Risk-return Evaluation Based On Possibilistic Mean And Variance

The mean-variance methodology for portfolio selection problem, proposed originally by Markowitz, combines probability and optimization techniques. In the mean-variance portfolio selection problem, previous research includes the contributions from Merton,Pang and Perold, etc.. The key principle of the mean-variance model is to use the expected return of a portfolio as the investment return and to use the variance of the expected returns of the portfolio as the investment risk. The basic assumption for using Markowitz's mean-variance model is that the situation of asset markets in future can be correctly reflected by the past asset data, that is the mean and covariance of assets in future is similar to the past one. In fact, it is difficult to ensure this kind of assumption in the real ever-changing asset markets.Recently, behavioral finance caused by the suspicion of rational expectations and efficient market hypothesis attracts more attention in the finance development. Fuzzy theory, an efficient tool to deal with the nonrandom uncertainty, is superior to describe the uncertainty of the people's knowledge and behavior and is an effective and potential method in behavioral finance study. And basing on fuzzy theory to select portfolio is a new research area lately.After introducing the basic concepts and theorems of fuzzy theory and modern portfolio theory, this thesis presents the possibilistic distribution in portfolio. Based on the possibilistic mean and variance, it proposes a novel weighted possibilistic variance of fuzzy numbers by using conventional approach, which is different from that proposed by Robert Fuller and Peter Majlender, the expected value of the squared deviations between the arithmetic mean and the endpoint of its level sets. Although Markowitz proposed the mean-variance methodology for portfolio selection by probability method and established the investment model, it falls short of dealing problems only via probability approach under this uncertainty environment intermixed by randomness and fuzziness. Therefore, we apply the weighted possibilistic mean and variance to portfolio selection with the quadratic utility function and possibilistic efficient portfolio model. At last, some examples are presented for explaining that the investor who does not need to devote all his capital to risky assets is also able to get the expected return by empirical analysis, and the investment proportion is less than that with respect to general possibilistic mean and variance under the condition of the same expected return.