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

In the Vasicek single-factor model for a large homogeneous portfolio, each borrower's latent asset value is driven by a common factor and an idiosyncratic factor. As the number of borrowers grows very large, which statement best describes the portfolio's loss rate?

The loss rate converges to the default probability conditional on the common factor. Idiosyncratic risk is diversified away in a large homogeneous portfolio, leaving only systematic risk, so the loss rate stays random through the common factor and is not fixed at the unconditional PD.

  1. AIt converges to a function of the common factor alone, because idiosyncratic risk diversifies awayCorrect
  2. BIt converges to the unconditional default probability in every state of the economy
  3. CIt becomes independent of the asset correlation parameter
  4. DIt becomes normally distributed with mean equal to the default probability

Explanation

With many obligors the idiosyncratic shocks average out, so the realised default rate equals the conditional default probability given the common factor. The loss rate therefore remains random through the common factor only. The unconditional PD is only the mean of that distribution, not its value in each state, and the distribution is not normal.

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