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The Minimum Variance Hedge Ratio Under Stochastic Interest Rates

  • Abraham Lioui

    ()

    (Department of Economics, Bar-Ilan University, 52900 Ramat Gan, Israel)

  • Patrice Poncet

    ()

    (University of Paris I---Sorbonne, 17 rue de la Sorbonne, 75005 Paris, France, and ESSEC, Département Finance, Avenue Bernard Hirsch B.P.105, 95021 Cergy-Pontoise Cedex, France)

In an environment where interest rates are stochastic, we examine the case of a "pure" hedger endowed with a fixed position in a long term bond. In contrast to conventional wisdom according to which the difference between hedging through forward contracts and futures is immaterial, it turns out that the minimum variance hedge ratio using forwards comprises two terms instead of one only when using futures. The magnitude of the difference between the two hedge ratios may be important under some plausible assumptions. This result is due to the presence of additional interest rate risk that bears on the profit-and-loss statement associated with the forward position. This sheds some additional light on the respective features of forward and futures contracts written on interest rate-sensitive securities.

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File URL: http://dx.doi.org/10.1287/mnsc.46.5.658.12045
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Article provided by INFORMS in its journal Management Science.

Volume (Year): 46 (2000)
Issue (Month): 5 (May)
Pages: 658-668

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Handle: RePEc:inm:ormnsc:v:46:y:2000:i:5:p:658-668
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  1. Adler, Michael & Detemple, Jerome B, 1988. " On the Optimal Hedge of a Nontraded Cash Position," Journal of Finance, American Finance Association, vol. 43(1), pages 143-53, March.
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  7. Poncet, Patrice & Portait, Roland, 1993. "Investment and hedging under a stochastic yield curve : A two-state-variable, multi-factor model," European Economic Review, Elsevier, vol. 37(5), pages 1127-1147, June.
  8. Benninga, Simon & Protopapadakis, Aris, 1994. "Forward and Futures Prices with Markovian Interest-Rate Processes," The Journal of Business, University of Chicago Press, vol. 67(3), pages 401-21, July.
  9. Stephen Figlewski & Yoram Landskroner & William L. Silber, 1991. "Tailing the hedge: Why and how," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(2), pages 201-212, 04.
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  13. Richard, Scott F. & Sundaresan, M., 1981. "A continuous time equilibrium model of forward prices and futures prices in a multigood economy," Journal of Financial Economics, Elsevier, vol. 9(4), pages 347-371, December.
  14. Bjorn Flesaker, 1993. "Arbitrage free pricing of interest rate futures and forward contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 13(1), pages 77-91, 02.
  15. Lioui, Abraham & Poncet, Patrice, 1996. "Optimal hedging in a dynamic futures market with a nonnegativity constraint on wealth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1101-1113.
  16. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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