Title

Cumulative Prospect Theory and Mean Variance Analysis: A Rigorous Comparison

Abstract

We propose a numerical optimization approach that can be used to solve portfolio selection problems  that include several assets and involve objective functions from the cumulative prospect theory.  Implementing the suggested algorithm, we conduct a numerical study with the following goal.  We compare asset allocations that are derived for cumulative prospect theory (CPT) based on two different methods: maximizing CPT along the mean-variance efficient frontier and maximizing CPT without this restriction. We find that with normally distributed returns, the difference between these two approaches is negligible. However, if standard asset allocation data for pension funds are considered, the difference is considerable. Moreover, for certain types of derivatives, such as call options, the restriction of asset allocations to the mean-variance efficient frontier produces sizable losses in various respects, including decreases in expected returns and expected utility. As one of the reasons for this difference, we identify the preference of CPT investors for positively skewed securities, and we numerically verify this preference.