Anomalies to Markowitz’s Hypothesis and a Prospect-Theoretical Interpretation

Abstract

Markowitz hypothesized a fourfold pattern of risk preferences, with risk aversion for large gains and small losses, but risk seeking for small gains and large losses. We test his hypothesis, and obtain two major results. One is the dispersion effect: A majority exhibits risk seeking and risk aversion for small and large gains, but disperses into five preference groups for small and large losses. There are the ‘Markowitzians’ (risk aversion and risk seeking), the ‘non-Markowitzians’ (risk seeking and risk aversion), the ‘Cautious’ (global risk aversion), the ‘Audacious’ (global risk seeking), and the ‘Wavering’ (who exhibit no definite preference pattern). The other result is the migration effect: The composition of the preference groups changes across risk levels. More specifically, when going from high to moderate risk levels, the shares of the Markowitzians and the Cautious fall while the shares of the Audacious and the non-Markowitzians rise. We show that, if prospect theory accommodates the dispersion effect by allowing for heterogeneity in the elasticity of the value function and the elevation of the probability-weighing function, it correctly predicts the migration effect.

Keywords: Risk aversion, risk seeking, choice time, choice inconsistency, Markowitz, prospect theory