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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A reduced-form model assumes a constant hazard rate of 2% per year and a recovery rate of 40% of face value. Using the credit triangle approximation, what is the annual credit spread, and approximately what is the five-year cumulative default probability using the exponential survival function (1 - e^(-0.1))?

The spread is about 120 basis points, computed as the 2% hazard rate times the 60% loss given default. The five-year cumulative default probability is 1 minus e to the power of minus 0.1, roughly 9.5%. Quoting 200 bps would ignore the recovery rate.

  1. ASpread of 120 bps; cumulative probability about 9.5%Correct
  2. BSpread of 200 bps; cumulative probability about 9.5%
  3. CSpread of 120 bps; cumulative probability about 10.0%
  4. DSpread of 80 bps; cumulative probability about 18.1%

Explanation

Spread ≈ hazard × (1 − recovery) = 2% × 0.60 = 1.20% = 120 bps. Cumulative probability = 1 − e^(−0.02×5) = 1 − e^(−0.1) = 1 − 0.9048 = 9.52%. Using 200 bps ignores recovery.

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