Naive Diversification Preferences and their Representation

TL;DR

This paper provides a formal foundation for naive diversification, showing it as a preference for equality over inequality, characterized by permutation invariance and convexity, with implications for utility functions and rebalancing transformations.

Contribution

It offers a mathematically rigorous axiomatization of naive diversification, linking it to permutation invariance, Schur-concavity, and turnover in decision weights.

Findings

Naive diversification is characterized by permutation invariance and convex preferences.

Schur-concave utility functions model inequality aversion alongside risk aversion.

Rebalancing transformations are described in terms of their turnover implications.

Abstract

A widely applied diversification paradigm is the naive diversification choice heuristic. It stipulates that an economic agent allocates equal decision weights to given choice alternatives independent of their individual characteristics. This article provides mathematically and economically sound choice theoretic foundations for the naive approach to diversification. We axiomatize naive diversification by defining it as a preference for equality over inequality and derive its relationship to the classical diversification paradigm. In particular, we show that (i) the notion of permutation invariance lies at the core of naive diversification and that an economic agent is a naive diversifier if and only if his preferences are convex and permutation invariant; (ii) Schur-concave utility functions capture the idea of being inequality averse on top of being risk averse; and (iii) the transformations, which rebalance unequal decision weights to equality, are characterized in terms of their implied turnover.