[ Music ] >> Alright, arbitrage pricing theory and multi-factor models. So just take a step back. You can think about like if many stocks available, as we talked about, remember our example going gambling and to [inaudible], firm specific risk is always going to be able to be diversified away by just adding more stocks to the portfolio. So this firm specific risk shouldn't show up in required returns or stock prices, because that can be diversified away very easily. Common shocks, on the other hand, can't be diversified away and will be priced. So kind of the same intuition that we had behind the capital asset pricing model, we also have behind arbitrage pricing theory. Now, as we talked about, you know, kind of one example of a common shock would be the sensitivity to the overall market, reflected by beta in the capital asset pricing model. But these common shocks need not be limited to sensitivity to the overall market, ad that is what arbitrage pricing theory is, basically expanding upon the capital asset pricing model. So you can think of, you know, kind of having a more complicated asset pricing model, with more risk factors included in it. So look at the expected return here of asset I, have it be a function of sensitivities to various risk factors, okay, or you can express in the second equation just simply an excess return being, you know, related to various risk factors in the economy. The betas will be called factor loadings, the factors may also be called factor risk premium. So, a simple one factor model, capital asset pricing model. The factor in the capital asset pricing model is the market risk premium. We have kind of, you know, well-plowed ground at this point, in the course. Or at least I hope so! Now, perhaps investors care more about the mean variance tradeoff that is reflected in models like the cap-M. Maybe that risk is more multi-faceted. There could be other state variables that represent risk that investors care about. Now, we might not know exactly what these state variables are, but maybe we can observe certain factors, observable characteristics, that are correlated with these state variables. For example, there may be certain firm characteristics that are associated with some stocks doing better than others, and maybe firms that have those characteristics, those stocks move up and down together. There is some kind of correlation in the performance of stocks, associated with this characteristic. These factors would represent a different type of risk that is accounted for in this simple capital asset pricing model, with the only risk that is being priced is sensitivity to the overall market, you know, reflected by beta. Thus, we would need a more complicated asset pricing formula, or multi-varied approach, as opposed to just a single factor capital asset pricing model. Okay? So examples of two firm characteristics that could represent different types of risk to investors, just simply based on return patterns we've observed, and you know, at this point in the course you can probably guess where I'm headed. One could be firm size. We have observed that historically small firms have done better than large firms. Maybe this represents some type of risk that investors care about, therefore, we have this pattern in returns that we've observed historically? And then in particular, the value, growth differential value stocks historically outperforming gross stocks. That return pattern may be suggestive investors view value stocks as more risky than gross stocks. This value growth differential represents some state variable that represents a type of risk not accounted for in the capital asset pricing model. That is where arbitrage pricing theory and, you know, a manifestation of that the three factor model, then, you know, come into play. A developer of the three factor model, Eugene Fama, Nobel Prize winner in economics, along with his co-author, Ken French, who has this great data repository that we've used frequently throughout the course, I thought it would be useful to talk about Eugene Fama's research philosophy. Very scientific. So, you know, you should use the market to understand markets better. You should use market data to understand markets better, not to say this or that hypothesis is literally true or false. No model is every strictly true. The real criterion should be do I know more about markets when I'm finished than I did when I started? So I thought it is worth kind of mentioning this. I thought this was a very scientific way to approach research, and approach it, we should always take kind of coming in with open eyes and just trying to get a better understanding of the world, not coming in with some kind of hidden agenda. So, when we look at this Fama-French three factor model developed in 1993, we are relating the excess return on the stock, the left-hand side, to three factors now as opposed to just one factor. So the first factor we represent is representative of overall sensitivity to the market. This is the cap-M model, if we just stop with the first factor. The second factor here is relating the return, excess returns of a security, to how small stocks are performing relative to big stocks. So the small minus big factor. The size factor. Return on a benchmark portfolio, small stocks minus return on portfolio of large stocks. And then, finally, the third factor. This is a value factor, where we are relating the excess return of a security to how value stocks are performing relative to growth stocks that period. So, this represents a return on a benchmark portfolio of high book to market value firms, minus the return on portfolio of low book to market growth firms. So, for example, if you estimate this regression model, if we observe a positive beta on the small minus big factor, that would mean our security is doing better during periods of times when small stocks are doing better. If we observe a negative coefficient on the beta regarding this small minus big factor, the size factor, if it's negative, it means that our performance is doing better when large stocks are doing better. Okay? If we go to the value factor, if the beta on the value factor is positive, it means our performance is positively correlated with how value stocks are doing. So when value stocks are doing well, we're doing well. If it is negative, if the beta on the value factor is negative, it means that our stocks are doing well during periods of times when growth stocks happen to be doing well. Okay? So this Fama-French three factor model explains the returns of the ten book to market portfolios that we had in our earlier chart very well. You know, this is basically true by definition, right? Now we are accounting for value and size in our asset pricing model, so now we explain value and size. Okay? Alpha is no longer statistically different from zero in a three-factor model. When we look at these three portfolios formed by book to market, we're incurring beta risks now in the three factor model instead of producing alpha. So if we estimate a portfolio of value stocks in a capital asset pricing model, as we observe, we get a positive alpha. If we look at this value stock portfolio and put it in a three factor model, the alpha now is zero, okay? And instead, we have a positive loading on the value factor, a positive