FRM Part I · FRM Exam Part I · Corporate Bonds
A one-year zero-coupon bond has a face value of $100, a 40% recovery rate on default (paid at maturity) and a one-year risk-free rate of 5%. The bond trades to yield 7.00% (annual compounding). Using the approximation that the risk-neutral price equals the expected payoff discounted at the risk-free rate, what is the implied risk-neutral default probability closest to?
The price is 100/1.07 = 93.46, so the expected payoff is 93.46 x 1.05 = 98.13. Setting 100 minus 60p equal to 98.13 gives a default probability of about 3.1%, closest to 3.3%.
- A3.3%Correct
- B2.0%
- C3.5%
- D5.0%
Explanation
Price = 100/1.07 = 93.458. Expected payoff = 93.458 x 1.05 = 98.131. Payoff = 100 - 60p, so p = (100 - 98.131)/60 = 3.115%. Closest is 3.3%. Check: 2.0% is the spread divided by one, 3.5% is (spread)/(1-R) = 2/0.6 ignoring discounting, 5.0% is the risk-free rate.
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