SOMA in financial modeling

Abstract

The basic problem in portfolio theory (based on Markowitz theory) is the selection of an appropriate mix of assets in a portfolio in order to maximize portfolio expected return and subsequently to minimize portfolio risk. Another approach takes into account portfolio performance expressed by various measurement techniques e.g. Sharpe ratio, Treynor ratio, Jensen’s alpha, Information ratio, Sortino ratio, Omega function and the Sharpe Omega ratio that are focused to determine the allocation of the available resources in the selected group of assets. This chapter presents an alternative approach to the computation of weights of assets in portfolio based on the nonlinear measure techniques: Sortino ratio and Omega function. The proposed alternative includes principle of self-organizing migrating algorithm (SOMA). The experiments are set up on assets included in Dow Jones Industrial Index. Presented original approach lends itself also to other evolutionary techniques in the area of portfolio selection based on different measurement techniques.