’ Why do you spose CFAI refers to this as an Information Ratio? Information Ratio = (Information coefficient) x (Investor Breadth)^2 For one thing, it doesn’t really seem like a ratio… shouldn’t a ratio have both a numerator and a denominator? For another thing, we already have a different information ratio: The one with excess return in the numerator, and standard deviation of excess return in the denominator.
Information Ratio = (Information coefficient) x (Investor Breadth^0.5) All numbers are ratios!
Lol… Sorry I had to
And the result should be the same as IR = alpha/std(alpha) which is a ratio
IR = IC * Breadth^2 is ex-ante IR (theoretical) IR = Excess return / Std Dev of Excess return is ex-post IR