MITOCW | watch?v=JE80wLNIhjE The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. ANDREW LO: What I want to do today is to continue where we left off last time in talking about the capital asset pricing model, and we're going to finish that off in the next 15 or 20 minutes. And then, I'm going to turn to applications of the capital asset pricing model. In particular, I want to focus on capital budgeting. That's going to be the last major topic we take on for this course. So let me finish the capital asset pricing model and then I'll talk a little bit about where we're going to go for the remainder of the lectures. You remember last time where we left off was, I decided to estimate the CAPM relationship for a couple of stocks, Biogen and Motorola. And we found that the estimated alphas, the deviations from the CAPM, were pretty sizable for both of these companies. And the interpretation is either, wow these companies are really exceptional values, they offer investors much, much larger expected return than justified by the appropriate market betas. That's one interpretation, or the other interpretation is there something missing with the CAPM. The CAPM doesn't quite capture all of the risks that are giving you these kinds of expected rates of return. So I'm going to come back to that debate in just a few minutes. But I thought, that to continue along these lines, let's explore a little bit about the goodness of fit of these measures. Now, I mentioned last time that the R-squareds, as a measure of goodness of fit, was 17.5 percent for Biogen and 33% for Motorola. Both of which are reasonably representative of the kind of goodness of fit measures that you're going to see with financial data, for the simple reason that financial data is very noisy. And so you're not going to get any single theory that can explain 99.9 percent of the fluctuations in any kind of financial series. So here's a plot of Biogen versus the market. Now the market, as I reminded you last time, is the valuated return, including dividends, of all stocks on the NYSE, Amex, and NASDAQ. So this market portfolio, you can think of as being a broader version than the S&P 500, but it's meant to capture the market. So this is a plot of Biogen versus the market. And you can see that there is some slope that fits this scatter of points, and of course the equation is 1.42 times the market, minus a particular value for the alpha, and then R-squared of about 33% over this particular sample period. So there is a line that goes through these points, but it's not a perfect straight line by any
means. You can see there's a scatter. And so there's a tendency for Biogen to move together with the market, but it's not a perfect linear relationship by any means. That's why the R- squared is not 100%. It's because we're not able to explain all of the fluctuations with a simple linear relationship. Life is more complicated than that, and so the CAPM is really just an approximation to a much more complex reality. Now, a particular stock has a lot of idiosyncratic risk. That's what we talked about last time as the dancing the Irish jig on that catwalk when you're window washing on these skyscrapers. So you can see that that idiosyncratic risk is really quite significant. What happens if we plot, not Biogen against the market, but another market portfolio against the market. like let's say NASDAQ. Well, the next plot shows you. Look at NASDAQ versus the market as a whole. Now NASDAQ, as you know, tends to have smaller stocks, stocks that seem to be technology oriented, and as a result NASDAQ might be more volatile. But nevertheless, there is a very strong common relationship between these two market indexes. And so now, look at this. Scatter of points is a lot tighter. Right? Still, it's not exactly linear, but comparing this to that, you can see the difference. Right? There was a stronger relationship here. And not surprisingly, when you put securities into a portfolio, what gets averaged out? AUDIENCE: Outliers. ANDREW LO: Exactly, the outliers, and what else? What other component? Leland. AUDIENCE: The idiosyncratic risk. ANDREW LO: Exactly. The Idiosyncratic risk, The unusual stock specific kinds of randomness that gets averaged out. So not surprisingly, when you put things into portfolios the noise, or the idiosyncratic risks average out and what you're left with is whatever common factors remain. So I'm going to show you some evidence for how well, or how poorly the CAPM works by looking not at individual stocks, because we know there's a lot of noise with individual stocks. I want to show you what happens when you put stocks into portfolios and you look at how those portfolios do. So let's do one simple example, market cap portfolios. Let's take a look at small stocks and big stocks. Remember at the introduction of this series of lectures, I showed you some empirical evidence that illustrated the fact that small stocks seem to do really well relative to large stocks, the size anomaly. So let's now take the size anomaly and look at it through the lens of the CAPM and ask the
So let's now take the size anomaly and look at it through the lens of the CAPM and ask the question, with the CAPM can we explain the difference between small and large? OK. Well, let's take a look. Over the 40 years from 1960 to 2000, approximately, we see that the small stock portfolio, the smallest decile, the smallest tenth of stocks, in terms of market cap, as a group, as a portfolio, had an average monthly return of 1.33% and a beta of 1.4. On the other hand, the large stock portfolio had an average monthly return of 0.9% and a beta of 0.94. So that seems like it's sort of consistent. Lower risk, lower expected return, but let's plug it in and see if the CAPM relationship actually can tell us something. So the expected return of the stock, according to the CAPM, is going to be given by the risk free rate, plus beta, multiplied by the market risk premium over the sample period that I'm looking at. The market risk premium is about a half a percent per month. So roughly 6% a year. And the risk free rate is also about a half a percent per month during this time period. So now, let's ask the question, what is the expected return of a large stock portfolio? Well according to this, it should be 93 basis points per month. What about the small stock portfolio? According to this, it should be 1.16% per month. Now, this is an amazingly good fit, so I wouldn't take this as typical in the finance literature. But it just so happens that over this 40 year period, the CAPM actually works pretty darn well. 0.99 is the average realize return and 0.93 is what was predicted. For the small cap portfolio, 1.33 is what was realized and 1.16 was what was predicted. So that's pretty good. Now, I want to emphasize the point that this is really good because, let's take a look at other ways of dividing up the universe and seeing whether or not we can get a better explanation of risk and expected return. Here's a picture of size sorted portfolios along the security market line. So remember, security market line is a graph of beta and expected return. Right? The security market line applies to all portfolios and securities, unlike the capital market line that applies only to efficient portfolios and securities. So in this case, we expect a linear relationship. And with the exception of this little outlier up here. From 1960 to 2001 there was actually a pretty reasonable relationship between beta and expected return. In other words, the CAPM looks like it's actually doing OK for size sorted portfolios. The higher the beta, the higher the expected return. The lower the beta, the lower the expected return for size sorted portfolios. Now, what about for beta sorted portfolios? Suppose you took a bunch of portfolio and grouped them into beta's and asked the
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