Risk Aversion and Optimal Hedge Ratio in Commodities Futures Markets

In this paper, our main objective is to show that the determination of the optimal hedge ratio for a raw material producer, who is submitted to income risk, depends on the type of its utility function. More precisely, we maximize the expected utility of wealth for the following four utility functions : quadratic, exponential, power and expo-power. We then derive an explicit formula of the optimal hedge ratio when using the first two functions and an implicit function when the agent's preferences are modeled by power or expo-power utility functions. The results obtained are then applied to data on quantity and prices collected from the NCCB and ICCO from 1980 to 2013. The implementation with some Matlab programs provides the estimated value of the optimal hedge ratio for a Cameroonian cocoa producer around 80% for quadratic and exponential utility functions, and 87.9% for power utility and between 50% and 65% for the expo-power utility function