FRM Part I · FRM Exam Part I · Measuring Credit Risk
A single loan has EAD of USD 2,000,000, PD of 4%, and LGD of 50% (deterministic). Default is a Bernoulli event. What is the standard deviation of the credit loss (unexpected loss) on this loan?
Unexpected loss is the standard deviation of loss. With fixed LGD it is EAD x LGD x the square root of PD times (1 minus PD). That is USD 1,000,000 x 0.19596, or about USD 195,959. USD 40,000 is the expected loss instead.
- AUSD 195,959Correct
- BUSD 40,000
- CUSD 1,000,000
- DUSD 39,192
Explanation
With deterministic LGD, loss = EAD x LGD x default indicator, so UL = EAD x LGD x sqrt(PD(1-PD)) = 1,000,000 x sqrt(0.04 x 0.96) = 1,000,000 x 0.195959 = USD 195,959. USD 40,000 is the expected loss (0.04 x 1,000,000), not the standard deviation.
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