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

A bank's simulated exposure for a single uncollateralised forward at a future date is normally distributed with a mean mark-to-market of zero and standard deviation of USD 8 million. Using the standard approximation that expected exposure equals the mean of the positive part of the distribution, which is sigma/sqrt(2*pi), what is the approximate EE at that date? (sqrt(2*pi) ≈ 2.5066)

For a zero-mean normal mark-to-market, expected exposure equals sigma divided by the square root of 2 pi. With sigma of USD 8 million, that is 8 / 2.5066, approximately USD 3.19 million, because only the positive half of outcomes counts.

  1. AUSD 3.19 millionCorrect
  2. BUSD 6.38 million
  3. CUSD 8.00 million
  4. DUSD 4.00 million

Explanation

For a zero-mean normal variable, E[max(X,0)] = sigma/sqrt(2*pi) = 8/2.5066 = 3.19 million. Using 6.38 would double this by wrongly using 2*sigma/sqrt(2*pi); 4.00 is simply half of sigma, which is not correct.

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