The asset allocation decision in a loss aversion world

The purpose of this paper is to derive explicit formulae for the asset allocation decision for the loss aversion utility function proposed by Kahneman and Tuversky. We show that these utility functions exhibit constant absolute risk aversion. We also give analytic results which interpret the assumptions of risk-aversion with respect to gains but risk-a!ection with respect to losses in terms of changes of the optimal investment of equity when the probability that equity outperforms cash goes up. For the Knight, Satchell and Tran (1995) family of distributions, it is straightforward to derive closed form expressions for the optimal portfolio weights in all cases. Using UK and US data, we confirmed that the values of the parameters in the loss aversion function suggested by many previous studies are compatible with the observed proportions held in equity in both the UK and the US. The distributional assumptions are not innocuous. However, whilst modelling upside and downside returns by gamma distributions leads to plausible results, modelling upside and downside by truncated normals does not.