Given data on risk factors and portfolio returns, it is useful to estimate the portfolio's exposure, that is, how much the risk factors drive portfolio returns, as well as how much the exposure to a given factor is worth, that is, the what market's risk factor premium is. The risk premium then permits to estimate the return for any portfolio provided the factor exposure is known or can be assumed.
More formally, we will have i=1, ..., N asset or portfolio returns over t=1, ..., T periods and each asset's excess period return will be denoted 
. The goals is to test whether the j=1, ..., M factors explain the excess returns ...
