FRM Part II · FRM Exam Part II · Credit Risk
A risk manager explains why the Basel IRB formula can be applied to a bank's whole portfolio by summing exposure-level capital charges. Which assumption underlies this portfolio invariance property?
Portfolio invariance rests on the asymptotic single systematic risk factor model: the portfolio is assumed granular enough that idiosyncratic risk diversifies away, leaving one systematic factor. Each exposure's capital then depends only on its own parameters, so charges can be summed without regard to portfolio composition.
- APortfolio is well diversified so that only a single systematic risk factor matters, and capital depends only on each exposure's own characteristicsCorrect
- BDefaults across all obligors are perfectly correlated, so charges add linearly
- CEach obligor's default is independent of all others, so idiosyncratic risk is fully priced
- DLoss given default is stochastic and negatively correlated with the default rate
Explanation
The IRB formula derives from the asymptotic single risk factor model, which assumes a large, granular portfolio where idiosyncratic risk diversifies away and a single systematic factor drives correlation. Capital is then additive across exposures. Perfect correlation (B) and independence (C) are not the assumptions.
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