FRM Part I · FRM Exam Part I · Measuring Credit Risk
A single loan has exposure at default of 10 million, a one-year default probability of 4% and a fixed loss given default of 60%. Treating default as a Bernoulli event, what is the standard deviation of the loss on this loan (unexpected loss), to the nearest 0.01 million?
The unexpected loss is about 1.18 million. Loss given default exposure is 6 million, and default is a Bernoulli event with standard deviation sqrt(0.04 x 0.96), about 0.196. Multiplying 6 million by 0.196 gives roughly 1.18 million.
- A1.18 millionCorrect
- B1.20 million
- C0.23 million
- D0.24 million
Explanation
Loss standard deviation = EAD x LGD x sqrt(PD x (1 - PD)) = 6 million x sqrt(0.04 x 0.96) = 6 million x 0.19596 = 1.18 million. Using sqrt(PD) gives 1.20 million, which ignores the (1 - PD) term. 0.24 million is the expected loss, not the volatility.
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