FRM Part II · FRM Exam Part II · Portfolio Credit Risk
A bank allocates economic capital to business units using each unit's contribution to total portfolio unexpected loss rather than its standalone unexpected loss. What is the main reason the sum of standalone ULs exceeds the portfolio UL?
The sum of standalone unexpected losses exceeds portfolio unexpected loss because of diversification: defaults across units are not perfectly correlated, so the portfolio standard deviation is below the simple sum. Contribution-based allocation spreads this benefit so allocated capital adds up to the total.
- ADiversification, because defaults are less than perfectly correlated across the units.Correct
- BExpected loss is being subtracted twice from each unit's loss.
- CLoss given default is assumed to rise in a downturn.
- DConfidence levels differ across the business units.
Explanation
Portfolio UL is a standard deviation, which is sub-additive when correlations are below one. Standalone ULs add as if perfectly correlated, so their sum exceeds portfolio UL by the diversification benefit. Contribution-based allocation distributes that benefit so the contributions sum to portfolio UL.
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