Weighting function in the behavioral portfolio theory

The Behavioral Portfolio Theory (BTP) developed by Shefrin and Statman (2000) considers a probability weighting function rather than the real probability distribution used in Markowitz’s Portfolio Theory (1952). The optimal portfolio of a BTP investor, which consists in a combination of bonds and lottery ticket, can differ from the perfectly diversified portfolio of Markowitz. We found that this particular form of portfolio is not due to the weighting function. In this article we explore the implication of weighting function in the portfolio construction. We prove that the expected wealth criteria (used by Shefrin and Statman), even if the objective probabilities were deformed, is not a sufficient condition for obtaining significantly different forms of portfolio. Not only probabilities but also future outcomes have to be transformed.