A Cumulative Prospect Theory approach for portfolio optimisation: empirical investigations using PSO algorithms

Abstract

One of the most important and influential economic theories dealing with portfolio optimisation is Cumulative Prospect Theory. Developed by Tversky and Kahneman, it is accepted worldwide as an alternative theory of Expected Utility Theory, which has faced several behaviourally criticisms in the last decades. After exploring how these two theories are implemented into the selection portfolio problem, the thesis fully describes both Index-Tracking and Cumulative Prospect Theory (CPT) models in terms of the optimisation problem. Next, an application of the CPT model for index tracking is derived. Since the optimisation problem becomes quite complicated, the literature recommends taking advantage of metaheuristics, i.e., the Particle Swarm Optimisation. It allows finding the optimum solution to the portfolio selection problem. The fundamental assumption is that the behaviourally based portfolio should provide better results than traditional approaches employed in passive fund management. The project takes into consideration the Dow Jones Industrial Average, a stock market index that contains 30 publicly-owned companies listed on the NASDAQ and the NYSE. The employment of metaheuristic to the behaviourally based model allows managing a large number of securities in a short time. To improve the performances of Cumulative Prospect Theory model, an analysis of the data is performed as the sentiment prospect investor varies. Finally, the performance of the examined models is compared.