A Robust Approach to Bond Portfolio Immunization

We consider one-period maximin portfolios to hedge the interest-rate risk of default-free and option-free bond portfolios. Our framework allows for general changes on the interest rates, and neither requires the specification of the yield curve dynamic nor the estimation of a model. We make three contributions. First, we show that maximin strategies solve a semi-infinite linear programming problem, give a simplex type algorithm to compute them, and efficiently solve this simplex. As a by-product, we show how to compute the infimum (and supremum) values of any bond portfolio in this robust framework, an additional interest-rate risk management tool. Second, let sâ‚ and sâ‚‚ be the first and the second period of the one-period model, respectively. The maximin portfolio does not depend on the hedging period, sâ‚‚-sâ‚ , an interesting robustness property. Third, we show in a few examples that, given an appropriate but simple set of hedging bonds, maximin portfolios encompass more than worst-case scenario strategies. Namely, (a), they are robust, they hedge against parallel and non-parallel shifts, (b), they are effective, they almost do not convey interest-rate risk, and (c), they resemble maturity-matching portfolios, demanded as the right hedging strategies for this problem (see Ingersoll (1983)). Hence, property (c) gives the theoretical support for properties (a) and (b), and is consistent with the second result