Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket

L\'eonard Vincent

Papers from arXiv.org

Abstract: Conventional wisdom warns against "putting all your eggs in one basket," and diversification is widely regarded as a reliable strategy for reducing risk. Yet under certain extreme conditions, this intuition not only fails - it reverses. This paper explores such reversals by identifying new settings in which diversification increases risk. Our main result - the one-basket theorem - provides sufficient conditions under which a weighted average of independent risks is larger, in the sense of first-order stochastic dominance, than a corresponding mixture model that concentrates all exposure on a single risk chosen at random. Our framework handles non-identically distributed risks and includes new examples, such as infinite-mean discrete Pareto variables and the St. Petersburg lottery. We further show that these reversals are not isolated anomalies, but boundary cases of a broader phenomenon: diversification always increases the likelihood of exceeding small thresholds, and under specific conditions, this local effect extends globally, resulting in first-order stochastic dominance.

Date: 2025-07
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2507.16265 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2507.16265

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().