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FRM Part II · FRM Exam Part II · Market-Driven Scenarios: An Approach for Plausible Scenario Construction

A risk team constructs a stress scenario by shocking the equity index by -3 standard deviations and then, to measure plausibility, computes the Mahalanobis distance of the entire multi-factor shock vector from the historical mean. Which conclusion is most appropriate about using this measure?

A larger Mahalanobis distance signals a less plausible scenario. Because it uses the covariance matrix, it captures both shock size and whether the factors move together as they historically do, so a shock vector contradicting usual correlations is judged less likely even if individual shocks are moderate.

  1. AA scenario with a larger Mahalanobis distance is more plausible because it is more severe
  2. BThe Mahalanobis distance is unaffected by the correlations among risk factors, so it only measures the size of each shock
  3. CPlausibility is measured only by the largest single-factor shock, so the distance adds no information
  4. DA larger Mahalanobis distance indicates a less likely scenario, and it accounts for correlations so a shock vector that conflicts with historical co-movements is judged less plausibleCorrect

Explanation

Mahalanobis distance scales deviations by the covariance matrix, so it reflects both magnitude and consistency with historical co-movements. Larger distance means a less likely scenario. Options claiming it ignores correlation or that severity implies plausibility are wrong.

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