If we go back to the capital asset pricing model

**,**you’ll see that the expected return of security**(Ri)**is equal to the risk-free rate of return**(Rf)**plus beta**(βi)**for the security, which is a measure of systemic risk and we multiply that by the**market premium**. So, in that sense, the expected return of any security is just a function of one factor, which is systemic risk. How exposed is this security to changes in the overall market? How does it react to systematic risk? There’s just a single factor and as we discussed in another article. We can also have multiple factors in a model. We could have more than one beta. So if we think about this in a regression analysis, we have one independent variable when we use the capital asset pricing model, but we could actually have two or three or four different independent variables, trying to explain the expected return of a security. Perhaps the most well-known multi-factor model is this**Fama French model**, which was developed by**Eugene Fama**and**Kenneth French**.## What is the Fama and French Three-Factor Model?

Basically what Fama and French realize over time historically, if we look at stock returns, there are two types of portfolios that would have a positive

**Alpha**. So if we think of an alpha greater than**0**that means the return is higher than what would have been predicted by the capital asset pricing model. So if we can improve on this model by factoring into things that over time, companies that were of a smaller size and when I say smaller size, I’m talking about the market capitalization was small-cap stocks tend to outperform large-cap stocks. So there’s this size effect and then also companies stocks that had a high**book-to-market ratio**in so we commonly call those**value stocks**. Value stocks would outperform**growth stocks**. So high book-to-market firms would outperform Low book to market firms in terms of their stock return. We’ve got these two different things that we’ve noticed historically, there are these two effects and Fama and French included those in the model. So, instead of just having a single factor that captures systemic risk, we still have this factor for Market risk, and we still have the risk-free rate but now we’re going to include two additional factors, so that’s why it’s a three-factor model. We’re going to include the**size effect**and then we’re going to include the**book to market**, those are going to be the two additional things that we’re going to look at.When you see this

**SMB**, this is common for it to be written. That just means small minus big. So you could think about it like this, what if we went long, what if we purchase stock and made a portfolio, that was just small-cap stocks and then we went short on a portfolio that had large-cap stocks. So think about the return of that portfolio, if that’s what we did. So we’re basically saying the small-cap stocks outperform large-cap stocks. Then we want to buy the small-cap stocks and then go and sell short the large-cap stock. So that’s what we’re talking about.So then the

**HML**, we’re talking about high minus low and again High minus low we’re talking about book-to-market ratio. Book to Market is the ratio of the book value of the firm’s equity to the market value of its Equity. When you have the book-to-market ratios, you would get put together a portfolio that has the High book-to-market ratio firms. And then we could sell short a portfolio of firms that have a low book to market ratio so the low book to market would be growth stocks. And companies that are expected to grow, have a low book-to-market ratio, and then a high book to Market, we traditionally call them value stocks as I mentioned earlier.So if we are looking at these two effects, we’re capturing a size effect. We’re just capturing the fact that smaller firms are small-cap stocks tend to outperform high-caps stocks historically. We’re capturing that with the capital asset pricing model where not everything with a capital asset pricing model is just caught under systemic risks. We just have one factor, but now we’re saying, we’re going to have this market risk factor and we’re also going to have size, and then we’re also going to control for the fact that these value stocks tend to outperform the growth stocks over time.