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

A bank has a 1-year FX forward with a counterparty and models the exposure at time t. The forward's mark-to-market value at t=0.5 is normally distributed with mean 0 and standard deviation USD 8 million. What is the expected positive exposure at t=0.5, to the nearest USD 0.1 million? (Use E[max(X,0)] = σ/√(2π), with √(2π)≈2.5066.)

Expected positive exposure equals the standard deviation divided by the square root of 2π for a zero-mean normal value. With a standard deviation of USD 8 million, that is 8 divided by 2.5066, or about USD 3.2 million.

  1. AUSD 1.6 million
  2. BUSD 3.2 millionCorrect
  3. CUSD 4.0 million
  4. DUSD 8.0 million

Explanation

EPE = 8 / 2.5066 = 3.19, about USD 3.2 million. USD 4.0 million is half the standard deviation, which wrongly assumes half the volatility. USD 1.6 million divides by an extra 2. USD 8.0 million ignores the truncation at zero.

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