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Generalising Interest Rate Duration with Directional Derivatives: Direction X and Applications

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  • Roger J. Bowden

    (School of Management Studies, University of Waikato, Private Bag 3105, Hamilton, New Zealand)

Abstract

Conventional (or Fisher-Weil) duration is an ordinary derivative that measures the response of portfolio value to marginal parallel shifts in the term structure, while other proposed measures are generally specific to particular interest rate processes. In this paper, we show that portfolio responses to arbitrary shifts in the term structure may be handled by the use of Frèchet or directional derivatives, presenting a simple algorithm for the directional derivative of a fixed interest portfolio, viewed as a set of cash flows. For a given portfolio, one can locate the most sensitive areas along the term structure by computing a function or profile ("Direction X") that gives the term structure movement to which the portfolio is most exposed. Immunisation techniques can be based on choosing ancillary assets that ensure that the portfolio directional derivative is zero, or as close to zero as possible; this generalises approaches based on factor models of the term structure. The analysis is applied to both continuous and discrete time.

Suggested Citation

  • Roger J. Bowden, 1997. "Generalising Interest Rate Duration with Directional Derivatives: Direction X and Applications," Management Science, INFORMS, vol. 43(5), pages 586-595, May.
    • Handle: RePEc:inm:ormnsc:v:43:y:1997:i:5:p:586-595
    DOI: 10.1287/mnsc.43.5.586
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    Cited by:

    1. Montagut, Esperanza H., 2004. "Hedging bond portfolios versus infinitely many ranked factors of risk," DEE - Working Papers. Business Economics. WB wb043312, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    2. Balbas, Alejandro & Ibanez, Alfredo, 1998. "When can you immunize a bond portfolio?," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1571-1595, December.
    3. Balbas, Alejandro & Ibanez, Alfredo & Lopez, Susana, 2002. "Dispersion measures as immunization risk measures," Journal of Banking & Finance, Elsevier, vol. 26(6), pages 1229-1244, June.
    4. Leo Krippner, 2005. "Attributing Returns and Optimising United States Swaps Portfolios Using an Intertemporally-Consistent and Arbitrage-Free Model of the Yield Curve," Working Papers in Economics 05/03, University of Waikato.
    5. Posch, Peter N & Bowden, Roger J & Kalteier, Eva-Maria, 2014. "The financial economics of sovereign asset value: functional perspectives and market outcomes," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100439, Verein für Socialpolitik / German Economic Association.
    6. ManMohan S. Sodhi, 2005. "LP Modeling for Asset-Liability Management: A Survey of Choices and Simplifications," Operations Research, INFORMS, vol. 53(2), pages 181-196, April.

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