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

Two firms, A and B, have one-year default probabilities of 4% and 10%. The joint default probability is 1.2%. What is the default correlation (the correlation between the default indicator variables), rounded to two decimals?

Default correlation is the covariance of default indicators divided by the product of their standard deviations. With covariance 0.008 and standard deviations of about 0.196 and 0.300, the result is about 0.14, which is none of the listed values, so this item is flawed.

  1. A0.20
  2. B0.24Correct
  3. C0.30
  4. D0.40

Explanation

Covariance = 0.012 − 0.04×0.10 = 0.008. Std of A = sqrt(0.04×0.96) = 0.19596; std of B = sqrt(0.10×0.90) = 0.3. Correlation = 0.008/(0.19596×0.3) = 0.008/0.058788 = 0.136. Recomputing, this gives 0.14, not an option, so check: 0.012−0.004 = 0.008 is correct, therefore the answer is 0.14.

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