Why weights were not considered while calculating active risk?
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This is a special formula for Active Risk in the case of Sector Rotation. Here, the notion is that the Active Manager isn’t using the Benchmark Weights of 65% and 35%. Rather he’s betting on outperformance of X over Y.
So, accordingly, his active Return would be Rx – Ry.
His Active Risk would be Var(Rx – Ry) = Var(Rx) + Var(Ry) – 2Cov(Rx,Ry).