Why in the Arbitrage Pricing Theory (APT), one of the assumptions is that the factors has to be orthonogal? what if not?
If you want to describe excess returns in terms of exposure to common risk factors, you want the risk factors to be orthogonal. However, if you have $k$ factors with no perfect collinearity, you can always orthogonalize them and use those. You then call the orthogonalized factors the risk factors.