All right, welcome back. Where we left off last time was with the CAPM model, and we talked about this Nobel Prize-winning model that was a single-factor model. And we said we're going to move on to other Nobel Prize-winning territory, which is an extension of the CAPM, is the best way to think about it, called the Fama French Model. What I'm going to do is actually take a sort of engineering approach here where I'm going to just show you what they did and then we'll look at why it's a factor model. So what they did here is they took the universe of stocks and they sorted them into ten buckets or deciles. And these deciles are based on size, in the first case, and then the book to price ratio, the book to price ratio is essentially a measure of value, right? Because if the book to price is very very high, it means a relative to the book value, the book value is high relative to the price or the price is low relative to the book value, which means it's cheap, okay? So book to prize is basically a measure of value. Okay, so what they did was they sorted the stocks into these deciles and then they looked at the performance of the top decile portfolio compared to the bottom decile portfolio. In other words, you take the top 10% smallest stocks and compare it with the top 10% largest stocks, would you get? Here's what you get in the small versus large. So, the black line is really a very simple portfolio of the top 10% stocks, whereby size, actually the bottom 10% by size, the smallest 10%. And the red line are the largest 10% stocks, largest decile stocks. And you see the separation, you see that the small caps very systematically outperform large cap stocks. This is basically what we call the size effect. The size effect is a well-observed effect that seems to suggest that small cap stocks outperform large cap stocks. Now remember that in a CAPM world, the only thing that should matter should be beta, right? So, if you find some effect like this that is not explained by beta, then clearly it is an anomaly from the perspective, the CAPM, and isn't really well-explained by the CAPM. So, what we're seeing here is the separation between small caps and large caps really shouldn't happen if the cAPM were an accurate description of the world because the CAPM says beta of the stock is the only thing that's important, the size of the stock shouldn't really matter. Okay, when you look at the value versus growth, exact same story, value stocks outperform growth stocks. Now, we do have to do some sort of an adjustment to make sure that this isn't somehow just beta in another form, and that's why you have to run this in the form of multiple regression, which is exactly what they did. But the point is, when you did that regression, you find that even after accounting for beta there is still a very significant part of the returns of assets that are explained by exactly this effect that value stocks outperform growth stocks. So, you could do this for other things, Fama and French in the original paper just did it for value minus, v alue versus growth and small cap versus large cap. A very popular extension is what's called a Carhart model where you do the exact same thing where you look at winners versus losers, in other words it's the momentum factor. What's going on here is you build deciles in exactly the same way where the top deciles are the winners and the bottom decile are the losers and you look at the difference in returns between these two portfolios. And if you see this kind of separation that suggest to you that maybe that is a factor that isn't captured when you run the multiple regression, you do that, multiple regression to actually establish the fact that there is statistical significance to this. So, that's essentially what the Fama French Model is. The Fama French Model is the addition of small minus big, in other words, the portfolio that you get of small stocks going long small stocks and going short big socks. So that difference, that separation, is essentially the return of the factor, and that's essentially what we call a factor mimicking portfolio, it is a portfolio whose returns are the returns of the factor, right? So you've got to construct this portfolio in a careful way to make sure that the only returns that you're getting are due to the factor and not some extraneous effect. And so that's exactly what SMB is designed to do, SMB is designed to give you a portfolio that is long and small stocks, shortened big stocks, and the difference between them is basically the return of the factor, right? And so, what Fama and French really did was to extend the CAPM by interpreting the size effect and the value of X as being systemic factors. So they introduced these new factors in addition to the market factor. And they establish the fact that you get a better explanation of the returns of assets when you add these additional factors beyond just simply the market factor, all right? So it's an extension in that sense. And you can see it has the same structure as a factor model, right? Now, there's no reason for you to stop there, right? You could of course add momentum, but people have studied other factors and the general state of the art today seems to be an agreement that low vol and quality are probably factors as well, right? Now, of course, there are people who argue in favor of hundreds of other factors but those are very controversial and it's very hard to really establish that that's a real factor. So, the state of the art today is actually that low vol, value, momentum and quality are sort of treated as factors. Interestingly, size in practice does not tend to be treated as a factor quite as much and it tends to be treated as a universe choice. So, for example, you would do all of these things in small caps and then you would do all of these things, and when I say all of these things, I mean build factor portfolios constructed from these four factors in large caps. And that's really going to be the focus of the remaining part of these lectures. We're going to start building factor portfolios in order to try and harvest this. But before we can do that, we're going to do one last thing that we can do with factors in a very very interesting way, and that is to use them as a diagnostic to try and understand, to try and decompose the returns and learn something about how a mutual fund or an asset manager is achieving his or her returns, and that is the subject of what we call style analysis, which is what we're going to do next. Thank you very much. [MUSIC]