Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912958889590784 |
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| author | Vincent, Léonard |
| author_facet | Vincent, Léonard |
| contents | Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this reversal by comparing a diversified portfolio (a weighted average) of risks to a "one-basket" benchmark that concentrates the full exposure on a single component chosen at random according to the same weights. In the iid case, the benchmark reduces to a single risk, recovering the classical comparison between a single risk and a diversified portfolio. Our main result -- the one-basket theorem -- provides new sufficient conditions under which the diversified portfolio has larger tail probabilities for all thresholds (first-order stochastic dominance) than this benchmark. The theorem enables weight-specific verification of the stochastic dominance relation and yields new applications, notably to averages of infinite-mean discrete Pareto risks. We further show that these failures of diversification are boundary cases of a general phenomenon: diversification always increases the likelihood of exceeding thresholds near zero, and under specific conditions this local effect extends to all thresholds, yielding first-order stochastic dominance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16265 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket Vincent, Léonard Risk Management Probability 60E15 (Primary) 60G70, 60G50, 91G10 (Secondary) Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this reversal by comparing a diversified portfolio (a weighted average) of risks to a "one-basket" benchmark that concentrates the full exposure on a single component chosen at random according to the same weights. In the iid case, the benchmark reduces to a single risk, recovering the classical comparison between a single risk and a diversified portfolio. Our main result -- the one-basket theorem -- provides new sufficient conditions under which the diversified portfolio has larger tail probabilities for all thresholds (first-order stochastic dominance) than this benchmark. The theorem enables weight-specific verification of the stochastic dominance relation and yields new applications, notably to averages of infinite-mean discrete Pareto risks. We further show that these failures of diversification are boundary cases of a general phenomenon: diversification always increases the likelihood of exceeding thresholds near zero, and under specific conditions this local effect extends to all thresholds, yielding first-order stochastic dominance. |
| title | Diversification and Stochastic Dominance: When All Eggs Are Better Put in One Basket |
| topic | Risk Management Probability 60E15 (Primary) 60G70, 60G50, 91G10 (Secondary) |
| url | https://arxiv.org/abs/2507.16265 |