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

A sovereign bond yields 9.0% and a comparable US Treasury yields 4.0%. Using the simple one-year approximation with a recovery rate of 40% and ignoring risk premia, what is the implied annual default probability of the sovereign?

The implied default probability is about 8.3%. The 5.0% yield spread equals default probability times loss given default, which is 60% when recovery is 40%. Dividing 5.0% by 0.60 gives roughly 8.3% per year.

  1. A5.0%
  2. B8.3%Correct
  3. C12.5%
  4. D3.0%

Explanation

Spread = 9.0% - 4.0% = 5.0%. Spread ≈ PD × (1 - recovery) = PD × 0.60, so PD = 5.0%/0.60 = 8.33%. Choosing 5.0% ignores recovery; 12.5% wrongly divides by the recovery rate of 40%; 3.0% multiplies spread by 0.6.

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