When can you immunize a bond portfolio?

This paper presents a condition equivalent to the existence of a Riskless Shadow Asset that guarantees a minimum return when the asset prices are convex functions of interest rates or other state variables. We apply this lemma to immunize default-free and option-free coupon bonds and reach three main conclusions. First, we give a solution to an old puzzle: why do simple duration matching portfolios work well in empirical studies of immunization even though they are derived in a model inconsistent with equilibrium and shifts on the term structure of interest rates are not parallel, as assumed? Second, we establish a clear distinction between the concepts of immunized and maxmin portfolios. Third, we develop a framework that includes the main results of this literature as special cases. Next, we present a new strategy of immunization that consists in matching duration and minimizing a new linear dispersion measure of immunization risk. (C) 1998 Elsevier Science B.V. All rights reserved.