Skip to content

FRM Part II · FRM Exam Part II · Estimating Default Probabilities

An analyst uses the approximation that the credit spread equals the hazard rate times (1 - recovery rate). A five-year bond trades at a spread of 240 basis points over the risk-free rate, and the assumed recovery rate is 40%. What is the implied average annual hazard rate, and the approximate five-year cumulative default probability using continuous compounding?

The hazard rate is 4.0% a year and the five-year cumulative default probability is about 18.1%. The spread of 2.4% divided by the 60% loss given default gives the hazard rate, and one minus exp of minus 0.04 times five gives the cumulative probability.

  1. A4.0% hazard rate; cumulative probability about 18.1%Correct
  2. B4.0% hazard rate; cumulative probability about 20.0%
  3. C2.4% hazard rate; cumulative probability about 11.3%
  4. D6.0% hazard rate; cumulative probability about 25.9%

Explanation

Hazard = 0.024/(1-0.4) = 4.0%. Cumulative probability = 1 - exp(-0.04*5) = 1 - exp(-0.2) = 1 - 0.8187 = 18.1%. The 20.0% option simply multiplies 4% by five, ignoring compounding of survival. The 2.4% option forgets to divide by the loss given default.

Did you get it right without looking?

One question tells you little. A timed set on Estimating Default Probabilities shows your real accuracy, how long you take and where you lose marks.

Practise Estimating Default ProbabilitiesFree diagnostic mock

More Estimating Default Probabilities questions