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FRM Part II · FRM Exam Part II · Future Value and Exposure

A bank computes exposure for a netting set whose mark-to-market at a future date is normally distributed with mean USD 5 million and standard deviation USD 10 million. The 97.5% one-sided PFE is computed on the exposure, max(V,0). Using z = 1.96 at the 97.5% quantile, what is the PFE, and how does it compare with the mean mark-to-market?

PFE at 97.5% is the mean plus 1.96 standard deviations: 5 + 1.96 x 10 = USD 24.6 million. Since this is positive, it equals the quantile of the exposure. It is far above the USD 5 million mean mark-to-market.

  1. AUSD 24.6 million, well above the mean mark-to-market of USD 5 millionCorrect
  2. BUSD 19.6 million, because the mean is excluded from the quantile
  3. CUSD 14.6 million, because exposure is capped at the mean plus one sigma
  4. DUSD 5.0 million, because the PFE equals the mean for positive exposure

Explanation

The 97.5% quantile of V is 5 + 1.96 x 10 = 24.6 million, which is positive so it equals the quantile of max(V,0). Omitting the mean gives 19.6 million, which is wrong because the distribution is not centred on zero. PFE is a tail quantile, far above the mean.

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