Portfolio Choice When Relative Income Matters

Abstract

This paper derives conditions under which concerns about relative income cause an individual's optimal share of the risky investment to increase with the aggregate share (rational herding). The model uses a measure of relative income that can flexibly capture the effects of both consumption externalities and status concerns, makes no assumption about the functional form of utility, and makes minimal behavioral assumptions. Key results are derived from the implicit function theorem. A comprehensive look at interdependent utility and the generality of results are the key contributions of this paper. The two most critical conditions for rational herding are substitutability between one's own income and relative income and diminishing marginal utility of relative income. The keeping-up-with-the-Joneses (KUJ) motive unambiguously contributes to rational herding. When relative income is viewed as a measure of status, however, the KUJ motive is neither a necessary nor a sufficient condition. Concerns about status can contribute to rational herding either positively or negatively. Many questions need to be answered at the empirical level. The key empirical issues identified by this study include the effect of relative income on status, curvature of the utility curve with respect to status, and the effect of status on the marginal utility of one's own income. Answering these questions may take empirical and experimental studies examining both economic incentives and psychology.