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

A risk manager simulates default times for a portfolio of 100 obligors with a one-factor Gaussian copula, in which each obligor's latent variable is x_i = √ρ·M + √(1-ρ)·Z_i. She increases ρ from 0.10 to 0.40 while keeping every obligor's marginal default probability unchanged. Which outcome is most likely for the portfolio loss distribution?

Expected loss stays roughly the same because marginal default probabilities are fixed, but a higher copula correlation increases clustering of defaults. The loss distribution becomes more dispersed, with a fatter right tail and more scenarios of both very many and very few defaults.

  1. AExpected portfolio loss rises materially while tail losses stay unchanged
  2. BExpected portfolio loss falls and the distribution becomes more symmetric
  3. CExpected portfolio loss is roughly unchanged, but the distribution gets fatter in the right tail, with more probability of many joint defaults and also of very few defaultsCorrect
  4. DBoth expected loss and loss volatility are unchanged because marginals are unchanged

Explanation

Expected loss depends on marginal default probabilities, which are fixed. Higher ρ increases the weight of the common factor M, so defaults cluster: more scenarios with very many defaults and more with very few. Loss variance and tail risk rise, so options 1, 2 and 4 are wrong.

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