (2002–2004 and 2003–2004). Results indicate superior performance of the portfolios based on the GARCH-X model estimated hedge ratio during all periods.

Transfer of risk is one of the main functions of the futures markets. Risks are transferred to those willing to bear them, as hedgers reduce their risk by paying a premium to speculators. For agricultural commodities, risk may occur due to drought, near record production, an increase in demand, a decrease in international production, etc. Hedging by the agricultural producers generally involves selling the commodity futures because producers of the commodity want to lock in a price floor. Simultaneously speculators and investors looking to lock in a price ceiling are buying the contract. The commodity futures markets thus provide a means to transfer risk between persons holding the physical commodity (hedgers) and investors speculating in the market.1 This paper empirically investigates the hedging effectiveness in the agricultural commodity futures' market. Our paper is motivated by Yang and Awokuse (2003) who indicated that knowledge of how effective hedging function performs on the commodity futures market is essential to understanding these markets. This paper tries to expand the knowledge in this area by investigating and comparing the risk-reducing ability of different optimal time-varying hedge ratios for the futures of seven agricultural commodities: corn, coffee, wheat, sugar, soybeans, live cattle and hogs. An optimal hedge ratio is defined as the proportion of a cash position that should be covered with an opposite position on a futures market. Corn, coffee, wheat, sugar, and soybeans are storable commodities and live cattle and hogs are non-storable commodities.2 According to Covey and Bessler (1995) commodity futures markets with different storability characteristics may perform in different manners. Yang and Awokuse (2003) provide some proof of it by showing that hedging effectiveness is stronger for storable agricultural commodities than non-storable commodities. The traditional constant hedge ratio obtained by means of the ordinary least square (OLS) has been discarded as being inappropriate, because it ignores the heteroskedasticity often encountered in price series. Baillie and Myers (1991) further claim that if the joint distribution of cash price and futures prices is changing over time, estimating a constant hedge ratio may not be appropriate. In this paper time-varying hedge ratios are estimated and employed. They are estimated using four different types of the generalized autoregressive conditional heteroskedasticity (GARCH) models: the standard bivariate GARCH, bivariate BEKK GARCH, the bivariate GARCH-X, and the bivariate BEKK GARCH-X.3Haigh and Holt (2002), Bera, Garcia, and Roh (1997), Sephton (1993), Baillie and Myers (1991) and Myers (1991) using agricultural commodities futures show that GARCH hedge ratios are superior to the ones based on the traditional regressions. The GARCH-X and the BEKK GARCH-X models applied in this paper are different from the other two GARCH models because they take into consideration the effects of the short-run deviations from the long-run relationship between the cash and futures prices on the conditional variance and covariance (second conditional moments of the bivariate distribution) of log difference of the cash and the futures prices. The BEKK GARCH and the BEKK GARCH-X models are also unique because they allow time variation in the conditional correlations as well as the conditional variance. To our knowledge, no other paper applies the GARCH-X and/or the BEKK GARCH-X in the estimation and comparison of time-varying hedge ratios for agricultural futures market. All GARCH methods applied take into consideration the effects of the short-run deviations on the first moment (mean) of the bivariate distributions of the variables. If the four time-varying hedge ratios are different, then more than one interesting question arises: first, which method is more effective? And second, does taking into consideration the effects of the short-run deviations make the hedge ratio more effective? A further inquiry and contribution of this paper is comparing the strength of the hedging effectiveness for storable commodities against the non-storable commodities, especially talking into consideration the short-run deviations. The short-run deviations are represented by the error correction term from a cointegration relationship between the commodities cash and the futures prices.4 Long-run relationship between the commodities cash price and the futures price is determined by means of the Engle and Granger (1987) cointegration test. Yang, Bessler, and Leatham (2001) claim that prevalent cointegration between cash and futures prices on commodity markets suggest that cointegration should be incorporated into commodity hedging decisions.5 Even when the GARCH effect is considered, allowance for the existence of cointegration is argued to be an indispensable component when comparing ex-post performance of various hedging strategies. To check for the effects of cointegration on hedging effectiveness in agricultural futures markets via the GARCH-X and BEKK-X is one of the main objectives of the paper. The risk-reducing effectiveness of the time-varying hedge ratios is investigated by checking performance of the ratios in the within sample period (1980–2004) and two out-of-sample periods (2002–2004 and 2003–2004). The hedging effectiveness is estimated and compared by checking the variance of the portfolios created using these hedge ratios. The lower the variance of the portfolio, the higher is the hedging effectiveness of the hedge ratio. The structure of the paper is as follows: Section 2 describes and discusses the optimal hedge ratio and the four GARCH models: the data and its basic statistics are described in Section 3: the empirical results are presented in Section 4: and Section 5 is the conclusion.

