When IRs are equal,

$$\text{Total IR} = \text{IR}_i \sqrt{N}$$ $$\text{IR} = \frac{\alpha}{\text{TE}} = \frac{0.05}{0.084} = 0.595$$ $$\therefore \text{Total IR} = 0.595 \sqrt{3} = 1.031$$

Note that the law of active management, also known as the total information ratio, states that the overall information ratio for a group of N managers can be calculated as IR multiplied by the square root of N. As N increases, the theoretical information ratio of a fund would approach infinity. However, in reality, it is challenging to find a significant number of completely unrelated trading strategies.