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FRM Part II · FRM Exam Part II · Credit Value at Risk

A portfolio manager applies CreditMetrics to two bonds from different issuers. Compared with assuming independent rating migrations, what happens to portfolio credit VaR when asset return correlation between the issuers is set positive, and how is the joint migration distribution derived?

Portfolio credit VaR rises with positive correlation. CreditMetrics derives joint migration probabilities from a correlated multivariate normal asset-return model, with rating thresholds calibrated to each obligor's transition probabilities, making joint downgrades and defaults more likely than under independence.

  1. AVaR rises; joint probabilities come from a multivariate normal asset-return model with thresholds set from transition probabilitiesCorrect
  2. BVaR falls; joint probabilities are the product of marginal transition probabilities
  3. CVaR rises; joint probabilities are read directly from the transition matrix
  4. DVaR is unchanged; correlation affects only expected value

Explanation

CreditMetrics links each obligor's rating thresholds to asset return levels consistent with its transition probabilities and uses a correlated normal asset-return model to get joint migration probabilities. Positive correlation raises the chance of simultaneous downgrades or defaults, fattening the loss tail and raising VaR. Multiplying marginals assumes independence, which is wrong here.

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