FRM Part II · FRM Exam Part II · Non-parametric Approaches
A risk manager is considering volatility-weighted historical simulation (Hull-White) instead of BRW age-weighting. Today's EWMA volatility for a portfolio is 2.0%. A historical return of -3.0% occurred when the estimated volatility was 1.5%. What return is used for that observation in the VaR distribution?
The adjusted return is -4.00%. Hull-White scales each historical return by the ratio of current volatility to the volatility at the time of the observation: 2.0 divided by 1.5 is 1.333, and multiplying by -3.0% gives -4.0%.
- A-2.25%
- B-3.00%
- C-4.00%Correct
- D-1.50%
Explanation
Volatility adjustment scales the return by current volatility divided by volatility at the time: -3.0% x (2.0/1.5) = -4.0%. Option A inverts the ratio (1.5/2.0), a classic error. Option B ignores the adjustment.
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