This paper uses an autoregressive approach to test a multi-factor model with time-varying risk premiums. A quasi-differencing approach is used to eliminate the unobservable factors in the model. It is found that the model is capable of capturing the “size effect” and the “dividend yield effect, ” but is incapable of explaining the “book-to-market effect” and the “earnings-price ratio effect.” Thus, it is concluded that a constant-beta multi-factor model will not be able to explain the cross-sectional variation in expected returns.