In equation 66-21 they break up active return into two parts: Factor Tilt Returns, and Asset Selection. Active Return= SUMMATION[(Portfolio Sensitivity)j - (Benchmark Sensitivity)j] * (Factor Return)j + Asset Selection I understand that the differences in sensitivities to the factors multiplied by the factor returns gives you the excess return over the benchmark due to active management. But what is the “Asset Selection” part?? Isn’t that already encompassed into the first part? How is this not double counting?
I think I might have answered my own question. Does this make sense? Active Return is what you get for assuming Active Risk. Active Risk can be broken into: Active Factor Risk, and Active Specific (Asset) Risk Active Factor Risk is the risk that can be attributed to the factors in the model. Active Specific Risk is the residual risk not explained by the factors. Since this risk is not explained by the factors, you need to be compensated for it. Thus Active Return is broken up into two components of return: Factor Returns, and the Asset Specific Returns that compensate you for the residual risk of the asset not explained by the factor model.