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What's Wrong with Risk Matrices?

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  • Louis Anthony (Tony)Cox

Abstract

Risk matrices—tables mapping “frequency” and “severity” ratings to corresponding risk priority levels—are popular in applications as diverse as terrorism risk analysis, highway construction project management, office building risk analysis, climate change risk management, and enterprise risk management (ERM). National and international standards (e.g., Military Standard 882C and AS/NZS 4360:1999) have stimulated adoption of risk matrices by many organizations and risk consultants. However, little research rigorously validates their performance in actually improving risk management decisions. This article examines some mathematical properties of risk matrices and shows that they have the following limitations. (a) Poor Resolution. Typical risk matrices can correctly and unambiguously compare only a small fraction (e.g., less than 10%) of randomly selected pairs of hazards. They can assign identical ratings to quantitatively very different risks (“range compression”). (b) Errors. Risk matrices can mistakenly assign higher qualitative ratings to quantitatively smaller risks. For risks with negatively correlated frequencies and severities, they can be “worse than useless,” leading to worse‐than‐random decisions. (c) Suboptimal Resource Allocation. Effective allocation of resources to risk‐reducing countermeasures cannot be based on the categories provided by risk matrices. (d) Ambiguous Inputs and Outputs. Categorizations of severity cannot be made objectively for uncertain consequences. Inputs to risk matrices (e.g., frequency and severity categorizations) and resulting outputs (i.e., risk ratings) require subjective interpretation, and different users may obtain opposite ratings of the same quantitative risks. These limitations suggest that risk matrices should be used with caution, and only with careful explanations of embedded judgments.

Suggested Citation

  • Louis Anthony (Tony)Cox, 2008. "What's Wrong with Risk Matrices?," Risk Analysis, John Wiley & Sons, vol. 28(2), pages 497-512, April.
    • Handle: RePEc:wly:riskan:v:28:y:2008:i:2:p:497-512
    DOI: 10.1111/j.1539-6924.2008.01030.x
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    References listed on IDEAS

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    1. Louis Anthony (Tony) Cox & Djangir Babayev & William Huber, 2005. "Some Limitations of Qualitative Risk Rating Systems," Risk Analysis, John Wiley & Sons, vol. 25(3), pages 651-662, June.
    2. Louis Anthony (Tony) Cox & Douglas A. Popken, 2007. "Some Limitations of Aggregate Exposure Metrics," Risk Analysis, John Wiley & Sons, vol. 27(2), pages 439-445, April.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    4. Dimitris Bertsimas & José Niño-Mora, 1996. "Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 257-306, May.
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