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

A risk analyst compares two portfolios of 100 identical loans, each with a 2% one-year default probability. In Portfolio A defaults are independent. In Portfolio B the pairwise default correlation is positive. Which statement best describes the effect of the positive default correlation on Portfolio B relative to Portfolio A?

Positive default correlation leaves the expected number of defaults unchanged because it depends only on the default probabilities, but it raises loss variance and fattens the right tail of the loss distribution, making large clustered defaults more likely.

  1. AThe expected number of defaults is higher, while the loss distribution has the same tails
  2. BThe expected number of defaults is unchanged, but the loss distribution has a fatter right tailCorrect
  3. CThe expected number of defaults is lower, but the variance of losses is higher
  4. DBoth the expected number of defaults and the variance of losses are unchanged

Explanation

Expected defaults equal N times PD, so they are 2 in both portfolios. Positive correlation adds covariance terms, increasing loss variance and making clusters of defaults more likely, which fattens the right tail. The option claiming higher expected defaults confuses the mean with the dispersion.

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