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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A five-year CDS spread on a firm is 150 basis points and the recovery rate is 40%. Historical data for the firm's rating class show an average annual default intensity of 1.8%. Using the approximation hazard rate = spread/(1-R), the ratio of risk-neutral to real-world default intensity and the correct interpretation are:

The risk-neutral hazard rate is 1.5%/0.6 = 2.5%, which is about 1.39 times the 1.8% real-world intensity. The risk-neutral rate exceeds the historical one, consistent with investors demanding positive compensation for default risk beyond expected loss.

  1. ARatio about 1.39; risk-neutral intensity exceeds real-world, consistent with positive risk premiaCorrect
  2. BRatio about 0.72; risk-neutral intensity is below real-world, indicating mispricing by the market
  3. CRatio about 1.39; real-world intensity exceeds risk-neutral, indicating negative risk premia
  4. DRatio about 0.83; the two intensities are consistent after adjusting for recovery

Explanation

Risk-neutral hazard rate = 1.50%/(1-0.40) = 2.5%. Ratio = 2.5%/1.8% = 1.389. Because the implied rate exceeds the historical rate, the market is charging a premium for default risk, which is the normal pattern. Option B inverts the ratio (1.8/2.5 = 0.72).

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