Selecting portfolios given multiple eurostoxx-based uncertainty scenarios: a stochastic goal pro-gramming approach from fuzzy betas

Resumen

We deal with the ¿satisficing¿ choice of portfolios of funds for buy-and-hold strategies by considering fifteen goals defined from fifteen future (uncertain) states of the world. Each state is a scenario specified from historical values of the Eurostoxx market index. These values are a pair of potential events characterizing profitability and risk, in this case, the expected value and variance of returns to be received from the market index if the scenario under consideration was the true state. Potential returns on each fund are related to each scenario by using betas, which are elicited by fuzzy logic taking into account their various measures (weekly, monthly, etc.). For this purpose, triangular membership functions are used as an appropriate tool from which expected values (Heilpern, 1992) are computed. As an opportunity set of assets, we use a large set of funds. A frontier of portfolios is then derived by stochastic goal programming (SGP) as a recent uncertainty multiobjective model characterized by the following aspects: (a) it is built from Eu(R) principles in a framework of bounded rationality; (b) under some assumptions, it leads to efficient frontiers of portfolios; and (c) its moderate computational burden allows easy application to large scale problems. In SGP, the variability matrices of goals are aggregated by Arrow¿s risk aversion coefficients. Concerning the case study, numerical tables are developed to highlight the computational process and results, including sensitivity analysis and comparisons. Our approach is new in the sense of combining SGP and fuzzy tools.