Portfolio selection by cumulative prospect theory and its comparison with mean-variance model

Abstract

The modeling of risk and uncertainty in finance requires the consideration of several factors. One of the main factors in modeling is the decision-maker’s attitude towards risk. Cumulative prospect theory (CPT) has emerged as an important approach for assessing the actions of decision-makers under uncertainty with ambiguity. Considerable experimental evidence indicates that human behavior can differ significantly from the conventional expected utility maximization paradigm. CPT has the ability to model the irrationality of the decision makers’ behavior in real complex situations. This paper studies the portfolio selection problem based on the cumulative prospect theory (CPT) risk criterion. We encounter two types of risks during problem handling, first internal (imposed by risk management departments) and second external (accredited regulatory institutions). Therefore, we propose a new CPT-based model for the portfolio selection problem under uncertainty with ambiguity. By taking some listed stocks from Nifty-50, the National Stock Exchange, India, as the study sample, the efficient frontier for the proposed CPT-based model is generated. The empirical analysis compares the classical Markowitz’s mean-variance efficient frontier with mean-variance values obtained by the proposed CPT-based efficient frontier. We also compare the investment performance of the behavioral investor with that of a rational investor. A detailed numerical illustration is presented to substantiate the proposed approach.