FRM Part I · FRM Exam Part I · Corporate Bonds
A one-year zero-coupon corporate bond is priced to yield 6.00% while the risk-free one-year rate is 4.00%, both annually compounded. Assuming investors are risk neutral and the recovery rate on default is 50% of face value paid at maturity, what is the approximate implied one-year probability of default (closest value)?
Under risk neutrality the promised payoff of 1.06 less the default shortfall must equal the risk-free growth of 1.04. Solving 1.04 = 1.06 - 0.56q gives a default probability of about 3.6%, closest to 3.8%. Ignoring recovery would understate default probability at about 1.9%.
- A3.8%Correct
- B1.9%
- C2.0%
- D7.6%
Explanation
Risk-neutral pricing: (1+0.04) = (1-q)(1.06) + q(0.5). So 1.04 = 1.06 - 0.56q, giving q = 0.02/0.56 = 3.57%, closest to 3.8%. Option 2.0% ignores recovery (0.02/1.06 ≈ 1.9%), and 7.6% is double-counting.
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