Collective mental accounting: an integrated behavioural portfolio selection model for multiple mental accounts

We propose a behavioural portfolio selection model called collective mental accounting (CMA), which integrates all mental sub-portfolios (mental accounts) in one mathematical model. Moreover, this study contributes to the literature of behavioural portfolio selection in three further ways: first, the CMA model can determine the proportions of wealth allocated to each mental sub-portfolio with and without input from the investor. Second, unlike other mental accounting models (MA), in CMA it is possible to define constraints on total asset holdings such as short-selling, and cardinality constraints. Third, in order to make CMA more tractable and mathematically elegant, we obtain a semi-definite programming representation of the model. We also present a numerical example to investigate the effects of short-selling constraints as well as to compare the portfolio recommendations, utility functions, feasibility, and optimality of the CMA and MA models. The results reveal that although both models’ solutions are mean-variance efficient, CMA outperforms MA in terms of behavioural efficient frontier and utility functions.