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

Using a conditional expected shock approach, a risk manager stresses factor X by 3 standard deviations. Factor Y has correlation 0.5 with X. Under joint normality, what is Y's conditional expected shock in Y standard deviations, and how does its conditional volatility compare with its unconditional volatility?

Y's conditional expected shock is 1.5 of its standard deviations (0.5 times 3), and its conditional volatility falls to about 0.87 of its unconditional level because variance is scaled by one minus the squared correlation, 0.75.

  1. A1.5 standard deviations; conditional volatility is lower, about 0.87 of unconditionalCorrect
  2. B3.0 standard deviations; conditional volatility equals unconditional
  3. C1.5 standard deviations; conditional volatility is unchanged
  4. D0.5 standard deviations; conditional volatility is about 0.87 of unconditional

Explanation

Expected shock = rho x 3 = 1.5 sigma_Y. Conditional variance = sigma_Y^2(1 - rho^2) = 0.75, so volatility is sqrt(0.75) = 0.866 of unconditional. Leaving volatility unchanged ignores the information gained from X.

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