The following example is from the book Active Portfolio Management by Grinold and Kahn. Suppose we have the factor returns and want to estimate the exposures/factor loadings. Say the factor returns are returns on the value-weighted NYSE, gold, a government bond index, a basket of foreign currencies, and a basket of traded commodities. The authors mention that to estimate the exposures, we can set the exposure of each stock to the NYSE equal to 1, and then run a regression to estimate the exposures to other factors. I don't understand why we should set the exposure to NYSE to 1. Why can't we just run a regression of the stock return on all the factor returns and take the coefficients as the exposures?