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 $

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

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