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

A one-year zero-coupon corporate bond yields 6.0% and a comparable one-year risk-free zero yields 4.0% (both annual compounding). The recovery rate on default is 40% of the bond's face value, paid at maturity. Using the one-year no-arbitrage relationship, what is the approximate risk-neutral probability of default?

The risk-neutral default probability is about 3.1-3.2%. Equating the expected risky payoff, 1 minus 0.6 times Q, to the ratio of risk-free to risky discount factors, 1.04/1.06, gives Q of roughly 0.0315. Using only the 2% spread would ignore recovery and understate default probability.

  1. A3.17%Correct
  2. B2.00%
  3. C1.90%
  4. D5.00%

Explanation

Set (1-Q)*1 + Q*0.4 = 1.04/1.06 = 0.98113, so 1 - 0.6Q = 0.98113 and Q = 0.01887/0.6 = 3.14%. Rounded with exact computation: 0.018868/0.6 = 0.03145, i.e. about 3.1-3.2%. The 2.00% option ignores recovery (spread alone), and 1.90% is the spread divided by one minus recovery... incorrectly using discounted loss rather than the 0.6 loss rate.

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