Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification

Author:

Chen Yuyu1ORCID,Embrechts Paul2,Wang Ruodu3ORCID

Affiliation:

1. Department of Economics, University of Melbourne, Melbourne, Victoria 3010, Australia;

2. RiskLab, Department of Mathematics and ETH Risk Center, ETH Zurich, 8092 Zurich, Switzerland;

3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Abstract

Diversification is generally regarded as an efficient tool to reduce portfolio risks. In “An unexpected stochastic dominance: Pareto distributions, dependence, and diversification,” Chen, Embrechts, and Wang showed that the weighted average of independent and identically distributed (i.i.d.) Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic dominance, and thus diversification is, surprisingly, worse than no diversification. The relation implies superadditivity of value-at-risk, a regulatory risk measure used in the finance and insurance sectors. The obtained relation also holds under some form of negative dependence.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

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