# 6 – M4 L2A 17 Fama French Size Factor V3

Notice that while we calculated our returns for one particular portfolio, if we chose different stocks, we could create another portfolio to represent the size factor. If we decided to buy in short twice as much, this could potentially be another portfolio representing the size factor. How do we generalize this to other portfolios that buy small-cap stocks in short large-cap stocks? Well, rather than trying to create an infinite number of long-short portfolios, we can use a single standard portfolio and then see how other portfolios co-vary with it. In other words, portfolios that are just like the standard portfolio would move up or down in the same percent as the standard portfolio. Some other portfolio that may not have such an extreme bet on the market cap of stocks may move a fraction as much as the standard portfolio. In fact, we don’t have to limit ourselves to portfolios. We could check to see how much a single stock moves in relation to this long-short portfolio. If we perform the regression in which the independent variable was the return of this size portfolio and the stock return was the dependent variable, then the beta coefficient of that regression would give us a measure of how exposed the stock is to the movements of this size-based portfolio. Let’s look at what Fama and French did to create the size factor. Start with an estimation universe, which is a set of stocks that are representative of a region or countries stock market. Sort the stocks by market cap. The top 90 percent by market cap are put into a portfolio called “Big”. The bottom 10 percent by market cap are put into a portfolio called “Small”. Calculate the equal weighted return of the Small portfolio, and the equal weighted return of the Big portfolio, then take the difference, the return of small minus the return of big. This difference gives us a measure of the return that can be attributed to investing based on the hypothesis that small-cap stocks tend to outperform large-cap stocks. We can think of this in terms of a long-short portfolio which buys the small cap stocks and shorts and equal dollar amount of the large-cap stocks. The daily returns of this long-short portfolio are the factor returns of this size factor. So, we now have a factor time series that we can use in a factor model. Note that in the Fama-French notation, this size factor is written with the acronym SMB. Can you guess what that stands for? SMB stands for Small Minus Big.