Securities portfolio optimization using multiple criteria optimization methods

Abstract

The article deals with the analysis of financial reporting components, the inclusion of which into the set of constraints improves the original securities portfolio multiple criteria optimization model. Two models of securities portfolio multiple criteria optimization, which have appeared recently, are being scrutinized in it. The researcher used Amadeus database. The data were downloaded for a five-year period till December 2006. Initially the researcher selected the top fivescore companies, rated according to the size of their sales. Then she excluded from the original sample those companies whose data, concerning the average monthly share prices, were missing from the database. Cases with missed information about the variables selected for the analysis, were excluded too. The secondary rejection was made in respect of the evidence which did not contain any information about the variables selected for the sake of the analysis. As a result, 181 samples were taken for consideration. Further, the data were tested in NeuroShell 2. The research in NeuroShell 2 is based on the Group Method of Data Handling, (GMDH), developed and designed by Academician A.G. Ivakhnenko.. The method is based on the theory of self-regulation, which improves the regression analysis and adapts it to the so-called linear model-building of complex systems applying a limited or small amount of experimental evidence. The GMDH is combining the regression analysis with regulation techniques. ( A.G.Ivakhnenko, 1975, p.29). As a result of the study, 12 variables out of 30 were selected - the variables affecting equity return for half a year since the month the company financial reporting was published. The author of the article scrutinizes some mistakes, which to regret, one can find in setting the securities portfolio optimization problem. Evidently, they arise from mixing up 'λ' for quadratic utility (in this case 'λ' is a priori bound risk-averse parameter) with Lagrange coefficient, having the same symbol 'λ'. Lagrange coefficient is a non-dimensional quantity which can be deduced in the process of estimation, i.e. it is not a priori bound.