The Tb model is a small actively selected portfolio combined with a market portfolio. say like 95% Portfolio 5% selection. So you're hoping to make a gain off of that 5% to beat the market . The formula with unsystematic risk is how to weight to an active portfolio of 2 shares. The one with larger unsystematic risk has a smaller weighting.
the denominator in the information ratio is active risk
Active risk squared is equal to active factor risk and active specific risk
There are 2 kinds of information ratio, ex-post and ex-ante ratio. The ex-post ratio has active risk as its denominator and measures the excess return over the prior period. The ex-ante ratio is used together with the TB model and uses unsystematic risk as its denominator. It measures the expected excess returns that you are forecasting to generate using the active portfolio.
is specific risk(numerator) under TB model a unsystem risk? is this specific risk same as the specific risk under active risk square=factor risk +specific risk? what's the relation ship between factor variance and factor rik?