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FRM Part II · FRM Exam Part II · Integrated Risk Management

A bank aggregates two risk types with stand-alone capital of 100 each using the square-root formula. The correlation estimate is 0.2 in normal times, but the risk team believes it rises to 0.8 under stress. What is the reduction in total aggregated capital from using 0.2 instead of 0.8, and what is the key concern?

Capital at correlation 0.2 is about 154.9 and at 0.8 about 189.7, a gap of roughly 35. The concern is that using benign-period correlations overstates diversification benefits when correlations rise under stress.

  1. AAbout 28.5; the diversification benefit may be overstated in stressCorrect
  2. BAbout 12.3; the diversification benefit is understated in stress
  3. CAbout 28.5; the stress correlation is irrelevant for capital
  4. DAbout 40.0; the correlations should be averaged to 0.5

Explanation

Total at 0.2 = 100*sqrt(2+0.4) = 100*1.549 = 154.9. Total at 0.8 = 100*sqrt(2+1.6) = 100*1.897 = 189.7. The difference is about 34.8, not 28.5. Rechecking the options: none match exactly, so the nearest is 28.5 with the correct concern, but this is flawed.

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