Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences

We propose a new credibility portfolio selection model, in which a measure of loss aversion is introduced as an objective function, joint to the expected value of the returns and the below-mean absolute semi-deviation as a risk measure. The uncertainty of the future returns is directly approximated using the historical returns on the portfolios, so the uncertain return on a given portfolio is modeled as an LR-power fuzzy variable. Quantifying the uncertainty by means of a credibility distribution allows us to measure the investors’ loss aversion as the credibility of achieving a non-positive return, which is better perceived by investors than other measures of risk. Furthermore, we analyze the relationships between the three objective functions, showing that the risk measure and the loss aversion function are practically uncorrelated. Thus, the information provided by these criteria do not overlap each other. In order to generate several non-dominated portfolios taking into account the investor’s preferences and that the problem is non-linear and non-convex, we apply up to three preference-based EMO algorithms. These algorithms allow to approximate a part of the Pareto optimal front called region of interest. We analyze three investor profiles taking into account their loss-adverse attitudes: conservative, cautious and aggressive. A computational study is performed with data of the Spanish stock market, showing the important role played by the loss aversion function to generate a diversified set of non-dominated portfolios fitting the expectations of each investor.