Extending the mean absolute deviation portfolio optimization model to incorporate downside risk aversion

Extending the mean absolute deviation portfolio optimization model to incorporate downside risk aversion

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Article ID: iaor20021544
Country: United States
Volume: 48
Issue: 3
Start Page Number: 185
End Page Number: 200
Publication Date: Apr 2001
Journal: Naval Research Logistics
Authors: ,
Keywords: programming: linear
Abstract:

A mathematical model of portfolio optimization is usually represented as a bicriteria optimization problem where a reasonable tradeoff between expected rate of return and 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 developed by Konno and Yamazaki, where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is easily transformed into a linear programming problem. An extension to the MAD model proposed in this paper allows us to measure risk using downside deviations, with the ability to penalize larger downside deviations. Hence, it provides for better modeling of risk averse preferences. The resulting m-MAD model generates efficient solutions with respect to second degree stochastic dominance, while at the same time preserving the simplicity and linearity of the original MAD model.

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