One of the main functions of the futures market is to provide a hedging (risk transfer) mechanism. It is also a well-documented claim in the futures market literature that the optimal hedge ratio should be time-varying and not constant. An optimal hedge ratio is defined as the proportion of a cash position that should be covered with an opposite position on a futures market. Lately, different versions of the GARCH models have been applied to estimate time-varying hedge ratios for different futures markets. This paper investigated the hedging effectiveness of GARCH estimated time-varying hedge ratios in seven agricultural commodities futures: corn, wheat, coffee, sugar,soybeans, live cattle and hogs. Live cattle and hogs are non-storable agricultural commodities, the others are storable. In this way this paper also provided a comparison between the hedging effectiveness of storable and non-storable futures commodities. Our paper was motivated by Yang and Awokuse (2003) who indicated that knowledge of how effective hedging function performs on commodity futures market is essential to understanding these markets. The time-varying hedge ratios were estimated by means of four different types of GARCH models: the standard bivariate GARCH, bivariate BEKK, bivariate GARCH-X, and bivariate BEKK-X. The GARCHX and the BEKK-X are unique among the GARCH models in taking into consideration the effects of the short-run deviations from a long-run relationship between the cash and the futures price indices on the hedge ratio. The long-run relationship between the price indices is estimated by the Engle–Granger cointegration method. One of the main objectives of the paper is to test the effects of the cointegrationbetween the cash and the futures prices on the hedging effectiveness in the agricultural futures markets. The hedging effectiveness is estimated and compared by checking the variance of the portfolios created using these hedge ratios. The lower the variance of the portfolio, the higher is the hedging effectiveness of the hedge ratio. The empirical tests were conducted by applying daily data. The effectiveness of the hedge ratio was investigated by comparing the within sample period (August 1980–July 2004) and out-of-sample period performance of the different hedge ratios for two periods, August 2002–July 2004 (two years) and August 2003–July 2004 (one year). The two different lengths of out-of-sample periods were then applied to investigate the effect of changing the length on the hedging effectiveness of the hedge ratios. Results show that during the within sample period and the two out-of-sample periods, the GARCH-X-oriented hedge ratio overall performs better than the other GARCH methods and the unhedged portfolio. This result backs the claim by Yang et al. (2001) and others regarding the importance of the use of cointegration between cash and futures prices in hedging ratios. Among the GARCH models applied, the standard BEKK-oriented hedge ratios provided the worst performance. Also, changing the length of the out-of-sample period does not change the hedging effectiveness of the GARCH-oriented hedge ratios. This is especially true in the case of standard GARCH and the GARCH-X method. Results do not show much difference in the hedging effectiveness of storable and non-storable commodities. This contradicts of what was reported by Yang and Awokuse (2003). As stated by Bera et al. (1997) further study is needed to assess the costs of GARCH models specification and implementation relative to the gains in variance reduction. The implementation of the GARCH models can require frequent and costly position changes in the futures market. In addition, the estimation and continual updating of GARCHmodels for practical use can be time consuming and costly. Future studies of the hedging performance of these models in framework which explicitly incorporates these costswill provide amuch better understandingof the usefulness of these models for managing price risk.