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

A Monte Carlo simulation of a netted portfolio gives the following ten equally likely portfolio values (in USD millions) at a future date: -6, -4, -2, -1, 0, 2, 3, 5, 7, 10. What are the expected exposure (EE) and the 90% potential future exposure (PFE, using the 90th percentile of the ten ordered exposures taken as the 9th lowest value) at that date?

Expected exposure is 2.7 million, found by flooring each value at zero and averaging (sum 27 over ten scenarios). The 90% PFE is 7 million, the ninth lowest of the ordered exposures. Using unfloored values would wrongly give 1.4 million.

  1. AEE = 2.7; PFE = 7Correct
  2. BEE = 1.4; PFE = 7
  3. CEE = 2.7; PFE = 10
  4. DEE = 2.7; PFE = 5

Explanation

Exposure is max(V,0): 0,0,0,0,0,2,3,5,7,10. Sum = 27, so EE = 2.7. The 9th lowest of ten ordered exposures is 7, so PFE = 7. Using the unfloored mean (1.4) is the mistake in option B; 10 is the maximum, not the 90th percentile.

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