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THE DOWNSIDE RISK OPTIMAL PORTFOLIO SELECTION PROBLEM

Anton Abdulbasah kamil et al.

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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