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FRM Part II · FRM Exam Part II · Portfolio Credit Risk

Two obligors each have a one-year default probability of 10%. The joint default probability is 3%. What is the default correlation between them?

The default correlation is about 0.22. The covariance is the joint default probability 3% minus the product 1%, which is 2%. Dividing by the variance of 0.09 for each obligor gives 0.0222/0.09, which equals roughly 0.222.

  1. A0.20
  2. B0.22Correct
  3. C0.30
  4. D0.025

Explanation

Covariance = 0.03 - 0.1*0.1 = 0.02. Each variance = 0.1*0.9 = 0.09, so the standard deviation is 0.3. Correlation = 0.02/0.09 = 0.222. The option 0.20 uses 0.02 divided by 0.10, the wrong base. The option 0.30 is the joint probability divided by the standard deviation, which is also incorrect.

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