On securities portfolio optimization, preferences, payoff matrix estimation and uncertain mixed decision making

Abstract

Securities portfolio optimization has been analysed so far on the assumption that the estimation of the probability distribution concerning future rates of return is possible thanks to historical data. However, sometimes it is desirable to forecast profits by considering factors which are not included in past and present results. The purpose of the paper is to investigate the stocks portfolio optimization in the context of decision making under complete uncertainty, i.e. uncertainty with unknown probabilities, which allows the investor to refer to scenario planning. In the contribution, we propose the use of a decision rule for portfolio optimization under complete uncertainty. The procedure takes into account the decision maker’s nature and enables one to select the optimal mixed strategy, which is characteristic of portfolio optimization where variables denoting the share of particular securities are continuous (not binary). The decision process is discussed for two types of decision makers: an active one (who estimates the profit matrix on his own) and a passive one (who uses a profit matrix generated by experts). Additionally, we analyse the impact of the profit matrix estimation (subjectively or objectively) on the decision making process.