# Proof that Sharpe ratio of the benchmark is related to the maximal information ratio and Sharpe ratio

I understand the economic logic behind it, that the active portfolio with the highest information ratio will also have the highest Sharpe ratio, but I can't see how $SR_B^2 = SR_P^2 - IR^2$

• It follows from "sum of independent variances" type reasoning. The portfolio return is equal to the benchmark return plus the tracking error. So $SR_P^2=SR_B^2+IR^2$ – noob2 Apr 26 '17 at 8:40
• @noob2 that's the independence part I don't get, why wouldn't there be correlation between the bench and the active part? – user1627466 Apr 26 '17 at 8:42