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FRM Part II · FRM Exam Part II · The Evolution of Stress Testing Counterparty Exposures

A bank models the exposure of a netting set at a 1-year horizon. The mark-to-market value of the netting set is normally distributed with mean zero and standard deviation USD 20 million. The 97.5% quantile of the standard normal is 1.96 and the standard normal density at zero is 0.399. Which pair of values is closest to the 97.5% PFE and the EE at that horizon?

The 97.5% PFE is 1.96 times 20, or USD 39.2 million. For a zero-mean normal, expected exposure equals sigma times 0.399, which is USD 7.98 million, because only positive values are counted. Doubling it to 15.96 would count negative values as well.

  1. APFE USD 39.2 million; EE USD 7.98 millionCorrect
  2. BPFE USD 39.2 million; EE USD 15.96 million
  3. CPFE USD 20.0 million; EE USD 7.98 million
  4. DPFE USD 78.4 million; EE USD 3.99 million

Explanation

PFE = 1.96 x 20 = 39.2 million. For a zero-mean normal, EE = E[max(V,0)] = sigma x 0.399 = 20 x 0.399 = 7.98 million. The 15.96 option doubles EE by using the expected absolute value, which is wrong since only positive values count. The other options misuse sigma or the multiplier.

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