Abstract

This paper finds optimal portfolios for the reference-dependent preferences of Koszegi and Rabin, with piecewise linear gain-loss utility, in a one-period model with a safe and a risky asset. If the return of the risky asset is highly dispersed relative to its potential gains, two personal equilibria arise, one of them including risky investments, the other one only safe holdings. In the same circumstances, the risky personal equilibrium entails market participation that decreases with loss aversion and gain-loss sensitivity, whereas the preferred personal equilibrium is sensitive to market and preference parameters. Relevant market parameters are not the expected return and standard deviation, but rather the ratio of expected gains to losses and the Gini index of the return.

Highlights

  • Standard portfolio theory imagines investors as utility maximizers, unencumbered by personal past references, who are sensitive to consumption and wealth outcomes alone

  • Less than half of households participates in the stock market (Guiso, Haliassos, and Jappelli, 2002; Vissing-Jorgensen, 2003), and the prospect theory of Kahneman and Tversky (1979) recognizes reference dependence as a major determinant of preferences, though it remains silent on the origin of such references

  • The theorem below finds that three regimes arise: (i) there are no personal equilibria; (ii) the safe portfolio is the unique personal equilibrium; and (iii) any risky position with positive expected return is a personal equilibrium

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Summary

Introduction

Standard portfolio theory imagines investors as utility maximizers, unencumbered by personal past references, who are sensitive to consumption and wealth outcomes alone. This paper solves the one-period portfolio choice problem for an investor with the reference-dependent preferences of Koszegi and Rabin (2006), and finds that its solution supports two competing personal equilibria—expectations about one’s choice that make such choice optimal. The role of the Gini index as relevant measure of dispersion stems from the definition of referencedependent utility, which contributes to preferences through the expected gain-loss of payoff-reference outcomes. Though Koszegi and Rabin (2006) define reference-dependent utility for general S -shaped gainloss functions ν(·), which make agents potentially risk-seeking in losses, this paper focuses on a more parsimonious setting, in which ν(·) is piecewise linear for gains and losses, with a concave kink at zero that preserves loss aversion. PPE(w0) ⊆ R denotes the set of preferred personal equilibria

Linear utility
Concave utility
Example
Conclusion
Auxiliary results
Proofs of Sections 3 and 4
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