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Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach

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  • Zaremba Leszek

    (Academy of Finance and Business Vistula, Institute of Finance, Warsaw, Poland)

Abstract

In the following, we offer a theoretical approach that attempts to explain (Comments 1-3) why and when the Macaulay duration concept happens to be a good approximation of a bond’s price sensitivity. We are concerned with the basic immunization problem with a single liability to be discharged at a future time q. Our idea is to divide the class K of all shifts a(t) of a term structure of interest rates s(t) into many classes and then to find a sufficient and necessary condition a given bond portfolio, dependent on a class of shifts, must satisfy to secure immunization at time q against all shifts a(t) from that class. For this purpose, we introduce the notions of dedicated duration and dedicated convexity. For each class of shifts, we show how to choose from a bond market under consideration a portfolio with maximal dedicated convexity among all immunizing portfolios. We demonstrate that the portfolio yields the maximal unanticipated rate of return and appears to be uniquely determined as a barbell strategy (portfolio) built up with 2 zero-coupon bearing bonds with maximal and respective minimal dedicated durations. Finally, an open problem addressed to researchers performing empirical studies is formulated.

Suggested Citation

  • Zaremba Leszek, 2017. "Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach," Foundations of Management, Sciendo, vol. 9(1), pages 99-110, February.
    • Handle: RePEc:vrs:founma:v:9:y:2017:i:1:p:99-110:n:8
    DOI: 10.1515/fman-2017-0008
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    References listed on IDEAS

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    1. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    2. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
    3. Zheng, H. & Thomas, L.C. & Allen, D.E., 2001. "The Duration Derby: A Comparison of Duration Based Strategies in Asset Liability Management," Papers 01-176, University of Southampton - Department of Accounting and Management Science.
    4. Harry Zheng, 2007. "Macaulay durations for nonparallel shifts," Annals of Operations Research, Springer, vol. 151(1), pages 179-191, April.
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