[MUSIC] Welcome to module two, which has a focus on factor models. And today, we are going to talk about the typology of factor models. What are the kinds of factor models that people tend to use in practice? And what are the ones that have been found most useful in investment applications? Well, okay, so first of all, we talked about the single factor model, the market model, where there's a single factor and the factor is the market portfolio. And I guess the key question at this stage is, well, do really believe that the market portfolio is the only rewarded systematic factor impacting asset returns? So if you think about the decomposition of risk, well, systematic risk, in this case, accounts for something around 30 to 40%, using the single factor models. Meaning that about 60 to 40% of the returns remain unexplained. And the question is, is it because we are simply missing out important factors? Or is it because there are no important factors to speak and everything else is specific? Well, the answer to that very important questions have obviously been the focus of a lot of academic research of other years. A very important influential piece of research is a paper, a seminal paper, by Fama and French, 1992. And what they've done is they've tried and looked at the explanatory power in terms of cross-sectional differences in expected returns when looking at factors other than the market factor. So what they are doing is actually pretty simple, at least from a principle standpoint. They are looking at average return on on a set of securities, a set of stocks in this case. And then they are looking at the beta of each stock as an explanatory variable. They're also looking at something which will be the size factor, a proxy for the size factor, on something that would be a proxy for what we call the value factor. The size factor is essentially related to the market cap of the stocks. So how big is the company in terms of market gap? And the value factor is a proxy by a book to market estimate. So how's the book value of the company compares to the market value of the company? And then they do a cross-sectional regression, where they are trying to explain differences in average performance across stocks in terms of differences in details on the one hand. Exposure with respect to the market. And differences in market cap. And differences in book to market. Now, if the capital asset pricing model was correct. And if the market was the only meaningful and rewarded factor, what we would find is we would find insignificant premia associated with differences in size and book to market. So in other words, the meaningful differences in return or in performance will be all explained by differences in betas. Keeping in mind that the model suggests then that high beta stocks would have a higher performance. And low beta stocks would have a lower performance. Well, that's not exactly what they found. Actually, they found the opposite. They found that the most meaningful explanatory variables for explaining how sectional differences in expected returns were actually market cap and book to market. And as you can see in this equation, the t-stats would show up in the parentheses underneath the parameters here. In both cases, above two in absolute value, suggesting that those two parameters. I mean, those two variables are statistically significant in terms of explanatory power for those two factors. And we also see that after controlling for size and book to market, well, differences in beta are hardly significant in terms of explaining differences in expected returns. Okay, so, I mean, this paper has led to a lot of different interpretations. And there's a lot of debate in terms of how these studies should be conducted and what's the meaningfulness of those factors in the first place. But something to keep in mind is that now we are living in a world. And there's a fair consensus that a single factor model cannot explain all meaningful components of security returns, that we need more than one factors. So what are the factors that people are actually using in investment practice? So we talked about the market factor, which still remains as the first natural factor. That's the first one. Then we talked about the value factor and the size factor. And this is based on this finding that value stocks tend to outperform growth stocks on the one hand. And on the other hand, the finding that small cap stocks tend to outperform large cap stocks. So there seems to be a premium associated to value and to size. Which would tend to indicate, if we believe in a rational explanation for these premia, that value stocks and small cap stocks are riskier companies. Which might explain why they eventually have a higher return. Now, in addition to market value and size, the momentum factor has been also very often used as a meaningful, explanatory variable to try and explain differences in expected return. The momentum factor is defined as the difference in performance between the past winners and the past losers. And clearly, we see here that momentum, if you will, is an attribute of the stock. And you can think about the stock on a given sample period as being a past winner or a past loser. And that would tend to explain some persistence in performance because past winners tend to outperform past losers. Now, literature has also looked at other factors, including the low volatility factor, distinguishing the low volatility stocks from the high volatility stocks. And in this case, we found some anomaly in the sense that the low volatility stocks tend to outperform the high volatility stocks even though they are less risky. There's also liquidity factor. Less liquid stocks tend to have a higher risk premia associated to them compared to higher liquidity stocks, as expected. There are other factors, such as quality factor and some kind of juvenile factor, for example, that are attributes that people have been looking at. Now, there have been a number of studies based on US stocks over a long period of time that actually reports the excess performance of these factor-tilted portfolios with respect to the opposite tilt. And as you can see from this table, some of these performance have been pretty substantial. We think about the size, for example, the size premia around higher than 2%. Value premia historically has been pretty high annually, almost,7%. And same for momentum, as well. Now this brings us to the different types of factor models that tends to be used in practice. It's fair to say that there are at least three categories that people use to sort different types of factor models. The first type of factor model would be the macro-economic factor models. In which case, the factors will be these big macro-economic indicators, like GDP growth, inflation, interest rates, for example. So we are trying to go after economic variables that can explain collectively differences in risk and returns. Now we can move on then to micro-economic factor models and including the ones that we've been talking about so far when we are talking about size value and so on. Well, in this case, factors are actually fundamental attributes of the company, of the security. So if you think about the market cap, or the industry in which a company belong, or the past performance. In all those cases, we're looking at something that's actually an attribute of the company. And then the last kind of factor models are the so-called implicit factor models, where the factors are regarded as principle components and correlated linear combination of asset returns. Well, these factors in this case are statistical artifacts that actually are exhibit and extracted from the data. And the beauty of these implicit factor models is that the implicit factors can be extracted first without any prior economic view on what they should be. So in a way, it's kind of nice because we let the data tell us what the factors are even though, of course, it can lead to spurious type of factor showing up as important even though they are not. And also, another benefit of that, which eventually will prove useful, is that the factors are, in this case, uncorrelated linear combination of asset returns. In other words, the factor are orthogonal. There's no correlation between the factors. [MUSIC]
