One for the Gain, Three for the Loss

I derive indifference curves in mean-standard deviation space for investors with prospect theory preferences when returns are normally distributed. The normality assumption creates a mapping between model parameters and the investment opportunity set. The model is then calibrated to historical return data for various assumptions regarding the set of admissible risky assets. It is found that the parameter for loss aversion must be higher than three for investors to hold finitely leveraged portfolios. For lower rates of loss aversion, in particular those proposed in the earlier experimental literature, the allocation to risky assets is infinite. Numerical simulations produce similar results when the normality assumption is abandoned.