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

A bank has a 4-year FX forward and a 4-year interest rate swap, both with the same counterparty and no netting. Exposure is measured as the 95% PFE at each date, assuming normally distributed mark-to-market values with zero mean. The FX forward's mark-to-market standard deviation grows as 8 million × sqrt(t) (t in years). What is the FX forward's 95% PFE at 4 years (using 1.645 as the z-value)?

The 95% PFE is 26.32 million. The mark-to-market standard deviation at four years is 8 times the square root of 4, or 16 million, and multiplying by the 1.645 normal quantile gives 26.32 million, reflecting exposure growing with the square root of time.

  1. A26.32 millionCorrect
  2. B13.16 million
  3. C6.58 million
  4. D52.64 million

Explanation

Standard deviation at t=4 is 8 × sqrt(4) = 16 million. PFE = 1.645 × 16 = 26.32 million. Using 8 million (t=1) gives 13.16; using sqrt(4) as 2 only on z gives 6.58 mistakes; doubling again gives 52.64.

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