OPTIMAL FUTURES HEDGE WITH STOCHASTIC BASIS : THE CASE OF OIL FUTURES

Abstract

The fluctuation of basis or basis risk is due to the fact that the spot and futures market are not fully integrated, as one may expect. A large number of academic studies have supported that the information flow may hit the spot and the futures markets differently [e.g. Chan (1992)]. As a result, the spot-futures price difference or the basis may vary over the time. As shown in Brennan and Schwartz(1990) the basis can be extremely volatile over short periods of time. In addition, the non-stochastic assumption about basis behavior may considerably weaken the hedging performance. Therefore, in this paper, two '2-factor' stochastic basis hedging models and a simple '3-factor' model are tested. The fluctuation of basis or the basis risk is assumed to be caused by the stochastic movement of underlying risk factors, the instantaneous rate of the cost of carry, and the convenience yield. Both factors are assumed to follow a mean-reverting Ornstein-Unlenbeck process. The oil future price is assumed to depend only on the spot price of oil, S, the risk factors, and time to maturity T-t. By using conventional minimum variance hedge ratios as benchmark, an out-of-sample empirical test instead of an in-the-sample test is conducted to test the hedging performance of the stochastic hedge ratios because the in-the-sample test has to assume perfect foresight in determining the optimum hedge ratios. The result of this test has confirmed that the stochastic basis hedge ratios are generally more stable than the conventional hedge ratios, which are often over- or underestimated significantly relative to the corresponding stochastic basis hedge ratio. Also, as expected, by incorporating the stochastic basis behavior, the stochastic basis hedge models outperform the conventional in most of the cases. The stochastic models usually show a better performance when the market undergoes a dramatic movement. This means that by using the stochastic basis model, a large company can achieve a saving of millions of dollars due to the improvement of hedging effectiveness. The main reason for stochastic basis hedge ratios being able outperform the conventional hedge ratios is that the conventional hedge ratios fail to reflect the mean- reverting nature of the basis and thus tend to "overshoot” compared with the stochastic basis hedge ratios. On the other hand, the stochastic basis hedge ratios, incorporating the basis' mean-reverting movement, anticipate the basis' eventual bounce-back to the long term mean, thus leads to a better performance.