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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A bank's risk team compares age-weighted historical simulation with volatility-weighted historical simulation (Hull-White). Yesterday's estimated daily return volatility for an asset was 2.0%, while the volatility estimated for the day a historical return of -3.0% occurred was 1.0%. What return does volatility-weighted simulation use for that historical observation?

The adjusted return is -6.0%. Volatility-weighted simulation scales each historical return by current volatility divided by volatility at the time. Here that is 2.0% divided by 1.0%, a factor of two, so the -3.0% return becomes -6.0%.

  1. A-6.0%Correct
  2. B-1.5%
  3. C-3.0%
  4. D-2.0%

Explanation

Hull-White adjusts each return by the ratio of current to then-prevailing volatility: -3.0% x (2.0/1.0) = -6.0%. Option B inverts the ratio. Option C is the unadjusted return used in equal-weighted simulation.

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