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FRM Part I · FRM Exam Part I · Corporate Bonds

A bond has a constant annual hazard rate (default intensity) of 2% and a recovery rate of 40% of face value. Using the credit triangle approximation, which credit spread is implied, and what is the cumulative probability of default over 5 years assuming continuous compounding?

The credit triangle gives spread as hazard rate times loss given default: 2% x 60% = 120 basis points. Five-year cumulative default probability is 1 minus exp(-0.10), about 9.5%. Adding 2% five times to get 10% ignores survival compounding, and 200 bps ignores recovery.

  1. A120 bps spread; 9.5% five-year default probabilityCorrect
  2. B200 bps spread; 9.5% five-year default probability
  3. C120 bps spread; 10.0% five-year default probability
  4. D200 bps spread; 18.1% five-year default probability

Explanation

Spread ≈ hazard x (1 - R) = 0.02 x 0.60 = 1.20% = 120 bps. Cumulative PD = 1 - exp(-0.02 x 5) = 1 - 0.9048 = 9.52%. The 200 bps option forgets LGD; 10.0% is the simple sum of annual rates, ignoring compounding of survival.

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