Research on the Multi-Period Optimal Fee of the Money Manager Under Cumulative Prospect Theory

Abstract

We are interested in investors’ interaction with portfolio managers and investigate the manager’s optimal strategy under cumulative prospect theory. We create model to characterize the relative anxiety about investing in risk assets and trust in the manager. Besides, we research how anxiety and trust affect the manager’s fee and the investors’ portfolios under cumulative prospect theory. Compared with previous work, our main novelty is that we focus on a dynamic portfolio selection. In other words, we formulate the optimal problem under multi-period setting. Besides, relying on the sub-game perfect investment strategies, we attain an optimal fee in multi-period. Another contribution is to discuss multiple risky assets. We use elliptic distribution to reduce a high-dimensional optimal problem to a one-dimensional optimal one. We obtain the CPT-investors’ portfolio for multiple risky assets under a dynamic framework. Based on this result, we study the manager’s optimal fee. It is valuable to say that we explore the optimal strategy for the manager under cumulative prospect theory but not the classical mean-variance preferences.