Robust min}max portfolio strategies for rival forecast and risk scenarios

We consider an extension of the Markowitz mean}variance optimization framework to multiple return and risk scenarios. It is well known that asset return forecasts and risk estimates are inherently inaccurate. The method proposed provides a means for considering rival representations of the future. The optimal portfolio is computed, simultaneously with the worst case, to take account of all rival scenarios. This is a min-max strategy which is essentially equivalent to a robust pooling of the scenarios. Robustness is ensured by the noninferiority of min}max. For example, a basic worst-case optimal return is guaranteed in view of multiple return scenarios. If robustness happens to have too high a cost, guided by the min}max pooling, it is also possible to explore other pooling alternatives. A min}max algorithm is used to solve the problem and illustrate the robust character of min}max with return and risk scenarios. We study the properties of the min}max risk}return frontier and compare with the potentially suboptimal worst-case where the investment strategy and the worst case are computed separately. ( 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: C44; C61; C63; G11