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

A risk manager uses volatility-weighted historical simulation. Today's estimated daily volatility of a portfolio is 2.0%. A historical return of -3.0% occurred on a day when the estimated volatility was 1.5%. Another historical return of -2.0% occurred when volatility was 2.5%. What are the volatility-adjusted returns of these two observations, respectively, for use in today's simulation?

The adjusted returns are -4.0% and -1.6%. Each historical return is scaled by today's volatility divided by the volatility at that time: -3.0% times 2.0/1.5 equals -4.0%, and -2.0% times 2.0/2.5 equals -1.6%.

  1. A-4.0% and -1.6%Correct
  2. B-2.25% and -2.5%
  3. C-3.0% and -2.0%
  4. D-4.0% and -2.5%

Explanation

Adjusted return = historical return × (current vol / vol at that time). First: -3.0% × 2.0/1.5 = -4.0%. Second: -2.0% × 2.0/2.5 = -1.6%. Inverting the ratio gives the wrong values like -2.25%, and no adjustment leaves returns unchanged.

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