Diversification Preferences and Risk Attitudes

TL;DR

This paper explores the relationship between diversification preferences and risk attitudes, establishing conditions under which diversification behaviors imply different levels of risk aversion in decision-making.

Contribution

It provides a theoretical framework linking diversification preferences for various risk types to weak and strong risk aversion without assuming preference completeness.

Findings

Diversification for antimonotonic and identical risks implies weak risk aversion.

Exchangeable risk diversification is equivalent to strong risk aversion.

Independent risk diversification implies weak risk aversion under stronger continuity conditions.

Abstract

Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of diversification correspond to notions of risk aversion. We focus on the classical distinctions between weak and strong risk aversion, and consider diversification preferences for pairs of risks that are identically distributed, comonotonic, antimonotonic, independent, or exchangeable, as well as their intersections. Under a weak continuity condition and without assuming completeness of preferences, diversification for antimonotonic and identically distributed pairs implies weak risk aversion, and diversification for exchangeable pairs is equivalent to strong risk aversion. The implication from diversification for independent pairs to weak risk aversion requires a stronger continuity. We further provide results and examples that clarify the relationships between various diversification preferences and risk attitudes, in particular justifying the one-directional nature of many implications.