FRM Part I · FRM Exam Part I · Corporate Bonds
A 1-year zero-coupon corporate bond yields 7% and the 1-year risk-free rate is 3%, both with annual compounding. Assume a recovery rate of 40% on default and that recovery is paid at maturity. Using the approximation that the spread equals the default probability times loss given default, what is the implied 1-year default probability?
The implied default probability is about 6.67%. The spread is 4% and loss given default is 60% after a 40% recovery, so default probability is 4% divided by 0.60. Ignoring recovery would wrongly give 4%.
- A6.67%Correct
- B4.00%
- C10.00%
- D2.67%
Explanation
Spread = 7% - 3% = 4%. LGD = 1 - 0.40 = 60%. PD = 4%/0.60 = 6.67%. Ignoring recovery gives 4.00%; multiplying 4% by 0.6 gives 2.40%, and dividing by the recovery rate gives 10.00%.
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