Prospect Theory and Mean-Variance Analysis

Abstract

The experimental results of prospect theory (PT) reveal suggest that investors make decisions based on change of wealth rather than total wealth, that preferences are S-shaped with a risk-seeking segment, and that probabilities are subjectively distorted. This article shows that while PT’s findings are in sharp contradiction to the foundations of mean-variance (MV) analysis, counterintuitively, when diversification between assets is allowed, the MV and PT-efficient sets almost coincide. Thus one can employ the MV optimization algorithm to construct PTefficient portfolios. The Markowitz (1952a)-Tobin (1958) mean-variance (MV) rule is probably the most popular investment decision rule under uncertainty in economics and in finance, and it is widely employed by both academics and practitioners. The strength of the MV analysis is that in the case of normal return distributions the choice of any expected utility maximizing risk-averse individual will be according to the MV rule. 1 The MV framework is the foundation of the Sharpe (1964)-Lintner (1965) capital asset pricing model (CAPM), which is a cornerstone of modern finance. Moreover, the MV framework provides a very important practical procedure for the construction of efficient portfolios. While standard economic theory and, in particular, MV analysis assume expected utility maximization and risk aversion, in a breakthrough article Kahneman and Tversky (1979) show that the actual behavior of individuals systematically and consistently violates these