Optimal Hedging Under Price, Quantity and Exchange Rate Uncertainty

Abstract

Abstract: This paper derives an optimal hedging strategy for a primary producer under price, quantity and exchange rate uncertainty. In this model, it is assumed that the producer is a mean‐variance maximizer with an exponential utility function. The derived optimal hedge ratio for the commodity is proportional to the coefficient of the commodity futures prices bias in a linear regression where revenue uncertainty is the dependent variable. This ratio differs from the result that would have been obtained under price‐quantity uncertainty when revenues are significantly correlated with the exchange rate variability, thereby suggesting that the foreign exchange risk is relevant only when the commodity exposure is unhedged.The model is empirically tested using Côte‐d'Ivoire, Ghana and Nigeria as cocoa producers and the US Dollar and the French Franc as currencies of numeraire to hedge UK Pound revenues. The resulting cocoa hedge ratios range from 78 to 57 percent. For Ghana and the Côte‐d'Ivoire, there is little correlation between revenue and exchange rate variability. Therefore, the cocoa ratio is not significantly affected by the introduction of this additional source of uncertainty and the currency ratio in the joint hedge is trivial for both the dollar and the franc. Nigeria's revenues are correlated to the dollar and the cocoa ratio is de facto lowered by the currency effect in a joint cocoa‐dollar hedge.Résumé: Cet article presente un modele de couverture optimale a terme contre les risques conjoints de prix, de quantite et de change pour un producteur de matieres premieres dont l'objectif est de maximiser ses revenus. Le taux de couverture optimal est proportionnel au coeficent obtenu dans une regression simple des revenus ou le biais des prix a terme est la variable independente. Ce taux ne direre de celui obtenu dans un modele d'incertitude prix‐quantite que lorsque l'incertitude de quantite est correlee a celle de change. Ceci suggere a contrario qu'une couverture optimale du risque des prix de matieres premieres permet en meme temps de parer au risque de change.