Nonnegative risk components

Jeremy Staum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We propose two new methods for attributing the risk of a portfolio or system to its components, in particular when it is required to produce nonnegative risk components that sum to the risk of the portfolio or system as a whole. The first method attributes risk entirely to losses, taking profits for granted. The second method allows profits in some scenarios to offset losses in other scenarios to a certain extent, but not in a way that could yield a negative risk component. We illustrate these methods by applying them to an example in which we attribute a firm’s expected shortfall to business units within the firm and an example in which we attribute systemic risk to banks. We prove that, under appropriate conditions, the methods proposed have some game-theoretic properties that are desirable for risk attribution.

Original languageEnglish (US)
JournalJournal of Risk
Issue number2
StatePublished - Dec 2015


  • Cost allocation
  • Cost attribution
  • Risk allocation
  • Risk attribution
  • Risk components
  • Systemic risk

ASJC Scopus subject areas

  • Finance
  • Strategy and Management

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