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

A netting set has two trades with a counterparty. Exposures at a future date are normally distributed and independent of each other: Trade 1 has mean 0 and standard deviation 8 million; Trade 2 has mean 0 and standard deviation 6 million. Under netting, what is the expected positive exposure of the netting set, approximately, using E[max(X,0)] = 0.4 × standard deviation for a zero-mean normal variable, compared to the sum of the standalone expected positive exposures?

Netted EPE is about 4.0 million versus a standalone sum of 5.6 million. The netted standard deviation is the square root of 64 plus 36, or 10 million, giving 0.4 times 10. Standalone EPEs are 3.2 and 2.4 million, which sum to 5.6 million.

  1. ANetted 4.0 million versus standalone sum 5.6 millionCorrect
  2. BNetted 5.6 million versus standalone sum 4.0 million
  3. CNetted 4.0 million versus standalone sum 4.0 million
  4. DNetted 2.4 million versus standalone sum 3.2 million

Explanation

Netted standard deviation is sqrt(64+36)=10 million, so EPE = 0.4×10 = 4.0 million. Standalone EPEs are 0.4×8 = 3.2 and 0.4×6 = 2.4, summing to 5.6 million. Netting reduces exposure because of diversification (correlation below 1). Option 2 reverses the figures.

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