Diversification for infinite-mean Pareto models without risk aversion

TL;DR

This paper demonstrates that for infinite-mean Pareto models, diversification universally enhances profitability without relying on risk aversion, contrasting with finite-mean scenarios.

Contribution

It establishes that diversification benefits in infinite-mean Pareto models are independent of risk preferences, extending stochastic dominance results to various Pareto-related distributions.

Findings

Diversification increases portfolio size in stochastic dominance sense.

The benefit holds across different Pareto tail scenarios and dependencies.

Diversification benefit is independent of risk aversion in infinite-mean models.

Abstract

We study stochastic dominance between portfolios of independent and identically distributed (iid) extremely heavy-tailed (i.e., infinite-mean) Pareto random variables. With the notion of majorization order, we show that a more diversified portfolio of iid extremely heavy-tailed Pareto random variables is larger in the sense of first-order stochastic dominance. This result is further generalized for Pareto random variables caused by triggering events, random variables with tails being Pareto, bounded Pareto random variables, and positively dependent Pareto random variables. These results provide an important implication in investment: Diversification of extremely heavy-tailed Pareto profits uniformly increases investors' profitability, leading to a diversification benefit. Remarkably, different from the finite-mean setting, such a diversification benefit does not depend on the decision maker's risk aversion.