Possibilistic Sharpe Ratio Based Novice Portfolio Selection Models

This paper uses the concept of possibilistic risk aversion to propose a new approach for portfolio selection in fuzzy environment. Using possibility theory, the possibilistic mean, variance, standard deviation and risk premium of a fuzzy number are established. Possibilistic Sharpe ratio is defined as the ratio of possibilistic risk premium and possibilistic standard deviation of a portfolio. The Sharpe ratio is a measure of the performance of the portfolio compared to the risk taken. The higher the Sharpe ratio, the better the performance of the portfolio is and the greater the profits of taking risk. New models of fuzzy portfolio selection considering the possibilistic Sharpe ratio, return and skewness of the portfolio are considered. The feasibility and effectiveness of the proposed method is illustrated by numerical example extracted from Bombay Stock Exchange (BSE), India and is solved by multiple objective genetic algorithm (MOGA).