Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments

We study the portfolio selection problem from the perspective of incorporating more information about the non-normality of asset returns by considering the mean-variance-skewness-kurtosis framework. Using additional criteria (namely asset turnover, earnings per share, earnings per share growth rate, leverage ratio, price/earnings ratio, and beta (β) value), we employ data envelopment analysis technique to construct a benefit criterion from the efficiency scores of the assets. To incorporate the uncertainty and vagueness of real financial markets, the input data (with respect of all criteria) are assumed as (λ, ρ) interval-valued fuzzy numbers constructed using the historical data. Marginal impacts of the assets on higher moments of the portfolio are used to formulate a fuzzy multi-objective linear programming model. The constraints of the proposed model include the bounds on investment in individual assets, full utilization of the investment capital, and no short selling of assets. The signed distance ranking method is used to obtain a numeric optimization model, which is solved through a weighted max-min approach (in order to incorporate the investor's preferences regarding investment criteria). A case of real financial market portfolio selection is presented to demonstrate the efficiency of both the proposed model and the solution method.