The cost of hedging and the optimal hedge ratio

Abstract

Hedging benefits offered by the futures market come at a cost. This article develops a concept of hedging costs, shows how it impacts the hedging decision, and derives an optimal hedge ratio in the context of the cost concept. The hedging cost of using futures is comprised of two components. The first component represents the fixed costs of setting up and managing a hedging program. The second component is the result of spot/futures arbitrage and the fact that the futures contract is an imperfect substitute for a commercial transaction.' It is shown that arbitrageurs drive the expected futures return equal to the spot risk premium. Thus as hedgers take a short futures position, expected return is reduced by the amount of futures shorted times the spot risk premium.Hedgers can seldom create a perfect hedge due to mismatches between spot and futures delivery dates and contract specifications. Thus, the hedger faces the situation of paying full cost (i.e., reducing expected return by the amount of the fixed costs plus the spot risk premium) while receiving less than the full benefits (i.e., the elimination of all risk). The hedger, therefore, is required to make a risk/return decision since, as will be demonstrated, the marginal cost of hedging The authors would like to thank Dean Paxson, Bruce Benet, and participants at the Front Range Workshop held at the University of Colorado and the 1992 Financial Management Association meeting for helpful comments. Suggestions made by an anonymous referee for this journal led to significant revisions. All remaining errors are the responsibility of the authors. 'Certain costs are included here in the fixed component. Also, some variable costs are ignored.For example, transaction costs may be influenced by the size of the hedge, price, and the place at which the hedge is lifted. It is assumed that the simple equation used in this article adequately captures the salient costs of future hedging.

Optimal hedging under nonlinear borrowing cost, progressive tax rates, and liquidity constraints

“…This approach usually finds optimal hedge ratios close to one (Ederington 1979;Howard & D'Antonio 1994;Kolb & Okunev 1993;Mathews & Holthausen 1991;Peck 1975). Others (Grant 1985(Grant , 1989Miller & Kahl 1987;Lapan & Moschini 1994) added basis and yield risk and found lower, but still high, optimal hedge ratios.…”

Optimum Hurricane Futures Hedge in a Warming Environment: A Risk–Return Jump‐Diffusion Approach

“…Howard and D'Antonio () adopt this linear cost structure when studying optimum futures hedge in a one‐period framework.…”

Cost-Effective Hedges and Accounting Standards

“…As is shown in Howard and D'Antonio (1994), the cost-effective hedge ratio (b CE ) is a function of the risk minimum hedge ratio (b RM from Ederington 1979) as follows: 9…”

“…Both of these assumptions are close to the situation that many actual hedgers face and so using them for demonstration purposes seems reasonable. 17 SeeHoward and D'Antonio (1994) for the derivation of this equation. The value mc is the slope of the curve inFigure 2evaluated at the given hedge ratio.…”