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

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.