Both authors from the Graduate School of Business, Columbia University. A previous version of this paper was presented at the American Finance Association meetings in New Orleans, December 1986. All remaining errors are our own.
On the Optimal Hedge of a Nontraded Cash Position
Article first published online: 30 APR 2012
1988 The American Finance Association
The Journal of Finance
Volume 43, Issue 1, pages 143–153, March 1988
How to Cite
ADLER, M. and DETEMPLE, J. B. (1988), On the Optimal Hedge of a Nontraded Cash Position. The Journal of Finance, 43: 143–153. doi: 10.1111/j.1540-6261.1988.tb02594.x
- Issue published online: 30 APR 2012
- Article first published online: 30 APR 2012
In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the “cash-commodity-price” space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the “wealth-commodity-price” space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean-variance term and (b) a minimum-variance component that is a classic feature of models with nontraded assets. Since the first-best (nonmyopic) optimum is attained, however, the deviation from a mean-variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first-best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first-best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set.