# Arbitrage Pricing Theory (APT), orthogonal factors

Why in the Arbitrage Pricing Theory (APT), one of the assumptions is that the factors has to be orthonogal? what if not?

• Do you have a citation for this? Campbell, Lo, and Mackinlay (on p. 220) doesn't have an orthogonality restriction on f in their introduction to APT. Nor, when they talk about portfolios of risk factors (on p. 223) do they require the portfolios to be orthogonal. – BKay Jan 26 '15 at 15:37

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.