Abstract
We investigate the interaction between investors and portfolio managers under cumulative prospect theory. We model trust in the manager and the relative anxiety about investing in a risky asset in an original way. Moreover, we study how trust and anxiety affect the manager’s fee and the portfolios of cumulative prospect theory investors. In contrast to previous work using the classical mean-variance preferences, there are two main novelties in our contribution. First, our research relies on cumulative prospect theory (CPT) rather than the classical mean-variance framework. Second, we focus on a dynamic portfolio selection. In other words, we formulate the optimal problem under multi-period setting. Besides, we attain an optimal portfolio choices in multi-period relying on the sub-game perfect investment strategies. Moreover, our research differs from traditional CPT work through an improved value function that accurately characterizes the reduction in anxiety suffered by the CPT investors from bearing risk when assisted by the portfolio managers’ help relative to when they lack such assistance.
Highlights
Evidence indicates that investors feel overly anxious or nervous when they invest in risky assets without assistance because investors have little financial knowledge and related information
We model the investor’s trust in the manager and associated anxiety from investing in a risky asset to determine a cumulative prospect theory (CPT) investor’s optimal portfolio and a manager’s optimal fees
The value function and probability distortions are the key contributions of cumulative prospect theory and allow our CPT model to outperform traditional theory in real financial markets. Another innovation is that we focus on the dynamic portfolio selection but not the static portfolio choices
Summary
Evidence indicates that investors feel overly anxious or nervous when they invest in risky assets without assistance because investors have little financial knowledge and related information. The choice of many indicates risk aversion for Decision 1, but risk seeking for Decision 2 This problem shows that risk attitude is not same across gains and losses, implying that it is the change in wealth, rather than the level, that matters to people. Based on the subgame perfect investment strategies, we obtain the CPT investor’s optimal portfolio in multi-period In their analysis of multiple financial products, Gennaioli et al (2015)only consider two risky assets, while we study two or more such assets. In a discrete-time setting, Bernard and Ghossoub (2009) consider how a CPT investor chooses his/her optimal portfolio in a single-period model with one risky and one riskless asset.
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