# 8 – M4 L2A 19 Fama French SMB And HML V2

So, now we’ve seen how Fama and French used theoretical portfolios to create factor returns, time series that represents size and value. What Fama and French did when combining these factors was to define theoretical portfolios that were based on both size and value. Let’s see what I mean by that, first sort by market cap, define the group of small stocks and also define the group of big stocks. Then, for the small group, sort by book to market value. Divide this small group into three groups: value, neutral and growth. Do the same for the big group. Sort the stocks by market cap. Sort them by book to market value, then divide them into three groups: value, neutral and growth. Now, we’ll effectively have six portfolios which are six building blocks, with which we’ll use to construct the long short portfolios representing the size and value factors. The small minus big size factor is the sum of the three small portfolios minus the sum of the three big portfolios. The high minus low value factor is the sum of two value portfolios minus the sum of two growth portfolios. Notice that the two neutral portfolios aren’t used in this formula. Okay, one more thing. Notice that small minus big was constructed using three building blocks for the long position and three building blocks for the short position. However, high minus low was built using two building blocks for the loan and two for the short. Since we plan to use both factors in a multiple regression, we want to even out the effects of each factor. So, we’ll divide the small minus big by three and divide the high minus low by two. You can pause here to study these formulas.