Measuring Uncertainty in the Portfolio Selection Problem

In this paper, we propose a new index for ranking portfolios based on the credibility expected return and loss on their investment. We assume that the return on a given portfolio is modeled as a trapezoidal fuzzy variable, whose credibility distribution is built using the data set of its historical returns. The credibilistic loss on the investment for a given portfolio is measured by means of a suitable loss function. In order to take risk-adverse investor attitudes into account, we analyze the performance of some credibility measures related to loss and risk on the investment for a given portfolio and their relationship with similar possibility measures. A numerical example is presented showing the performance of different fuzzy ranking indices for real portfolios in the Spanish stock market.