The Pricing Mechanism Of Portfolio Managers Under Cumulative Prospect Theory

We are studied in how the portfolio managers charge optimal fees to the clients who are all the CPT-investors.These CPT-investors decide to hire the trusted portfolio managers in order to reduce anxiety and nervousness for investment in a risky asset.In the dynamie portfolio choice,Faced with different historic investment results(gain or loss),investors have different subjective probabilities,and the different subjective probabilities will affect the current deeision-making.In this context,we attain the useful results of the dynamic portfolio choices relying on the sub-game perfect investment strategies,derive the CPT-investor' s dynamic portfolio and the total utility model of money managers affected by different subjective probabilities.Compared with the previous research,the novel contributions of this article include three dimensions:1)the research relying on Cumulative Prospect Theory(CPT)rather than the classical mean-variance framework;2)the last novelty is we studied the dynamic portfolio choice but not the static portfolio selection involved by the previous research;3)in multi-period,the CPT-investor' s subjective probability is changing,therefore,we modified the classical probability weighted function.Our results differ in several respects from those obtained when using on classical preferences:First,the optimal fees are not symmetric.Specially,the dominant managers obtain higher fees than subordinate managers regardless of changes in risk of risky assets(a risky asset)and changes in the dispersion of trust in the population.Another difference is that these fees are not proportional to expected returns.In particular,the optimal fees increase nonlinearly as risk of risky assets(a risky asset)increases and the dispersion of trust in the population increases.In empirical research we found:In the loss condition,the portfolio manager' s utility with a modified probability weight function is more than the utility with a classical probability weight function.Because the investor is overly pessimistic,they could accept the higher charge of portfolio manager.But,in the gain condition,the money manager' s utility with the modified probability weight function is less than the utility with a classical probability weight function.It is in line with our assumptions.