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FRM Part I · FRM Exam Part I · Measuring Credit Risk

In a Merton model, a firm's zero-coupon debt has a face value of 150 million and matures in one year. The continuously compounded risk-free rate is 4%, and the model-implied market value of the debt is 138.12 million. What is the credit spread over the risk-free rate, using continuous compounding? (ln(1.0860) = 0.0825)

The credit spread is about 4.25%. The continuously compounded yield on the risky debt is ln(150/138.12), about 8.25%, and subtracting the 4% risk-free rate leaves roughly 4.25%. Using simple returns or forgetting to subtract the risk-free rate gives wrong answers.

  1. AApproximately 4.25%Correct
  2. BApproximately 4.60%
  3. CApproximately 8.25%
  4. DApproximately 2.15%

Explanation

The risky yield is ln(150/138.12)/1 = ln(1.0860) ≈ 8.25%. The spread is 8.25% - 4.00% = 4.25%. Using simple return (8.60%) gives 4.60%, which is inconsistent with continuous compounding. Reporting the yield itself gives 8.25%, which omits subtracting the risk-free rate.

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