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he single period model, because of its simplicity and often plausible representa-T tion, is used to describe a wide range of economic and financial decision making. Those who advocate such an approach recognize that the world is truly multiperiod and approximately infinite, but find that a single period model is adequate under certain conditions. Either decisions in one period have little or no effect on future periods or the interperiod dependencies are too complex to be captured in the modeling process. These two reasons are the ones most often cited, explicitly or implicitly, as justification for using a single period model. Leatham (1988), Black (1989), Gagnon et al. (1989), Gardner (1989), Lein (1989), McCabe and Solberg (1989), and Thomas (1989).However, hedgers frequently face a multiperiod situation in which a single period approach simply is not adequate. For example, consider an issuer of commercial paper who is paying off old and offering new commercial paper on a weekly basis. If the issuer finds it attractive to hedge interest costs on next week's issue, then all future weekly issues should be hedged, up to and including the final issue needed to fund the assets supported by the issue . This is because short term interest rates tend to follow a random walk and so higher (lower) interest cost next week will lead to higher (lower) interest costs in all the following weeks. Consequently, the hedge position taken today should take into consideration next week's issue as well as all future weekly issues.Not all series being hedged are autocorrelated. Take, for example, the management of a stock portfolio with negligible cash inflows and outflows and no reinvestment. The series being hedged is the return on the stock portfolio which portrays little or no autocorrelation. Thus, a single period approach is appropriate. Of course, this does not rule out the possibility that the hedger will continuously hold Do not quote without permission. 'See Baesel and Grant (1982) for an example of a multiperiod futures trading model.

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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.

The primary purpose of this study is to measure the hedging performance of Treasury Bill Futures on a risk‐return basis. A theoretical model is presented and hedging effectiveness is tested using T‐Bill cash and futures data. Successful hedging depends critically upon the ability to determine the optimal hedge ratio. The results also indicate that the traditional one‐to‐one hedge outperforms the more sophisticated hedge ratio models; however, even here the risk‐return benefits of hedging are minimal.