Skip to content

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

A one-year zero-coupon corporate bond yields 6.00% and the comparable risk-free zero yields 4.00% (both annually compounded). Recovery rate is 40% of face value. Using the one-year approximation that the risk-neutral default probability Q satisfies (1+r_f)/(1+y) = (1-Q) + Q*R, the risk-neutral default probability is closest to:

The risk-neutral default probability is about 3.14%. Setting the bond price equal to the expected payoff discounted at the risk-free rate gives 1 − 0.6Q = 1.04/1.06 = 0.98113, so Q = 0.018868/0.6 ≈ 3.14%, slightly below the simple spread over loss-given-default figure.

  1. A3.33%
  2. B3.14%Correct
  3. C5.24%
  4. D2.00%

Explanation

Ratio = 1.04/1.06 = 0.981132 hmm, this is the PV ratio: the bond's expected payoff discounted at the risk-free rate equals its price, so 1.04... Precisely: price = (1-Q+QR)/1.04 = 1/1.06, so 1-0.6Q = 1.04/1.06 = 0.98113, giving 0.6Q = 0.018868 and Q = 3.14%. Using the simple spread/(1-R) = 2%/0.6 = 3.33% ignores compounding, so A is wrong.

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