Hedging Multiperiod Forward Commitments: The Case of Period-by-Period Quantity Uncertainty

Hedging Multiperiod Forward Commitments: The Case of Period-by-Period Quantity Uncertainty This article considers the hedging problem of a producer with along-term forward commitment to deliver a commodity at multiple futurepoints in time. The aggregate quantity to be delivered over time is knownwith certainty; however, the period-by-period quantity is determined bythe customer and is unknown to the producer. A minimum-variancemultiperiod futures position that considers both price uncertainty andperiod-by-period quantity uncertainty is derived. The following resultsare obtained: The individual effects of price uncertainty and quantityuncertainty on the multiperiod minimum-variance are separable. In thetwo-period case, if the spot price is expected to decrease over time, therisk-minimizing hedge considering both price and quantity uncertaintiesis greater than that which considers price uncertainty only. If the spotprice is expected to increase over time, then the hedger would beover-hedged if only price uncertainty were considered. Convenience yieldpromotes a larger risk-minimizing futures position, whereas storage costsand financial costs reduce the size of the risk-minimizing futuresposition. In the multiperiod case, if forward prices are unbiasedestimators of future spot prices, or if spot prices are expected todecrease over time, then quantity uncertainty increases the size of therisk-minimizing hedge. If spot prices are expected to increase, then theeffect of period-by-period quantity uncertainty isindeterminate. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Review of Quantitative Finance and Accounting Springer Journals

Hedging Multiperiod Forward Commitments: The Case of Period-by-Period Quantity Uncertainty

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Finance; Corporate Finance; Accounting/Auditing; Econometrics; Operation Research/Decision Theory
ISSN
0924-865X
eISSN
1573-7179
D.O.I.
10.1023/A:1011279110196
Publisher site
See Article on Publisher Site

Abstract

This article considers the hedging problem of a producer with along-term forward commitment to deliver a commodity at multiple futurepoints in time. The aggregate quantity to be delivered over time is knownwith certainty; however, the period-by-period quantity is determined bythe customer and is unknown to the producer. A minimum-variancemultiperiod futures position that considers both price uncertainty andperiod-by-period quantity uncertainty is derived. The following resultsare obtained: The individual effects of price uncertainty and quantityuncertainty on the multiperiod minimum-variance are separable. In thetwo-period case, if the spot price is expected to decrease over time, therisk-minimizing hedge considering both price and quantity uncertaintiesis greater than that which considers price uncertainty only. If the spotprice is expected to increase over time, then the hedger would beover-hedged if only price uncertainty were considered. Convenience yieldpromotes a larger risk-minimizing futures position, whereas storage costsand financial costs reduce the size of the risk-minimizing futuresposition. In the multiperiod case, if forward prices are unbiasedestimators of future spot prices, or if spot prices are expected todecrease over time, then quantity uncertainty increases the size of therisk-minimizing hedge. If spot prices are expected to increase, then theeffect of period-by-period quantity uncertainty isindeterminate.

Journal

Review of Quantitative Finance and AccountingSpringer Journals

Published: Oct 3, 2004

References

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