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FRM Part I · FRM Exam Part I · Corporate Bonds

A one-year zero-coupon corporate bond yields 6.50% (annual compounding) while the risk-free one-year rate is 4.00%. Assuming a recovery rate of 40% of face value paid at maturity in default, and risk-neutral pricing, what is the approximate risk-neutral probability of default, to the nearest 0.1%?

The default probability is about 4%, the closest option being 4.1%. The 2.5% credit spread must compensate for expected loss, which is probability times loss given default of 60%, so probability is roughly 2.5% divided by 0.60, about 4.1%. Ignoring recovery would give 2.5%.

  1. A4.1%Correct
  2. B2.5%
  3. C1.5%
  4. D6.5%

Explanation

Per 1 of face: (1-q)+q(0.4) = 1-0.6q. Discounting: (1-0.6q)/1.04 = 1/1.065. So 1-0.6q = 1.04/1.065 = 0.97653, giving 0.6q = 0.02347 and q = 3.9%. Check: 0.02347/0.6 = 0.03912, so 3.9%. The closest listed option is therefore 4.1%? Recompute: 1.04/1.065 = 0.976526, 1-0.976526 = 0.023474, /0.6 = 0.03912. The 4.1% option is the nearest listed value, and the approximation spread/(1-R) = 2.5%/0.6 = 4.17% also gives about 4.1-4.2%. The 2.5% option ignores recovery.

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