Skip to content

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

Two risk factors have a bivariate normal relationship. A stress scenario shocks factor X by -3 standard deviations. The correlation between X and Y is 0.6. Using the conditional expectation approach (standardized units), what is the expected move in Y, and what is the conditional standard deviation of Y as a fraction of its unconditional standard deviation?

The expected move in Y is correlation times the shock, 0.6 times -3, or -1.8 standard deviations. The conditional standard deviation is the square root of one minus 0.36, which is 0.80 of the unconditional value. Using 0.64 omits the square root.

  1. A-1.8 standard deviations; 0.80Correct
  2. B-1.8 standard deviations; 0.64
  3. C-3.0 standard deviations; 0.80
  4. D-0.6 standard deviations; 0.36

Explanation

Expected Y given X = rho x (-3) = 0.6 x -3 = -1.8 standard deviations. Conditional standard deviation = sqrt(1 - rho^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.80. The 0.64 option forgets the square root; -3.0 assumes perfect correlation.

Did you get it right without looking?

One question tells you little. A timed set on Market-Driven Scenarios: An Approach for Plausible Scenario Construction shows your real accuracy, how long you take and where you lose marks.

Practise Market-Driven Scenarios: An Approach for Plausible Scenario ConstructionFree diagnostic mock

More Market-Driven Scenarios: An Approach for Plausible Scenario Construction questions