FRM Part I · FRM Exam Part I · Measuring Credit Risk
A single loan has EAD of USD 10 million, PD of 4%, and LGD of 50% that is treated as a fixed, non-random value. Exposure is fixed. Using the Bernoulli default model, what is the standard deviation of the credit loss (unexpected loss) on this loan?
The unexpected loss is about USD 0.98 million. With fixed LGD, the standard deviation is EAD times LGD times the square root of PD times one minus PD, which is 5 million times 0.196. Ignoring the (1 minus PD) term gives roughly USD 1.00 million.
- AUSD 0.98 millionCorrect
- BUSD 1.00 million
- CUSD 2.00 million
- DUSD 0.20 million
Explanation
Loss = EAD x LGD x default indicator. Standard deviation = 10m x 0.5 x sqrt(0.04 x 0.96) = 5m x 0.19596 = 0.98m. USD 1.00 million wrongly uses sqrt(PD)... actually 5m x 0.2 uses PD's root without the 1-PD term; USD 0.20 million is the expected loss.
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