۱٫ Introduction

۲٫ The model

۳٫ Equilibrium

۴٫ Example

۵٫ Conclusion

Acknowledgments

Appendix A. Supplementary materials

Research Data

References

Abstract

In Das et al. (2010), an agent divides his or her wealth among mental accounts that have different goals and optimal portfolios. While the moments of the distribution of asset returns are exogenous in their normative model, they are endogenous in our corresponding positive model. We obtain the following results. First, there are multiple equilibria that we parameterize by the implied risk aversion coefficient of the agent’s aggregate portfolio. Second, equilibrium asset prices and the composition of optimal portfolios within accounts depend on this coefficient. Third, altering the goal of any given account affects the composition of each portfolio.

Introduction

Das et al. (2010, DMSS) combine certain aspects of behavioral and mean-variance (MV) portfolio selection models. Like Shefrin and Statman (2000), DMSS consider an agent who divides his or her wealth among mental accounts (hereafter ‘accounts’) with different goals such as retirement or bequests.1 For each account, short sales are allowed and the agent maximizes its expected return subject to: (1) fully investing the wealth assigned to it; and (2) the probability of its return being less than or equal to some threshold return (e.g., −۲۰%) not exceeding some threshold probability (e.g., 5%).2 The threshold return and threshold probability (hereafter ‘thresholds’) can vary across accounts to reflect different goals. Assuming that a risk-free asset is absent and risky asset returns have a multivariate normal distribution, DMSS show that optimal portfolios within accounts and the resulting aggregate portfolio are all on the MV frontier of Markowitz (1952). In their normative model, the moments of this distribution are exogenous.

Our paper develops a corresponding positive model where these moments are endogenous in four types of economies. The first is a single-agent economy where the agent has an objective function defined over the expected value and variance of his or her future wealth as well as a single account (hereafter ‘MV agent’). The second is also a single-agent economy but the agent has an objective function as in DMSS (hereafter ‘DMSS agent’) and a single account. The third is a single-agent economy with a DMSS agent but with multiple accounts. The fourth is a two-agent economy with an MV agent (who has a single account) and a DMSS agent who has multiple accounts