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FRM Part II · FRM Exam Part II · Risk Measurement and Assessment

A bank's LDA model aggregates capital across seven risk cells. The first approach sums the stand-alone 99.9% VaRs of the cells, assuming perfect dependence. The second uses a copula with moderate positive dependence, producing a lower total. Which statement is the most accurate assessment?

A copula with moderate dependence can give a lower total than simply summing stand-alone VaRs, but dependence is hard to estimate from scarce loss data. Therefore the diversification benefit must be justified and sensitivity tested, rather than assumed to be conservative or irrelevant.

  1. AThe copula result is always the more conservative because it uses a richer dependence structure
  2. BThe sum approach is invalid because VaR is always subadditive and cannot be summed
  3. CThe copula total can be lower than the simple sum, but it depends on a dependence assumption that is hard to validate with limited data, so the diversification benefit requires justification and sensitivity testingCorrect
  4. DDependence between cells is irrelevant because frequency and severity are independent within each cell

Explanation

Summing stand-alone VaRs assumes comonotonic-style full dependence and generally gives a higher figure than a model with less than perfect dependence. However, dependence parameters are poorly estimated from scarce operational loss data, so the diversification benefit needs justification and stress testing. Independence within a cell says nothing about dependence across cells, and VaR is not always subadditive.

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