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Related Experiment Videos

Why risk is not variance: an expository note.

Louis Anthony Tony Cox1

  • 1Cox Associates, 503 Franklin Street, Denver, CO 80218, USA. tcoxdenver@aol.com

Risk Analysis : an Official Publication of the Society for Risk Analysis
|June 17, 2008
PubMed
Summary
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Financial risk analysis often uses variance, but this study proves mean-variance decision-making is flawed. It violates the principle that rational decision-makers prefer higher probabilities of gain, even without complex utility theory.

Area of Science:

  • Decision Analysis
  • Risk Management
  • Financial Engineering

Background:

  • Variance is a common risk metric in financial analysis.
  • Health, safety, environmental (HS&E), and reliability engineering use flexible risk definitions (probability and consequence).
  • The discrepancy between these approaches warrants investigation.

Purpose of the Study:

  • To demonstrate that mean-variance decision-making violates fundamental principles of rational choice.
  • To explain why HS&E and reliability analysts prefer probability-consequence risk models over variance-based models.
  • To provide a simple mathematical proof accessible without advanced utility theory.

Main Methods:

  • A simple mathematical proof is presented.
  • The proof relies on the principle that rational decision-makers prefer higher probabilities of gain.

Related Experiment Videos

  • The analysis uses basic indifference curve concepts.

    • Main Results:

    • Mean-variance decision-making can lead to irrational choices, forcing acceptance of prospects with a positive probability of gain and zero probability of loss.
    • The study shows a violation of the preference for higher probabilities of fixed gains.
    • The findings are derived without invoking von Neumann-Morgenstern utility theory.

    Conclusions:

    • Variance is an inadequate measure of risk when considering rational decision-making principles.
    • Probability-consequence models offer a more robust framework for risk analysis in HS&E and reliability engineering.
    • Simple mathematical reasoning can reveal limitations in widely used financial risk metrics.