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FRM Part I · FRM Exam Part I · Country Risk: Determinants, Measures, and Implications

A sovereign bond yields 7.5% in US dollars, while a US Treasury bond of the same maturity yields 4.0%. Assuming a recovery rate of 0%, and a one-year horizon with annual compounding, what is the approximate market-implied one-year probability of default for the sovereign? (Assume risk-neutral pricing.)

The implied default probability is about 3.26%. With zero recovery, the risk-neutral condition (1−p)×1.075 = 1.04 gives p = 1 − 1.04/1.075, which is roughly 3.26%, slightly less than the 3.5% raw spread.

  1. A3.26%Correct
  2. B3.50%
  3. C4.67%
  4. D7.50%

Explanation

With zero recovery, (1-p)(1.075)=1.04, so 1-p=0.96744 and p=3.26%. The 3.50% option is the simple spread, which ignores that the yield is paid on the promised amount. The 4.67% option wrongly divides the spread by the risk-free rate in the denominator, and 7.5% is just the yield.

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