beta on the value factor here. So that is the difference between the capital asset pricing model and the three factor model. And here, I'm assuming this is just an index fund invested in value stocks. If you have active management, picking certain value stocks, you could have a positive or negative alpha once you get to the three factor model. But the three factor model is you are only going to get an alpha in the three factor model if you're doing something different. You can't get a positive alpha in the three factor model by just simply investing in an index of value stocks. That will now be accounted for in the beta on the value factor. Won't be accounted for in the alpha in the cap-M model. So in terms of thinking of the Fama-French three factor model, the factors representing risk, you know, high cap-M beta firms might be more vulnerable to market downturns, therefore, they have, you know, higher required returns. Small firms may be also more vulnerable to economic downturns, so higher required returns as well. Same story for value stocks, or high book to market. Maybe they have higher financial leverage, and they get in distress in economic downturns. These would be risk stories as to why size small firms and value firms have historically had yielded higher returns. This would be the risk based explanation. Now, if you want to push back, you could say, well, hey, these may all be true. But isn't that reflected in the cap-M beta? Okay, so that debate then goes, you know, kind of back and forth. Is small and value factors representative of risk, or is it representative of something else? So there is, you know, various factor models. When we start with the one factor model, that is simply the capital asset pricing model. The one factor is sensitivity to overall market conditions. The three factor model we add on small minus big factor, value minus growth factor, so now we are basically in the three factor model, we are controlling for investment style of the security or the mutual fund. Along the size dimension and the value growth dimension. Four factor model. Well, this would be adding an additional factor controlling for momentum. Okay? So this is something we mention for, you know, high engagement students who are taking the course for a University of Illinois credit. We will talk more about this pattern in returns known as momentum. Stocks that have done well the past year continue to drift up the next month. Those that have done poorly the last year continue to drift down the next month. So four factor model takes into account momentum patterns in returns, and you know, more, you know, five, six, seven factor models, you know, let me kind of stop just talking a little bit about a fifth factor. Or what is usually a fifth factor if there is a five factor model. That is a liquidity factor. It is considered by many money managers and academics. So this accounts for the liquidity or illiquidity of a security or asset. So, particularly during a financial crisis, you know, some assets that people wanted to sell, they have found it was very hard to do so. They were illiquid. They could only sell them at a drastic reduction of price. So this illiquidity actually really hurt the investors at a time where they needed the ability to sell the asset the most. So, you know, kind of thinking through in terms of asset pricing, maybe securities and assets that are more illiquid, harder to sell, those are assets that should be giving you, you know, higher return to compensate for this liquidity risk. So liquidity factor could be, you know, if you have a five factor model that could typically be the fifth factor. So what should we make of this capital asset pricing model versus a three factor model? So, you know, cap-M versus three factor model. I think that cap-M has a very nice theoretical appeal. Nobel Prizes were awarded as a result of its development. You know, not one, not two, at least three. So you know, kind of, and I think it makes intuitive sense in terms of, you know, hey, why do we buy property insurance? Forget that your mortgage company may require you to, you buy the property insurance because you value the fact that you'll get the payment if your house burns down. The property insurance pays you when you need it the most. That is the intuition behind the capital asset pricing model. Certainly, it is imperfect at predicting returns, but I think it is also good to take a step back. This is just a one-variable model. The world is very complicated. It would be amazing if just one variable beta actually could predict returns. So maybe you should give the capital asset pricing model a little break. But the bottom line is the beta in the cap-M doesn't predict returns as well as the model suggests it should. Beta and alpha are frequently reported on common financial websites. We have gone through examples of that: finance.yahoo, Morningstar, others. So it is, you know, kind of, you know relevant still. And you know, you should kind of know the model, what alpha and beta represent. Cap-M is used a lot in a corporate finance setting to assess future, you know, discount or hurdle rates that a firm may use to evaluate a project, or maybe you want to, you know, kind of evaluate yourself. Conduct your own evaluation of your own firm. You need to come up with some discount rate to convert future cash flows into a value today. We will talk about survey evidence regarding what CFOs actually use. Capital asset pricing model is still at the top of the list. In terms of the asset pricing setting, among, you know, money managers, cap-M is maybe a nice starting point. Remember, it is reported on Morningstar, a summary statistic of, you know, kind of performance. But it is, you know, not the ending point. It is just a starting point. Then, you know, kind of more complicated asset pricing models will be used like three factor, four factor models, etc. Multi-factor models have emerged after discovery of the various patterns in, you know, kind of returns. Like the small firm effect, the value effect, now what does the three factor model mean? It could mean that, hey, we are accounting for different types of risk that are manifested in these patterns of returns. So maybe in the real world, risk is multi-faceted. It is not as simple as the mean variance tradeoff of the capital asset pricing model. If risk is multi-faceted, probably a multi-factor model will be better than, you know, kind of using this one factor, capital asset pricing model. Or, you can view the three-factor models. Just simply account for known patterns in returns, or patterns in returns that we've observed in the past. That is accounted for in the three factor model. So, in other words, to earn an alpha in the three factor model, you can't simply employ investment strategies that have been known to work in the past. You know, investing in an index of value stocks may yield an alpha in a capital asset pricing model, but it won't in the three factor model. To get an alpha in the three factor model, you have to be a good stock picker in the universe of value stocks. So you can think of the three factor model is building on the capital asset pricing model, but also controlling for differences in investment style related to the size of the stock as well as the value growth characteristics.
