Optimal Hedging under Price and Quantity Uncertainty: The Case of a Cocoa Producer
构建了考虑产量和价格双重不确定性的最优对冲模型，以加纳、尼日利亚等四个主要可可生产国为例，证明最优对冲比率应小于1，为发展中国家利用期货市场管理风险提供参考。
After devising expectational measures of production and price uncertainty, this paper presents a model that derives an optimal hedging strategy for a producing country that is subject to variability in both the price and the production of its output. The analysis is then used to derive the optimal hedging for representative cocoa producers of Ghana, Nigeria, Ivory Coast, and Brazil, four countries which account for close to 80 percent of world production. While the traditional definition of hedging recommends a hedge ratio of one, this paper shows that the ratio of optimal hedge to expected output should be below unity. To arrive at this result, individual preferences are represented by a logarithmic utility function (and also by a quadratic utility function for values of the risk parameter which are inferior to 0.001). Thus, limited usage of the futures market may be superior to a full short hedge of expected output when there is production variability. This result is a warning for developing countries whose agricultural produce is subject to high price and quantity volatility and should aid them in deciding upon the use of futures trading as a hedging instrument.