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.
Review of Quantitative Finance and Accounting – Springer Journals
Published: Oct 3, 2004
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