Prospect theory and asset allocation

We study the asset allocation of an investor with prospect theory (PT) preferences. First, we solve analytically the two-asset problem of the PT investor for one risk-free and one risky asset and find that the reference return and the level of risk aversion or risk seeking (diminishing sensitivity) affect differently less ambitious and more ambitious investors: the less ambitious investor decreases her exposure to the risky asset when increasing her reference return or the level of diminishing sensitivity, while the more ambitious investor increases her exposure to the risky asset when increasing her reference return or the level of diminishing sensitivity. However, both less and more ambitious investors decrease their exposures to the risky asset when increasing their degrees of loss aversion. In a comprehensive sensitivity analysis, we investigate how different aspects of the PT investor's preferences contribute to her risk taking, performance and happiness. We observe, for instance, that the investor's happiness decreases with her increasing level of ambition. Second, we perform simulations to examine concrete solutions of the theoretical two-asset problem for different types of the PT investor and for different characteristics of the risky asset and find that the assumption of skewness, as opposed to symmetry, changes the optimal investment in the risky asset. Third, we empirically investigate the performance of a PT portfolio when diversifying among a stock market index, a government bond and gold, in Europe and the US. We focus on investors with PT preferences under different scenarios regarding the reference return and the degree of loss aversion and compare their portfolio performance with the performance of investors under mean–variance (MV), linear loss averse and CVaR preferences. We find that, in the US, PT portfolios significantly outperform MV portfolios (in terms of returns) in most cases.