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

A bank uses the approximation that a sovereign CDS spread equals the annual default probability times loss given default (the credit triangle). The five-year CDS spread on Country Z is 3.00% and the assumed recovery rate is 40%. What is the implied annual risk-neutral default probability, and why might it overstate the real-world default probability?

The implied annual risk-neutral default probability is 5.00%, found by dividing the 3.00% spread by the 60% loss given default. It tends to overstate real-world default probability because the spread embeds risk premia and liquidity compensation as well as expected loss, so it is a risk-neutral measure.

  1. A5.00%; because the spread also includes risk premia and liquidity compensation beyond expected lossCorrect
  2. B1.80%; because the spread ignores the recovery rate
  3. C5.00%; because CDS spreads exclude any compensation for risk aversion
  4. D7.50%; because recovery was assumed to be zero

Explanation

LGD = 1 - 40% = 60%. Default probability = 3.00% / 0.60 = 5.00%. Check: 5.00% x 60% = 3.00%. Option 2 multiplies spread by LGD instead of dividing. Option 4 uses 40% as LGD (3/0.4). The spread includes risk premia, so the risk-neutral probability exceeds the real-world one.

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