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

A sovereign has a bond yielding 7.5% in US dollars. The US Treasury bond of the same maturity yields 4.0%. Historical data suggest an annual default probability implied by the spread, assuming a recovery rate of 30% and using the approximation spread = default probability x (1 - recovery rate). What is the implied annual default probability?

The implied annual default probability is 5.0%. The spread is 7.5% minus 4.0%, or 3.5%, and loss given default is 70% with 30% recovery. Dividing 3.5% by 0.70 gives 5.0%, consistent with spread equals default probability times loss given default.

  1. A3.5%
  2. B5.0%Correct
  3. C11.7%
  4. D2.45%

Explanation

Spread = 7.5% - 4.0% = 3.5%. Loss given default = 1 - 0.30 = 0.70. Default probability = 3.5% / 0.70 = 5.0%. Check: 5.0% x 0.70 = 3.5%. Option A ignores recovery, option D multiplies spread by 0.70 instead of dividing, and option C divides by the recovery rate (3.5/0.30).

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