A behavioural approach to financial portfolio selection problem: an empirical study using heuristics

Abstract

The behaviourally based portfolio selection problem with investor's loss aversion and risk aversion biases in portfolio choice under uncertainty are studied. The main results of this work are developed heuristic approaches for the prospect theory and cumulative prospect theory models proposed by Kahneman and Tversky in 1979 and 1992 as well as an empirical comparative analysis of these models and the traditional mean variance and index tracking models. The crucial assumption is that behavioural features of the (cumulative) prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large scale computational results for the (cumulative) prospect theory model have been obtained. Previously, as far as we aware, only small laboratory (2-3 arti cial assets) tests has been presented in the literature. In order to investigate empirically the performance of the behaviourally based models, a differential evolution algorithm and a genetic algorithm which are capable to deal with large universe of assets have been developed. The speci c breeding and mutation as well as normalisation have been implemented in the algorithms. A tabulated comparative analysis of the algorithms' parameter choice is presented. The performance of the studied models have been tested out-of-sample in different conditions using the bootstrap method as well as simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market. A cardinality and CVaR constraints have been implemented to the basic mean variance and prospect theory models. The comparative analysis of the empirical results has been made using several criteria such as CPU time, ratio between mean portfolio return and standart deviation, mean portfolio return, standard deviation , VaR and CVaR as alternative measures of risk. The strong in uence of the reference point, loss aversion and risk aversion on the prospect theory model's results have been found. The prospect theory model with the reference point being the index is compared to the index tracking model. The portfolio diversi cation bene t has been found. However, the aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to worse performance of this model in a bearish market compared to the index tracking model. The tabulated comparative analysis of the performance of all studied models is provided in this research for in-sample and out-of-sample tests.