Skip to content

FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

A analyst uses a one-factor Gaussian copula to model defaults of a large homogeneous loan portfolio. Each obligor's latent variable is M_i = sqrt(rho)*Z + sqrt(1-rho)*e_i. The analyst increases rho from 0.10 to 0.40 while leaving each obligor's default probability unchanged. Which is the most likely effect on the portfolio loss distribution?

Expected loss stays the same because individual default probabilities are unchanged, but higher correlation increases clustering of defaults. This fattens the tail of the loss distribution, raising the probability of extreme portfolio losses.

  1. AThe expected loss rises and the tails become thinner
  2. BThe expected loss is unchanged and the probability of extreme portfolio losses increasesCorrect
  3. CThe expected loss falls and the distribution becomes more symmetric
  4. DBoth the expected loss and the tail probability are unchanged because individual default probabilities are unchanged

Explanation

Expected loss depends on individual default probabilities, which are unchanged. Higher correlation raises the weight of the common factor, so defaults cluster, fattening the right tail (more probability of both very few and very many defaults). Option D is wrong because the tail changes even though the mean does not.

Did you get it right without looking?

One question tells you little. A timed set on Financial Correlation Modeling - Bottom-Up Approaches shows your real accuracy, how long you take and where you lose marks.

Practise Financial Correlation Modeling - Bottom-Up ApproachesFree diagnostic mock

More Financial Correlation Modeling - Bottom-Up Approaches questions