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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A loan has EAD of $5 million, PD of 4%, and a fixed LGD of 50%. Assuming default is a Bernoulli event and EAD and LGD are constant, what is the standard deviation of loss (unexpected loss) for this loan?

With constant EAD and LGD, loss is $2.5 million times a Bernoulli default indicator. Unexpected loss is $2.5 million times the square root of 0.04 times 0.96, which is about $490,000. It is far larger than the $100,000 expected loss.

  1. A$98,000
  2. B$490,000Correct
  3. C$500,000
  4. D$2,500,000

Explanation

Loss = EAD x LGD x default indicator = 2,500,000 x indicator. Std dev = 2,500,000 x sqrt(0.04 x 0.96) = 2,500,000 x 0.19596 = about $489,900, so $490,000. $98,000 would be 0.04-based confusion with expected loss of $100,000; $500,000 uses PD-related rounding; $2.5 million ignores the PD variance.

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