Skip to content

FRM Part II · FRM Exam Part II · Structured Credit Risk

A credit analyst compares two portfolios of 100 identical loans, each with a 4% one-year default probability. In Portfolio A the Gaussian copula asset correlation is 0.05 and in Portfolio B it is 0.45. Which statement about the one-year default count distributions is most accurate?

Both portfolios expect four defaults, but the higher-correlation portfolio has a larger variance in the number of defaults. Correlation does not change marginal default probabilities or the mean, yet it increases covariance between defaults and therefore widens and fattens the tails of the default count distribution.

  1. ABoth portfolios have the same expected number of defaults, but Portfolio B has a larger variance of the number of defaultsCorrect
  2. BPortfolio B has a higher expected number of defaults because of its higher correlation
  3. CPortfolio A has a larger variance of the number of defaults because diversification is lower
  4. DBoth portfolios have identical default count distributions because marginal probabilities are equal

Explanation

Expected defaults equal 100 x 4% = 4 in both portfolios regardless of correlation. Variance of the default count is the sum of individual variances plus covariance terms, which increase with default correlation. Portfolio B's higher correlation therefore produces a fatter-tailed, wider distribution.

Did you get it right without looking?

One question tells you little. A timed set on Structured Credit Risk shows your real accuracy, how long you take and where you lose marks.

Practise Structured Credit RiskFree diagnostic mock

More Structured Credit Risk questions