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Aggregation of downside risk and portfolio selection

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  • Spanaus, Conrad
  • Wenzelburger, Jan

Abstract

This article refines Markowitz’s classical portfolio theory by replacing standard deviation with a below-target deviation measure referred to as downside risk, in which only returns below the safe return of the market contribute to the quantification of risk. Downside risk is economically intuitive but neither a general deviation nor a coherent risk measure. We establish the existence and uniqueness of downside-efficient portfolios that aggregate the downside risks of finitely many assets. The tractability of downside-efficient portfolios allows for a risk analysis that parallels the classical mean–variance analysis. We show that all central tenets carry over if standard deviation is substituted with downside risk. A numerical example illustrates when downside-efficient portfolios outperform mean–variance efficient portfolios.

Suggested Citation

  • Spanaus, Conrad & Wenzelburger, Jan, 2025. "Aggregation of downside risk and portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    • Handle: RePEc:eee:mateco:v:119:y:2025:i:c:s0304406825000552
    DOI: 10.1016/j.jmateco.2025.103138
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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