Skip to content

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

A risk analyst observes a one-year zero-coupon corporate bond yielding 7.00% and a one-year risk-free zero-coupon bond yielding 4.00% (both annually compounded). Assuming a recovery rate of 40% of the face value paid at maturity, what is the approximate risk-neutral one-year probability of default?

The risk-neutral default probability is about 5%. The 3% credit spread equals the expected loss rate, which is default probability times loss given default of 60%. Dividing 3% by 0.60 gives 5%. Ignoring recovery would wrongly give 3%.

  1. A3.00%
  2. B5.00%Correct
  3. C7.50%
  4. D12.50%

Explanation

Using the exact approach: (1-Q)+Q*R = 1.04/1.07 = 0.97196. So 1 - Q(1-R) = 0.97196, giving Q*0.6 = 0.02804 and Q = 4.67%, about 5%. The approximation spread/(1-R) = 3%/0.6 = 5.00%. Option 3.00% ignores recovery and treats the spread as the default probability.

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