Continuous Cumulative Prospect Theory and Individual Asset Allocation

We implement the Cumulative Prospect Theory (CPT) framework (Tversky and Kahneman 1992) into a model of individual asset allocation, building on earlier work by Hwang and Satchell (2003) where they derive explicit formulae for the asset allocation decision using a loss aversion utility function. We apply Prelec’s probability weighting function (1998) to continuous distributions and derive the formulae for the optimal asset allocation between risky and safe assets. US equity returns data are used to examine the feasible parameter space. The earlier results of Hwang and Satchell are confirmed and the more complex model is compatible with observed equity proportions. The parameters are highly interconnected, but feasible combinations indicate that more inverse-S shaped deviations from linear probability weightings are associated with lower risk taking behaviour.