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

Two candidate scenarios each produce the same portfolio loss. Scenario X shocks equity by -20% with implied moves in other factors drawn from historical relationships, and its Mahalanobis distance from normal market conditions is 3.0. Scenario Y has a Mahalanobis distance of 5.0. A manager wants the most plausible scenario among equal-loss alternatives for setting a stress limit. Which choice is best?

Scenario X is preferable. Mahalanobis distance measures how unusual a combination of shocks is given historical covariances, so a smaller distance means the scenario is more likely. With equal losses, the more plausible scenario gives a better basis for a stress limit.

  1. AScenario Y, since a larger distance means higher likelihood
  2. BScenario X, since a smaller Mahalanobis distance indicates the scenario is more likely given historical co-movementsCorrect
  3. CNeither, since the distance says nothing about plausibility
  4. DBoth are equally plausible because losses are equal

Explanation

Mahalanobis distance measures how unusual a shock vector is relative to the historical covariance structure; a smaller distance means greater likelihood. With equal losses, X is more plausible and better supports a limit. Choosing Y confuses extremeness with likelihood.

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