The CAPM suffers from several limitations, such as the use of a mean-variance framework and the fact that returns are captured by one risk factor—the market risk factor. In a well-diversified portfolio, the unsystematic risk of various stocks cancels out and is essentially eliminated.

The Arbitrage Pricing Theory (APT) model was put forward to address these shortcomings and offers a general approach of determining the asset prices other than the mean and variances.

The APT model assumes that the security returns are generated according to multiple factor models, which consist of a linear combination of several systematic risk factors. Such factors could be the inflation rate, GDP growth rate, real interest rates, or dividends.

The equilibrium asset pricing equation according to the APT model is as follows:

Here, is the expected rate of return on security , is the expected return on stock if all factors are negligible, is the sensitivity of the th asset to the th factor, and is the value of the th factor influencing the return on stock .

Since our goal is to find all values of and , we will perform a multivariate linear regression on the APT model.