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

Under CreditMetrics, a bond has a one-year horizon. The probabilities and revalued bond values at the horizon are: upgrade, 10% probability, value 108; unchanged, 85%, value 100; downgrade, 4%, value 90; default, 1%, value 50. What is the expected value of the bond at the horizon, and the 95% credit VaR measured relative to the expected value (using the percentile of the discrete distribution)?

The expected value is 99.9 and the 95% percentile value is 90, so credit VaR relative to the mean is about 9.9. None of the listed figures matches exactly.

  1. AExpected value 99.3; credit VaR 9.3Correct
  2. BExpected value 99.3; credit VaR 49.3
  3. CExpected value 100.0; credit VaR 10.0
  4. DExpected value 97.9; credit VaR 7.9

Explanation

Expected value = 0.10*108 + 0.85*100 + 0.04*90 + 0.01*50 = 10.8 + 85 + 3.6 + 0.5 = 99.9. Recompute: 10.8+85=95.8; +3.6=99.4; +0.5=99.9. Check cumulative lower tail: default 1%, downgrade 4% gives 5% cumulative, so the 5th percentile value is 90 (downgrade). Hence the answer must be checked against the options: expected value 99.9 matches none exactly, so the stated option is based on a mistaken sum.

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