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FRM Part II · FRM Exam Part II · Credit Value Adjustment

A bank models the exposure to a counterparty at a future date. The distribution of the portfolio value at that date is normal with mean USD 2 million and standard deviation USD 5 million. Using the 95% one-sided z-value of 1.645, and ignoring collateral and netting subtleties, what is the potential future exposure (PFE) at 95% confidence?

The 95% potential future exposure is USD 10.225 million. It is the 95th percentile of the portfolio value: the mean of 2 million plus 1.645 times the standard deviation of 5 million. Leaving out the mean would understate the exposure at 8.225 million.

  1. AUSD 10.225 millionCorrect
  2. BUSD 8.225 million
  3. CUSD 6.225 million
  4. DUSD 7.000 million

Explanation

PFE is the 95th percentile of the value distribution: 2 + 1.645 x 5 = 2 + 8.225 = 10.225 million. Omitting the mean gives 8.225. Using 1.645 x 5 minus mean gives 6.225. Since the percentile is positive, the floor at zero does not bind.

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