Information Ratio not being affected by magnitude of active weights

Hi guys,

In the Wiley study text, the statement reads: “The Information Ratio is not affected by the magnitude of active weights”

Can you please give me an example to explain what this statement means?

It isn’t clear to me at all, even with the example given in the study text

Thank you and regards

Suppose that you’ve decided on active weights for securities A, B, and C in the ratio of 1:2:−3, respectively.

What it’s saying is that you get the same information ratio if your active weights are 1%, 2%, −3%, or 2%, 4%, −6%, or 10%, 20%, −30%, and so on. If you change the weights proportionally, you’ll change the active return by that proportion, and the active risk by that same proportion; the information ratio remains the same.