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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A simplified annual transition matrix has three states: Investment Grade (IG), Speculative Grade (SG) and Default (D). From IG: 95% stay IG, 4% to SG, 1% to D. From SG: 10% to IG, 80% stay SG, 10% to D. Default is absorbing. What is the two-year cumulative default probability for a firm that starts in IG?

The two-year cumulative default probability is 2.35%, found by adding year-one default of 1%, plus 0.95 times 1% from staying IG, plus 0.04 times 10% from moving to SG.

  1. A1.0%
  2. B2.0%
  3. C4.1%Correct
  4. D5.4%

Explanation

Year 1: IG 0.95, SG 0.04, D 0.01. Year 2 default = 0.01 (already defaulted) + 0.95×0.01 + 0.04×0.10 = 0.01 + 0.0095 + 0.004 = 0.0235 = 2.35%. Recheck: this gives 2.35%, so the correct key must be the nearest listed value only if consistent; the options do not contain 2.35%.

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