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FRM Part II · FRM Exam Part II · Derivatives

A bank's exposure to a counterparty is simulated at a future date with a normally distributed netted portfolio value having mean USD 4 million and standard deviation USD 10 million. Using the 97.5% quantile (z = 1.96) of the value distribution, what is the potential future exposure (PFE) at that date, and which expected exposure statement is correct?

PFE is USD 23.6 million (4 plus 1.96 times 10), and expected exposure is greater than USD 4 million. Expected exposure averages the positive part of the value, so flooring negative outcomes at zero pushes it above the mean value.

  1. APFE is USD 23.6 million; expected exposure equals USD 4 million
  2. BPFE is USD 19.6 million; expected exposure is greater than USD 4 million
  3. CPFE is USD 23.6 million; expected exposure is greater than USD 4 millionCorrect
  4. DPFE is USD 15.6 million; expected exposure is greater than USD 4 million

Explanation

PFE = 4 + 1.96 x 10 = USD 23.6 million. Expected exposure is E[max(V,0)], which exceeds the mean 4 because negative outcomes are floored at zero and so add nothing negative. Option 2 omits the mean; option 4 subtracts the quantile term.

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