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FRM Part II · FRM Exam Part II · VaR and Risk Budgeting in Investment Management

A manager wants to double the information ratio of a strategy while holding IC and the transfer coefficient constant. According to the fundamental law, what change in breadth is required?

Breadth must increase by a factor of four. Because the information ratio scales with the square root of breadth, doubling the ratio needs the square root to double, which means breadth must quadruple, while doubling breadth lifts IR only about 41%.

  1. ADouble breadth
  2. BIncrease breadth by a factor of fourCorrect
  3. CIncrease breadth by 41%
  4. DIncrease breadth by 50%

Explanation

IR is proportional to the square root of breadth. Doubling IR requires sqrt(breadth) to double, so breadth must rise fourfold. Doubling breadth only raises IR by about 41%.

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