I was reading that if we know a portfolios beta we can break the excess return on that portfolio into a market component and a residual component.
r_p = beta_p * r_m + e_p r_p - portfolio excess return r_m - market return e_p - residual return beta_p - portfolio beta
It then goes on to so say, the residual return (e_p) will be uncorrelated with the market return (r_m) and so the variance of the portfolio is
var_p = beta_p^2 * var_m + var_p_residual var_p - variance of portfolio beta_p^2 - beta of portfolio squared var_m - variance of market var_p_residual - variance of portfolio residual
So my question is how can we know the residual return will be uncorrelated with the market return?
I've found this web page which near the top it has a section titled The Key Assumption.
Consider, for example, a case in which the residual return is correlated with factor 1. By adjusting the factor exposure (bi1) appropriately, the correlation of the residual with the factor can be made to equal zero.
I'm not sure if this is linked to my question or not but I still don't follow it either