Selecting Portfolios Given Multiple Eurostoxx-Based Uncertainty Scenarios: A Stochastic Goal Programming Approach from Fuzzy Betas

We deal with the buy-and-hold choice of fund portfolios by considering multiple states of nature (future market scenarios). These states are associated with goals in the sense that the investor pursues to optimize a classical financial objective function as much as possible whatever the states of nature. As this classical function is very cumbersome for handling, a satisficing proxy is used. This proxy is Stochastic Goal Programming (SGP), a recent uncertainty multiobjective model characterized as follows: (a) it relies on Von Neumann and Morgenstern's-Arrow's Eu(R) principles in a framework of bounded rationality; (b) 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, the states of nature are Eurostoxx market index scenarios defined from time series. As an opportunity set of assets, we use a large set of funds managed by an international consultancy. Potential returns on each fund are related to each scenario by using betas. As eliciting betas can be made from different samples leading to different results, we use fuzzy logic to decide among these different results in a framework of imprecision/uncertainty. Our approach is new as it combines SGP and fuzzy tools.