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

Simulated exposures for a netting set at a future date are generated with 10 equally likely scenarios. After applying max(V,0), the exposures in USD million are: 0, 0, 0, 2, 4, 6, 8, 10, 12, 18. What are the expected exposure (EE) and the 90% potential future exposure (PFE) at that date, using the 9th ordered scenario as the 90th percentile?

EE is 6.0 million and the 90% PFE is 12 million. The average of all ten exposure scenarios, including zeros, gives 60/10 = 6. The 90th percentile is the ninth ordered outcome, 12, not the maximum of 18, because PFE is a quantile rather than a worst case.

  1. AEE = 6.0; PFE = 12Correct
  2. BEE = 6.0; PFE = 18
  3. CEE = 6.0; PFE = 10
  4. DEE = 8.0; PFE = 12

Explanation

Sum = 0+0+0+2+4+6+8+10+12+18 = 60, so EE = 60/10 = 6.0. With 10 ordered scenarios, the 9th value (12) is the 90th percentile, so the PFE is 12. Choosing 18 uses the maximum rather than the percentile. EE = 8 would divide by only the 7.5 positive... or ignore zero scenarios, which wrongly excludes them.

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