### THE DOWNSIDE RISK OPTIMAL PORTFOLIO SELECTION PROBLEM

#### Abstract

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

prograrnming. As an altemative, 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 opimal 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.

Keywords;-Portfolio optimizatiorr, Linear Programming, Downside risk.

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