Vol 4 page 465 quote" although most large-cap indexes usually have a β close to 1 to the Market factor, they usually have a negative sensitivity to the Size factor, indicating their large-cap tilt."
LC should have a positive factor sensitivity right? This is not clear to me. Can anyone enlighten me?
Think about it this way.
Small minus big - If the portfolio has a small cap tilt, it will have a positive sign in front of the beta, if it has a large cap tilt it will have a negative sign in front of the beta
Not sure if this answer your question.
Still, big should have a plus sign right?
The principal of Fama-French is to explain expected return. So think about that first. In simple logic: large cap has lower risk=lower returns (vs small cap) =negative effect to expected returns.
In more complex terms… the SMB factor sensitivity is basically the linear relationship between smallcap excess returns and largecap excess returns. Over time, we expect small excess returns to be greater than large (“negative factor” relation). The more tilted to large cap you are, the more you will experience this negative relation. The more tilted you are to small cap, the less you will lose out on the greater excess return over time (positive factor)
Thanks Hanner for the explanation- makes sense now.