Portfolio Selection Optimization under Cumulative Prospect Theory – a parameter sensibility analysis

The Cumulative Prospect Theory (CPT) is one of the most popular theories for evaluating the behavior of decision makers in the context of risk and uncertainty. This theory emerged as a generalization of the Expected Utility Theory (EUT) and being a relatively recent theory, its application has been somewhat reduced, especially when linked to optimization models. This paper intends to analyze the behavior of CPT, with a power value function and a two-parameter probability weighting function, as an objective function of a portfolio selection model. The parameterization of the objective function parameters allows us to analyze the composition of portfolios such as loss aversion, risk aversion in gains and risk preference in the range of losses. The results suggest that loss aversion and risk aversion in gains lead to the choice of portfolios with lower profitability and variability and that the risk preference in losses leads to the choice of portfolios with higher profitability and variability. The results are also compared with those obtained with EUT, and allow us to conclude that CPT leads to more diversified solutions which are therefore more easily adjusted to the investors’ behavioral profile.