Maxmin Portfolios in Models where Immunization is not Feasible

Abstract

En este capítulo sobre inmunización de carteras de bonos contra el riesgo de los tipos de interés introducimos las carteras Maximin. Estas carteras son interesantes por 3 motivos: (i) son carteras tipo worst-case-scenario, por lo tanto proporcionan un floor/suelo sobre el valor de la cartera; (ii) son muy robustas pues permiten cambios muy generales sobre la estructura de las tasas de interés; (iii) se resuelven por medio de programación linear semi-infinita. Además, aunque sean carteras tipo peor scenario, en los ejemplos y simulaciones mostramos que se comportan como una cartera inmunizada (i.e., garantizan el rendimiento prometido en la cartera de bonos).

This work illustrates the difference between the concepts of immunized and maxmin portfolios and extends the existent literature on bond portfolio immunization by analyzing and computing maxmin portfolios in models where complete immunization is not feasible. These models are important because they permit many different shifts on interest rates and do not lead to the existence of arbitrage. Maxmin portfolios are characterized by saddle point conditions and can be computed by applying a new algorithm. The model is specialized on the very general sets of shocks from which the dispersion measures M 2 and Ñ are developed. By computing maxmin portfolios in some practical examples, it is shown that they perform close to an immunized portfolio and are close to matching duration portfolios. Consequently, maxmin portfolios provide hedging strategies in a very general setting and can answer some puzzles of this literature.