A Market Beta of 1 in the Fama French Model

The Fama French model explains the average returns of portfolios using the average returns of three factors - the excess market return, the return on a long-short portfolio of small stocks and big stocks (SMB), and the return on a long-short portfolio of high book-to-market stocks minus and low book-to-market stocks (HML).

The Fama French model is so widely used because the model does a good job at explaining 90% or more of the variation of expected returns of portfolios in a cross section. This point is important - the Fama French model does not forecast future returns. Rather, the model explains variation in the cross section. What this means is that if you know the excess market return, the return on SMB and the return on HML and a portfolio's loadings on these 3 factors (estimated using historical data), then you can explain 90% of the difference in portfolio returns that day. This reduction of most of the variation of portfolio returns to three factors is quite remarkable!

Now, portfolios tend to all have a beta of 1 on the excess market return. This means that if you control for variation in SMB and HML, the average returns covary with the market one-for-one. In other words, if I give you a portfolio, you can estimate the portfolio's loadings on SMB and HML. You can use these estimated loadings to control for the portfolio's tilt towards SMB or HML. After controlling for the tilt of the portfolio, the remaining portfolio covaries with the market one-for-one.