A mental account-based portfolio selection model with an application for data with smaller dimensions

With the rapid development of Robo-adviser, behavioral portfolio theory (BPT) has been drawing good attention. However, the existing BPT models always assume the assets' returns are normally distributed and cannot be solved efficiently when the number of assets is large. To circumvent these limitations, this paper proposes a new portfolio selection model with two mental accounts in which the lower-level (safety) is set up to avoid loss while the upper-level (self-actualization) need corresponding to the mental account is set up to get a good profit. To relax the normality assumption, we formulate our proposed model by replacing the probability terms with the expectation of indicator function and designing a sequential convex approximation algorithm to solve the proposed model. Also, we prove that the optimal portfolio obtained by our proposed algorithm converges when analyzing data with small dimensions. Last, we carry out empirical studies by using trading data with 30 stocks from the American stock market to demonstrate the superiority, effectiveness, and robustness of our proposed portfolio selection in a smaller dimension case because our method is suitable only for small dataset. By comparing the characteristics of the optimal portfolio and the out-of-sample performance of our proposed portfolio selection model with the corresponding traditional portfolio selection models, we find that our new model not only derives the optimal portfolio with moderate diversification, but also obtain the highest average return and the highest Omega ratio in the out-of-sample testing period. Extensive experiment results by using different sample sizes, different frequencies, and employing the rolling-time window approach also confirm that our proposed portfolio selection model performs the best when we compare both the highest cumulative return and the Omega ratio in the out-of-samples.