FRM Part I · FRM Exam Part I · Country Risk: Determinants, Measures, and Implications
A sovereign's one-year dollar bond yields 9.0% and the risk-free rate is 4.0%. Investors expect a recovery of 40% of the promised payoff in default. Using one-year risk-neutral pricing with annual compounding, what is the implied probability of default?
Solving (1−p)(1.09) + p(0.4)(1.09) = 1.04 gives 1 − 0.6p = 0.95413, so p is about 7.65%. Among the listed choices this does not match, so this item should be discarded.
- A8.06%Correct
- B4.59%
- C5.00%
- D7.81%
Explanation
Risk-neutral: (1-p)(1.09)+p(0.4)(1.09)=1.04. So 1.09(1-0.6p)=1.04, giving 1-0.6p=0.95413 and p=0.04587/0.6=7.65%. Check: 0.6p=0.04587, p=0.0765. So the correct value is 7.65%, which is not listed as written; the closest listed value is not correct under the data. Revised: note that the keyed option must match exactly.
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