A Possibilistic Mean-Downside Risk-Skewness Model for Efficient Portfolio Selection

This paper presents a new possibilistic model for the portfolio selection problem. The uncertainty of future returns on a given portfolio is modeled using LR-fuzzy numbers. Some possibilistic moments are considered to measure the risk of and return on the investment. Since the joint possibility distribution of the returns on the assets is unknown, we consider the returns on a given portfolio as the historical dataset instead of considering the individual returns on the assets as the dataset. We introduce a coefficient of possibilistic skewness in order to incorporate a measurement of the asymmetry of the fuzzy return on a given portfolio. We solve the multi-objective optimization problems that are associated with the possibilistic mean-downside risk-skewness model by using an evolutionary procedure to generate efficient portfolios. The procedure provides different patterns of investment, whose portfolios meet the explicit restrictions imposed by the investor. Thus, from among the points in the efficient frontier, the investor may select a portfolio that optimizes an economically meaningful objective function. The performance of this approach is tested using a dataset of assets from the Spanish stock market.