Minimum Variance Immunization

59 Pages Posted: 12 Jan 2021

See all articles by Pascal Francois

Pascal Francois

HEC Montreal - Department of Finance

Franck Moraux

Université de Rennes I and CREM

Date Written: November 25, 2020


This paper analyzes immunization strategies in the mean-variance framework. We characterize the efficient portfolio allocations and identify the minimum variance immunization strategy. We show that the efficient allocations can be superior or inferior to the minimum variance allocation as time passes. Consequently, the efficiency of duration-based (Macaulay or stochastic) immunization strategies can be transient, which helps explain their mitigated performance documented in empirical studies. The minimum variance immunization strategy, characterized explicitly in the Vasicek model, appears robust to real yield curve fluctuations extrapolated from U.S. data from 1977 to 2020.

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

JEL Classification: G10, G11

Suggested Citation

Francois, Pascal and Moraux, Franck, Minimum Variance Immunization (November 25, 2020). Available at SSRN: or

Pascal Francois (Contact Author)

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
514-340-7743 (Phone)
514-340-5632 (Fax)

Franck Moraux

Université de Rennes I and CREM ( email )

IAE de Rennes
11, rue Jean Macé
Rennes, 35000
+33 (0)2 23 23 78 08 (Phone)
+33 (0)2 23 23 78 00 (Fax)


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