FRM Part II · FRM Exam Part II · Portfolio Construction
A manager's information ratio is 0.80 with a skill level (IC) of 0.04 under the basic fundamental law. The manager wants to raise the IR to 1.20 without changing skill per bet. Assuming bets stay independent, by what factor must the number of independent bets increase?
Breadth must rise by a factor of 2.25. Since the information ratio is proportional to the square root of the number of independent bets, a 1.5-times increase in IR (from 0.80 to 1.20) needs 1.5 squared, or 2.25 times as many bets, if skill is unchanged.
- A2.25Correct
- B1.50
- C3.00
- D1.20
Explanation
IR is proportional to sqrt(breadth), so breadth must scale with the square of the IR ratio: (1.20/0.80)^2 = 1.5^2 = 2.25. Choosing 1.50 forgets that IR grows with the square root of breadth. Original breadth is (0.80/0.04)^2 = 400, and the new breadth is (30)^2 = 900, which is 2.25 times.
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