The Mean-variance (in)Efficiency of Duration-based Immunization

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 paper provides a mean-variance framework to explore this puzzle. We characterize the efficient portfolio allocations for a stylized barbell strategy which trades off reinvestment risk with discounting risk. We show, in a model-free setting, that efficient allocations can be superior or inferior to the minimum variance allocation as time passes, meaning the efficiency of duration-based immunization strategies is transient. This result is numerically illustrated in a one-factor Gaussian model as well as in a two-factor non-Gaussian model. Using yield curve scenarios resampled from U.S. data over the 1977-2020 period, we further challenge our conclusions non-parametrically, and find that duration-based immunization entails allocations that are sometimes inefficient.

Keywords: Immunization, Bond portfolio, Mean-variance, Duration, Risk management

JEL Classification: G10, G11