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FRM Part II · FRM Exam Part II · Factors

A fund's active return volatility is 4% from a single factor tilt. It adds a second tilt with identical 4% active volatility, equal 50/50 allocation, and a correlation of 0.25 between the two factor active returns. What is the resulting active volatility, to the nearest 0.01%?

Active volatility is about 3.16%. Portfolio variance is 0.25×16 + 0.25×16 + 2×0.5×0.5×0.25×16 = 10, and the square root of 10 is roughly 3.16%, lower than 4% because correlation is below one.

  1. A4.00%
  2. B3.54%Correct
  3. C2.83%
  4. D3.16%

Explanation

Variance = 0.5²·16 + 0.5²·16 + 2·0.5·0.5·0.25·16 = 4 + 4 + 2 = 10. Wait: 0.25·16=4 per term, so 0.25*16=4, 4+4=8, cross term 2·0.25·0.25·16=2, total 10. Volatility = √10 = 3.16%. Check: this equals 3.16%, so the correct choice is the 3.16% option.

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