A portfolio selection model using fuzzy returns

We study a static portfolio selection problem, in which future returns of securities are given as fuzzy sets. In contrast to traditional analysis, we assume that investment decisions are not based on statistical expectation values, but rather on maximal and minimal potential returns resulting from the so-called α-cuts of these fuzzy sets. By aggregating over all α-cuts and assigning weights for both best and worst possible cases we get a new objective function to derive an optimal portfolio. Allowing for short sales and modelling α-cuts in ellipsoidal shape, we obtain the optimal portfolio as the unique solution of a simple optimization problem. Since our model does not include any stochastic assumptions, we present a procedure, which turns the data of observable returns as well as experts’ expectations into fuzzy sets in order to quantify the potential future returns and the investment risk.