Individual investors, wealth managers and fund managers are all concerned with the achievement of optimum investment asset portfolios. Regardless of whether portfolios are chosen for the derivative mix of a bank, the equity assets of an investor or the asset and liability management of a business, the common aim in all models is to mitigate some measure of risk while optimising some measure of reward. For optimal portfolio selection, a dynamic stochastic approach is proposed that maximises investment potential and minimises overall downside risk while taking into account the implied transaction costs incurred in initial trading and subsequent portfolio rebalancing. Both gains (upside deviations) and losses (downside deviations) are penalised in the same way by the popular mean variance (MV) model and mean absolute deviation (MAD) model. Investors, however, are concerned with downside deviations and are pleased with upside deviations. The suggested model therefore penalises only downside deviations and maximises upside deviations instead. The approach holds transaction costs at the amount prescribed by the investor. With stochastic data given in the form of a scenario tree, dynamic stochastic programming is used. Consideration is given to a set of discrete asset return scenarios and implied transaction costs, which deviate from each return scenario. By comparing its results with those of the MV, MAD and minimax models, model validation is achieved. The results show that optimal portfolios with the lowest risk, highest portfolio wealth and minimum implicit transaction costs are generated by the proposed model.
Dr. Sabastine Mushori
Central University of Technology, P.O. Box 1881, Welkom, 9460, South Africa.
Dr. Delson Chikobvu
University of the Free State, P.O. Box 339, Bloemfontein, 9300, South Africa.
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