The mean–variance (in)efficiency of duration‐based immunization

Pascal François and Franck Moraux ()
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Pascal François: HEC Montréal - HEC Montréal
Franck Moraux: UR - Université de Rennes, CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique

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Abstract: Empirical studies report inconclusive assessment of duration‐based immunization, notably showing that more sophisticated strategies do not outperform immunization relying on Macaulay duration. This article provides a mean–variance framework to explain this puzzle. We characterize the efficient portfolio allocations for a stylized barbell strategy trading off reinvestment risk with discounting risk. We show, in a model‐free setting, that barbell allocations form a convex set in the mean–variance space, and the endpoints of the efficient frontier can switch as time passes, reversing the set of efficient allocations. Consequently, duration‐based immunization, which is not minimum variance, can exhibit temporary inefficiency. This result is numerically illustrated in a one‐factor Gaussian and a two‐factor non‐Gaussian model. Using yield curve scenarios resampled from U.S. data over the 1977–2020 period, we further corroborate our conclusions non‐parametrically, and find that duration‐based immunization is sometimes inefficient.

Keywords: bond portfolio; duration; immunization; mean–variance; risk management (search for similar items in EconPapers)
Date: 2024
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Published in International Review of Finance, 2024, ⟨10.1111/irfi.12447⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04529445

DOI: 10.1111/irfi.12447

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