Testing for prospect and Markowitz stochastic dominance efficiency

Abstract

We develop non-parametric tests for prospect stochastic dominance Efficiency (PSDE) and Markowitz stochastic dominance efficiency (MSDE) using block bootstrap resampling. Under the appropriate conditions we show that they are asymptotically conservative and consistent. We employ Monte Carlo experiments to assess the finite sample size and power of the tests. We use the tests to empirically establish whether the value-weighted market portfolio is the best choice of every individual with preferences exhibiting certain patterns of local attitudes towards risk. Our results indicate that we cannot reject the hypothesis of prospect stochastic dominance efficiency for the market portfolio. This is supportive of the claim that the particular portfolio can be rationalized as the optimal choice for any S-shaped utility function. Instead, we reject the hypothesis for Markowitz stochastic dominance, which could imply that there exist reverse S-shaped utility functions that do not rationalize the market portfolio.