FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk
A bank holds a single USD 5 million loan with PD of 3% and LGD of 60%, with EAD fixed. Treat the loss as EAD x LGD x default indicator, with LGD deterministic. What is the standard deviation of the loss (unexpected loss)?
With deterministic LGD, the loss is a Bernoulli variable scaled by USD 3 million. The standard deviation is 3 million times the square root of 0.03 x 0.97, about USD 511,800, far above the USD 90,000 expected loss.
- AUSD 51,200
- BUSD 90,000
- CUSD 511,800Correct
- DUSD 900,000
Explanation
Loss on default = 5m x 0.6 = USD 3m. Standard deviation = 3,000,000 x sqrt(0.03 x 0.97) = 3,000,000 x 0.17059 = USD 511,760, about USD 511,800. USD 90,000 is the expected loss. USD 900,000 uses 0.3 instead of the square-root term.
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