Time-varying Optimal Hedge Ratio for Brent Oil Market

This paper examines the optimal hedging ratio (OHR) for the Brent Crude Oil Futures using daily data over the period 1990/17/8-2014/11/3. To estimate OHR, we employ multivariate BEKK MV-GARCH model. At last, the efficiency of this approach are compared with the constant OHR captured from OLS through Edrington's index.


INTRODUCTION
Price risk management, using hedging tools like futures and options and their effectiveness, is an active area of research. Hedging decisions based on futures contracts have to deal with finding optimal hedge ratio and hedging effectiveness. Role of hedging using multiple risky assets and using futures market for minimizing the risk of spot market fluctuation has been extensively researched.
The traditional approaches to the use of futures for hedging purposes has been to either adopt a naive one-to-one hedging ratio to determine the optimal hedge ratio using simple regression techniques, but to assumet hat this ratio will remain constant over the relevant time horizon. However, empirical financial markets research over the past two decades has supported the view that asset returns volatility is time-varying and, in particular, exhibits 'clustering', such that large (small) returns follow large (small)returns of random sign (Mandelbrot, 1963;Fama, 1965) and whereby the standard way of specifying volatility is through the generalized autoregressive conditional heteroscedasticity (GARCH) model (Engle, 1982;Bollerslev, 1986).1 Moreover, accurate estimation of the volatility process plays an essential role in many aspects of financial markets, for example,variation in market returns and other economy-wide riskfactors are a main feature of asset and portfolio managementand play a key role in derivatives pricing models. As suchaccurate measures and forecasts of volatility are crucial for theimplementation and evaluation of asset and derivative pricingmodels in addition to trading and hedging strategies. Therefore,knowledge of the volatility process should allow market agentsto improve their estimates of optimal cash-futures hedge ratiosover the implementation of strategies based upon constanthedging ratios.2 Moreover, Park and Switzer (1995) argue thatif the joint distribution of cash and futures prices is changingover time then a constant hedge ratio may not be appropriate,while Baillie and Myers (1991) likewise suggest that hedgeratios will vary over time as the conditional distributionbetween cash and futures price changes.

METHODOLOGY AND EMPIRICAL RESULTS
In this section we use the GARCH models to calculatethe optimal hedging ratio for Brent Oil Market. The financial variables used in the model are spot and futures price of Brent Oil.The data series are obtained from Energy Information Agency(EIA). The data are daily from 1990/17/8-2014/11/3.

OLS Method
In this method changes in spot price is regressed on the changes in futures price. The Minimum-Variance Hedge Ratio has been suggested as slope coefficient of the OLS regression. It is the ratio of  Thompson, 1989) and ignores the time varying nature of hedge ratios (Cecchetti, Cumby, &Figlewski, 1988). It also does not consider the futures returns as endogenous variable and ignores the covariance between error of spot and futures returns. The advantage of this model is the ease of implementation. Time varying hedge ratio is calculated as follows:

HEDGE RATIO AND HEDGING EFFECTIVENESS
Hedging effectiveness is defined as the ratio of the variance of the unhedged position minus variance of hedge position over the variance of unhedged position.

THE RESULTS OF ESTIMATES
OLS regression (equation [1]) has been used to calculate the hedge ratio and hedging effectiveness. The slope of the regression equation gives the hedge ratio and R 2 , the hedging effectiveness.

CONCLUSION
We calculate the optimal hedge ratio through OLS and VAR-MGARCH. The OHR calculated through OLS is constant over the time but VAR-MGARCH OHR represent time variation in the conditional covariance matrix and according to transaction cost, hedger should manage the risk. According to results of estimates, OHR calculated through BEKK VAR-MGARCH is higher than the OLS and efficiency of BEKK VAR-MGARCH is more than the OLS in Brent Crude oil market.