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

Using a jointly normal, zero-mean framework, an analyst finds that after a -2.5 standard deviation shock to an equity index, the conditional expected move in a credit spread factor is +1.75 of its own standard deviations (spread widening). What correlation between the two factors is implied, and what is the standard deviation of the spread factor conditional on the shock if the unconditional standard deviation is 50 bp?

The implied correlation is -0.70 and the conditional standard deviation is about 35.7 bp. The correlation comes from 1.75 divided by -2.5, and conditioning shrinks volatility by the factor square root of (1 minus 0.49), applied to 50 bp.

  1. ACorrelation -0.70; conditional standard deviation 35.7 bpCorrect
  2. BCorrelation -0.70; conditional standard deviation 50 bp
  3. CCorrelation +0.70; conditional standard deviation 35.7 bp
  4. DCorrelation -0.70; conditional standard deviation 25.5 bp

Explanation

Expected standardized move = rho * (-2.5) = +1.75, so rho = -0.70. Conditional standard deviation = sigma*sqrt(1-rho^2) = 50*sqrt(1-0.49) = 50*0.7141 = 35.7 bp. Keeping 50 bp ignores that conditioning reduces dispersion; the sign cannot be positive as the spread widens when equities fall.

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