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

A bank has a single netted portfolio with a counterparty. At a future date the portfolio value V is normally distributed with mean zero and standard deviation USD 10 million. Exposure is max(V, 0). Which of the following is closest to the expected exposure (EE) at that date? (Use E[max(V,0)] = σ/√(2π) for a zero-mean normal.)

For a zero-mean normal portfolio value with standard deviation 10 million, expected exposure is σ divided by the square root of 2π, about 10 divided by 2.507, or roughly USD 4.0 million. The truncation at zero cuts the average well below the standard deviation.

  1. AUSD 2.0 million
  2. BUSD 4.0 millionCorrect
  3. CUSD 5.0 million
  4. DUSD 10.0 million

Explanation

EE = σ/√(2π) = 10/2.5066 ≈ 3.99, about USD 4.0 million. Option 3 equals σ, ignoring that exposure is zero when V is negative. Option 2 treats EE as half of σ, wrongly using 50% of the distribution as the average positive exposure.

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