[ Music ] >> All right. So the capital asset-pricing model doesn't perform as well as we would like, although it does seem to perform pretty well on the days when macro economic news is released. But there's another problem if we want to kind of honestly evaluate the performance of the capital asset-pricing model. It not only has a prediction as to what should effect returns, data should predict returns in the capital asset-pricing model, but it also has predictions about what should not predict returns, and that's basically nothing else should predict returns except for beta. So for example, no firm characteristic other then beta should be able to predict stock returns. Looking at the data, some return anomalies have popped up. Now, if these are reflecting some type of risk, some type of multifaceted risk beyond the systematic risk that the CAPM emphasizes, then we probably shouldn't be calling these anomalies. These are higher returns because they represent risk. But for now, let's just kind of call these market return anomalies. One of these is small firm effect, stocks of small firms and by small firm, we need a market value equity of the stock has a low ranking. Small firms do better than large firms historically, higher returns particularly in the month of January. Book-to-market effect or value effect. Stocks with high book-to-market ratios-- remember this is a book value of equity that you see in a balance sheet in the annual report of the firm divided by the market value of the equity. Those type of firms we call them value firms historically have earned higher returns than growth firms, firms that have low book-to-market ratios. So for the growth company, think of a firm where there's like a great idea, but there aren't many tangible assets in place. Maybe a computer server and that's it. Valley stocks doing better than growth stocks, book-to-market effect. Momentum. This is another return anomaly or predictable pattern in return. Instead of calling these market anomalies, we could also call them predictable pattern in returns that have been found in the data, size, value and momentum. What's a momentum effect? Stocks that have done very well during the last year continue to drift up over the next month. Stocks have done very poorly over the last year continue to drift down over the next month. So for those of you who are taking this course for high engagement experience, you want to get credit through the University of Illinois for the course, you're going to have more experience with momentum. We'll do some back testing of the momentum strategy in the AQR momentum funds case study. So let's talk a little bit about the small firm effect. So this is data again from the Ken French Data Library where were rank forms and deciles based on the size of the market value of the equity. So decile 10 is the largest firms. So think like currently in 2015, Apple would be in this group here. Decile 1 are the smallest firms here, and then kind of all those in between. Just looking here at the average annual stock returns, 1927 to 2014, there's a clear pattern. Bigger firms have smaller returns. Difference here of almost 8 percentage points from the smallest stocks to the largest stocks here. Now, one explanation going back to this difference in returns, how much of this is just due to smaller stocks being riskier in a capital asset-pricing model sense? Maybe they have higher sensitivity to the economy, more likely to fail in bad times so to compensate for this kind of kicking you while you're down effect, they have to give a higher return on average because investors realize if we go into a recession, these small CAP stocks are really going to hurt their portfolio performance. So, you can do an analysis, estimate what is the capital asset-pricing model beta for each of these portfolios? Again, using this annual data, 1927-2014, and you do see the small stocks are riskier in that they have higher beta. So again, there's kind of a clear relationship. Smaller stocks, higher beta in the portfolio. For the smallest stocks, their beta is a little over 1.5, so they amplify movements in the broader market. For the biggest stocks, there are betas actually a little less than one. Now remember, when we look at the whole U.S. stock market, that's value weighted so when we look at the whole U.S. stock market, it's going to behave much more like the firms in deciles 10 and 9 because they're bigger so they have more weight in the overall portfolio than the firms in deciles 1 and 2, which are smaller so then have a much smaller weight in the market portfolio. So let's look at the small firm effect without and then with risk adjustment. Without risk adjustment-- and here instead of looking at the total return, we're looking at the return in excess of treasury bills so a simple excess return with no risk adjustment, again we see there's about an 8 percentage point difference. The returns of small firms being about 8 percentage points higher than the return of the largest firms. But once we take into account differences and risk, look at the alpha from the capital asset-pricing model, we see small stocks outperform by about the CAPM benchmark by about 2.6 percentage points per year while for large stocks, they basically are hitting right on their cap and benchmark. So of this roughly 8 percentage points difference in return, only about 2.7 of that is explained by the alpha of the small, small stocks. So the rest of that then obviously explained by difference in risk. So kind of summing up, small stocks over 1927 to 2014-- small stocks, the bottom decile ranked by size have outperformed big stocks the top decile rank by size on the order of about 8 percentage points per year. You might expect smaller stocks to be more sensitive to the economy, more likely to fail in a downturn. That shows up in the CAPM beta. For the small stocks, the beta is 1.54. For the largest stocks, it's 0.93. So there is a pretty big difference in risk. So you put all this information