A Mental Account-Based Portfolio Selection Model With an Application

Abstract

To obtain better optimal portfolios, academics develop the behavioral portfolio theory (BPT) with two mental accounts by minimizing the risk as well as maximizing the return. However, there are some limitations to the existing BPT. To circumvent the limitations, this paper proposes a new portfolio selection (PPMPSM) model with two mental accounts in which the lower-level problem of the model is used to avoid from getting big loss while the upper-level problem corresponds to the mental account is used to get good profit. We formulate our proposed PPMPSM model by replacing the probability terms with the expectation of indicator function and then design a sequential convex approximation algorithm to obtain the optimal solution of our proposed model. We prove that the optimal portfolio obtained by our proposed algorithm converges. We demonstrate the superiority and applicability of our proposed PPMPSM models, including both Maslow (0.10) and Maslow (0.11) models, over the traditional portfolio selection models, including the model generated by using the naive equal-weighted (EW) strategy, the model satisfying investors' safety needs (Safety model), and the model satisfying the self-actualization needs (SA model) by using trading data from the American stock market. We find that our proposed PPMPSM model can obtain the highest expected return and generate the highest final cumulative wealth such that the cumulative wealth for both of our proposed PPMPSM models, Maslow(0.10) and Maslow(0.11), uniformly outperform those for the Safety and EW strategies in any week and perform the best among all the strategies in the last 2 weeks, including the SA strategy.