Portfolio optimisation under prospect theory with an empirical test

Barberis et al. (2016. "Prospect Theory and Stock Returns: An Empirical Test." The Review of Financial Studies 29:3068–3107. https://doi.org/10.1093/rfs/hhw049.) show that a stock whose past return distribution has a high (low) prospect theory value (TK) earns a low (high) subsequent return on average. In this paper, we investigate whether portfolio optimisation techniques can make high-TK stocks (both long and short positions) more appealing to investors. Following the literature, we remove the probability distortion part of prospect theory to find a closed-form solution under the well-justified assumptions of a piecewise exponential value function and normally distributed returns for multiple risky assets in a single-period setting. We show that the optimal portfolio is proportional to the well-known Markowitz mean–variance portfolio. Our numerical results demonstrate that our portfolio optimisation approach yields higher subsequent gains for groups of stocks with high TK and lower gains for those with low TK in the US market. TK at the portfolio level is an important driver of portfolio returns under our optimisation approach, even after controlling for well-established stock return predictors, and it negatively affects portfolio returns.