together when we examine the capital asset-pricing model and we look at performance above and beyond the benchmark, the difference is only 2.7 percentage point once we adjust for risk. So of that difference of about 8 percentage points and the performance of small stocks relative to large stocks, about 2/3 of that is accounted for the difference in the underlying risk of the two types of firms, smaller firms riskier on average than higher firms so higher returns. But there is some of that that remains, 1/3 that just represents kind of the alpha or the outperformance, the performance above and beyond the benchmark of the small firms over this long time period, 1927-2014. Nothing stays a secret for long. Such a difference, 8 percentage points per year. People are going to talk about it and write about it, and there were academic articles documenting the size effect back in 1981. So I know there's a bunch of insert joke kind of moments here coming up in the video. What if we break the sample into two parts kind of pre the 1981 article and then post the 1981 article on the size effects? Does the size effect persist? Did the academic papers kind of contribute to diminishing of the size effect, post 1981? So, size doesn't matter as much as it used to. I make it easy for you guys who are kind of joking along at home here. So let's look at decile 1 versus decile 10. So this is looking at the smallest firms performance minus the performance of the largest firms when they focus in terms of decile or we can look at the small minus big factor SMB. This is basically looking at the firms whose size is below median versus those above. So two differentials reflecting size. Look at the dark bar here on the left represents the difference across all the years between small and big firms and again we have these two measures of small and big. The middle bar here kind of medium tone is the result [inaudible] years before 1981 and the final bar here is actually representing then the performance of small relative to big stocks after 1981 going to 2014. And I forgot to mention these returns we're looking at here are already risk adjusted. These are alphas from the capital asset-pricing model. So if you look at-- let's just focus here on the left side decile 1 through 10. The smallest stocks minus the biggest stocks. We have this alpha. Remember, we documented this before of 2.7 percent. This was over the full sample period. Go to prior 1981, 1927 to 1980, this difference was 5.3 percentage points per year. Since then, it's gone away to zero. So size doesn't matter like it used to. If you use this alternative size breakdown, so here it's not as disparate the firms, really focusing on small being below median, big being above median. Again, you still have the same pattern that most of this differential in the performance of small versus big firms occurs during the first part of the sample before 1981 after the academic papers are published documenting, hey small firms are doing historically very well, the small firm effect goes away, which is consistent with a bunch of people going out buying the stocks of small firms. That drives up their price, but that means and subsequently lower returns in the future and this picture here definitely is consistent with that story. Okay, so now we talked about the small firm effect. Let's talk about the famous value premium. If you're talking about the value premium, you certainly have to bring up Warren Buffett here, kind of very famous value investor. So, a good place to look for this kind of documentation of the value effect is work by Eugene Fama and Ken French. So remember that chart I had where they did an updated analysis of the performance of the capital asset-pricing model? Well, this chart is a little different. Here, they're looking at the performance of ten portfolios and within the portfolio they kind of value weight by the market capitalization of the stocks, but the portfolios are formed based on book to market ratio. So ten portfolios. Portfolio 10 has the firms with the highest book-to-market ratio so these are the cement companies, the companies that have a lot of tangible assets, the ratio book value to market value is high. They're right up here. Portfolio one are the growth companies, the lowest book-to-market ratios. So these are the companies that have a great idea so that's why you have a market value. People are willing to pay something to own their stock, but there currently aren't hardly any tangible assets in place that show up on the balance sheet like cash, property and equipment. Those would be in portfolio one. Now, what was kind of key observation from this analysis for each of these portfolios Fama and French had a prediction from the capital asset-pricing model about what the return should be, and they found that when you look at these portfolios, the value portfolios, those that have the biggest value tilt like portfolio 10, portfolio 9, portfolio 8, they outperform their CAPM benchmark by the greatest amount. For those that are more growth like for example, portfolio one, it underperforms its capital asset-pricing benchmark. It has a negative alpha. Therefore, value stocks are outperforming growth stocks. Those with the highest book to market ratio have the biggest alphas here relative to the CAPM benchmark 10, 9, 8 and 7. They're all earning returns historically much higher than would be predicted by the CAPM, which is given by this line here while portfolio one, those of the growth companies, it's actually underperforming its capital asset-pricing value. So value strategies go by several different names here. If you want to invest in value stocks, high book-to-market firms, low price-to-earnings firms, each of these are value stocks. Firms are paying high dividends would also be a value strategy. Just to throw some names out there, Warren Buffett, before him, Ben Graham, to throw out a University of Illinois connection, [inaudible] all of these are well known value investors.
