Mean–absolute deviation portfolio optimization problem

One of the basic problems of applied finance is the optimal selection of stocks, with the aim of maximizing future returns and minimizing the risk using a specified risk aversion factor. Variance is used as the risk measure in classical Markowitz model, thus resulting in a quadratic programming. As an alternative, mean absolute deviation was proposed as a risk measure to replace the original risk measure, variance. This problem is a straight-forward extension of the classic Markowitz mean–variance approach and the optimal portfolio problem can be formulated as a linear programming problem. Taking the downside risk as the risk leads to different optimal portfolio. The effect of using only downside risk on optimal portfolio is analyzed in this paper by taking the mean absolute negative deviation as the risk measure. This method is applied to the optimal selection of stocks listed in Bursa Malaysia and the return of the optimal portfolio is compared to the classical Markowitz model and mean absolute deviation model. The result show that the optimal portfolios using downside risk measure outperforms the other two models.