According to Grinold’s law the maximum attainable information ratio can be calculated using the following formula:

$$\text{IR} = \text{IC} \times \sqrt{\text{BC}}$$

The four managers will have IRs of:

$$\text{IR}_\text{A} = 0.5 \times \sqrt{20} = 2.24$$ $$\text{IR}_\text{B} = 0.05 \times \sqrt{200} = 0.71$$ $$\text{IR}_\text{C} = 0.1 \times \sqrt{100} = 1.00$$ $$\text{IR}_\text{D} = 0.8 \times \sqrt{10} = 2.53$$