Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion

Michalowski, W. & Ogryczak, W. (1998). Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-98-041

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Abstract

The mathematical model of portfolio optimization is usually expected as a bicriteria optimization problem where a reasonable trade-off between expected rate of return risk is sought. In a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we present an extension to the MAD model allowing to account for downside risk aversion of an investor, and at the same time preserving simplicity and linearity of the original MAD model.

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