Cumulative Prospect Theory and Mean Variance Analysis: A Rigorous Comparison

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.