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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A fund has an active risk (tracking error) budget of 4% and allocates it to two uncorrelated active strategies with information ratios of 0.50 and 0.25. Risk is allocated optimally, so each strategy's active risk is proportional to its information ratio. What is the expected total alpha?

Expected alpha is about 2.24%. For uncorrelated strategies the optimal combined information ratio is the square root of the sum of squared IRs, which is 0.559. Multiplying by the 4% active risk budget gives 2.236%, which is more than the best single strategy delivers.

  1. A1.50%
  2. B2.00%
  3. C2.24%Correct
  4. D3.00%

Explanation

With uncorrelated strategies, the optimal combined IR = sqrt(0.5² + 0.25²) = sqrt(0.3125) = 0.559. Alpha = 4% × 0.559 = 2.236%. Check: risk allocations are 3.578% and 1.789%, giving alpha 3.578(0.5) + 1.789(0.25) = 1.789 + 0.447 = 2.236%. The 3.00% option wrongly sums the IRs, and 2.00% uses only the larger IR.

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