A portfolio approach to optimal hedging for a commercial cattle feedlot

Abstract

he cattle feeding industry in the United States has been characterized in recent T years by wide swings in the prices of the major inputs-feeder cattle and feed grains-and the final product-fed cattle. Hedging with futures contracts is one technique that cattle feeders can use to stabilize prices and incomes, and it has become increasingly important as a risk management tool during the past decade.A number of strategies for placing hedges on fed cattle (Farris 1972; Purcell, Hague and Holland 1972;Menzie and Archer 1972;Leuthold 1975;McCoy and Price 1975;Erickson 1978) and on combinations of feeder cattle, feed grain, and fed cattle (Shafer, Griffin and Johnston 1978;Leuthold and Mokler 1979;Caldwell, Copeland and Hawkins 1982) have been published. These studies used fully-hedged and unhedged positions and did not permit the use of partial hedges. As a result, they were unable to determine how much of the cash position should be hedged and how many futures contracts would be required to achieve some desired level of risk reduction. This study treats the optimal hedging problem as a special case of the general portfolio problem. Previous studies using this approach have been unable to deal with multiple simultaneous short and long positions. They also have failed to produce optimal hedging solutions expressed in multiples of full contracts, rather than fractional contracts or percentages of the corresponding cash market positions. This article develops a general optimal hedging technique which eliminates these shortcomings, and then applies it over an extended period of time to a hypothetical cattle feeding problem. In an evaluation of some common assumptions about proper