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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A portfolio has a one-day 99% parametric VaR of USD 2.0 million, calculated assuming normally distributed returns with zero mean. The 99% normal quantile is 2.33. An analyst notes that the portfolio's returns have fat tails and wants a rough view of the loss at the 99.9% level (quantile 3.09) under the same normal assumption. What is the resulting VaR?

The 99.9% VaR is about USD 2.65 million. Scaling the 99% VaR by the ratio of normal quantiles, 3.09 divided by 2.33, gives 2.0 times 1.326. Because the normal assumption underestimates fat tails, the true loss at that level is likely larger.

  1. AUSD 2.65 millionCorrect
  2. BUSD 1.51 million
  3. CUSD 3.09 million
  4. DUSD 4.65 million

Explanation

Under normality with zero mean, VaR scales with the quantile. Portfolio sigma = 2.0/2.33 = 0.858 million. Then VaR at 99.9% = 3.09 × 0.858 = 2.65 million. Using 3.09 directly as a multiple of 2.0 ignores the original quantile; the 1.51 option inverts the ratio.

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