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FRM Part II · FRM Exam Part II · Portfolio Performance Evaluation

A portfolio has a beta of 1.0 to its benchmark, an annual active return of 1.8%, and an ex-ante tracking error of 6%. A risk budget allows tracking error of up to 4% by scaling the active positions proportionally (leaving beta at 1.0). If the manager's skill is unchanged, what is the expected active return and information ratio after scaling?

Active return falls to 1.2 percent and the information ratio stays 0.30. Scaling active positions by two thirds cuts both active return (1.8 to 1.2) and tracking error (6 to 4) proportionally, so the ratio of the two is unchanged.

  1. AActive return 1.2%, IR 0.30Correct
  2. BActive return 1.8%, IR 0.45
  3. CActive return 1.2%, IR 0.45
  4. DActive return 0.8%, IR 0.20

Explanation

Scaling active positions by 4/6 = 2/3 scales both active return and tracking error. Active return = 1.8 x 2/3 = 1.2%; TE = 4%. IR = 1.2/4 = 0.30, the same as the original 1.8/6 = 0.30. The IR is invariant to scaling, so options changing it are wrong.

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