ost agricultural production is characterized by a lag between the time the produc-M tion decision is made and the time the output actually reaches the market. Hence, the actual cash price that will be received is unknown when the production decision is made. For many commodities, futures markets exist in which a producer may hedge all or part of the production to reduce price risk. Numerous economic studies have determined optimal production and futures market positions under these circumstances using various criteria or assumed objectives of the firm.
If it is assumed that the producer minimizes the variance of his income, an optimal hedging ratio can be prescribed. This concept was developed by Ederington (1979) who drew on the original works of Johnson (1960) and Stein (1961). Empirical estimates of this ratio of the covariance between spot and futures prices and the variance of futures price are frequently and easily obtained by regressing spot on futures price using OLS.
Hence, the estimate of the minimum variance hedge ratio is often referred to as the p coefficient. Discussion about the empirical estimation of is abundant in both the economics and finance literature.
Rather than simply regressing spot on futures price to obtain an estimate of /3, Working (1953) proposed, for a number of reasons which will be discussed later in the article, that first differences in spot prices should be regressed on first differences in futures prices. Although Peck (1975) basically agreed with Working, she suggested that / 3 should be estimated using data based on unanticipated changes in spot and futures prices. Hence, the difference between spot price and producers' forecasts of spot price should be regressed on the difference between futures price and its forecast to determine an estimate of p. Grant and Eaker (1984) and Overdahl and Starleaf (1986) are among those who have used this approach as well.
Regardless of how fl is estimated, it will not in general be the optimal hedge ratio when it is assumed that the producer maximizes the expected utility of profit. Heifner (1972) shows that p is the optimal hedge ratio if a linear mean-variance expected utility