Portfolio Selection by Second Order Stochastic Dominance based on the Risk Aversion Degree of Investors

Second order stochastic dominance is an optimal rule for portfolio selection of risk averse investors when we only know that the investors' utility function is increasing concave. The main advantage of SSD is that it makes no assumptions regarding the return distributions of investment assets and has been proven to lead to utility maximization for the class of increasing concave utility functions. A number of different SSD models have emerged in the literature for portfolio selection based on SSD. However, current SSD models produce the same SSD efficient portfolio for all risk averse investors, regardless of their risk aversion degree. In this thesis, we have developed a new SSD efficiency model, SSD-DP, which unlike existing SSD efficiency models in the literature, provides an SSD efficient portfolio as a function of investors' risk aversion degrees. The SSD-DP model is based on the linear programming technique and finds an SSD efficient portfolio by minimizing the dual power transform (DP) of a weighted portfolio of assets for a given risk aversion degree. We show that the optimal portfolio of the proposed model is SSD efficient, i.e. it is not dominated by SSD by any other portfolio, and, through empirical studies of historical data, we show that the method is a promising tool for constructing trading strategies.Ph