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

Two candidate scenarios shock equities by -3 standard deviations. Scenario A also has credit spreads rising by 1.5 standard deviations. Scenario B has spreads falling by 1.5 standard deviations. Equity and spread changes are bivariate normal with correlation -0.5. Plausibility is measured by the squared Mahalanobis distance, (z1^2 - 2*rho*z1*z2 + z2^2)/(1 - rho^2), with z1 = -3 and z2 = +1.5 or -1.5 for A and B. Which statement is correct?

Scenario A is more plausible, with a squared Mahalanobis distance of 9 versus 21 for B. With negative correlation, spreads widening as equities fall is consistent with history, while spreads tightening in the same crash is not, so B is farther from the center of the distribution.

  1. AA is more plausible, with a distance of 9 against 21 for BCorrect
  2. BB is more plausible, because its spread move is smaller in magnitude and its distance is 9
  3. CThe scenarios are equally plausible, because both have the same equity shock and the same spread magnitude
  4. DA is more plausible, with a distance of 21 against 9 for B

Explanation

For A: (9 + 2.25 - 2(-0.5)(-4.5))/0.75 = (11.25 - 4.5)/0.75 = 9. For B: z1z2 = +4.5, so (11.25 + 4.5)/0.75 = 21. A has the lower distance because spreads widening alongside an equity fall fits the negative correlation. B is less plausible despite the same marginal sizes.

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