In our last session together we defined the capital asset pricing model, the CAPM. In this session, we're going to turn our attention to the empirical evidence concerning the performance of the CAPM in financial markets. So to quickly recap. The CAPM provides a very simple and intuitively appealing model that links the notions of expected return and systematic risk via linear model or relationship. Specifically, it suggests that the return that could be expected of the investment is equal to the risk freeing right of return. Plus some adjustment for the risk of the asset, where the specific risk that is compensated is systematic or non-diversifiable risk. Now, we saw how an asset's beta measured the asset systematic risk, by capturing the relationship between the returns of a risky asset and the broader market portfolio. This beta measure is a relative risk measure, in so much as it measures risk relative to the benchmark market portfolio. With assets that have betas greater than one, having greater systematic risk in the market, and assets with betas less than one being regarded as being less risky than the benchmark market portfolio. But the question is does the model work? That is does the CAPM provide an accurate measure of the expected return of a risky asset. If it does do this, then we have solved one half of every valuation problem, in that the value of an asset is simply the present value of the cash flows we expect the asset to generate over its life. Therefore, if the CAPM works, then we can use it to derive the discount rate to value any asset for which we can reliably estimate the systematic risk measure, beta. Well, let's think about this a little more closely. The CAPM is a model of expectations. To test the CAPM, I mean really test the CAPM, ideally, we would gather data on the expectations of what the returns will be from a whole lot of different risky assets. We would then compare these observed expectations with the expected returns generated by the Capitol Asset Pricing Model. If they matched up pretty well, then we could say that the CAPM is a pretty good model of expectations. The problem, of course, is that this isn't an easy thing to do, for a whole host of reasons. Firstly, as we have just pointed out, the CAPM is a model of forward-looking expectations. How can we possibly gather the market's expectation of the future return from a single risky asset? Famously, if I ask five economists for their expectations of inflation in the next year I'll get six different answers. So how much luck am I going to have when I attempt to work out the current expected return of a small unlisted company located in Yambuk, in the Australian countryside. Even if I could actually observe everybody's expectation of returns, how do I then collapse all of these numbers into a single rate of expected return? The second challenge I face in testing the CAPM is that the theory behind the CAPM does not provide specific guidance about exactly how to operationalize the model. For example, it requires the specification of a risk-free rate of return. But which risk-free rate of return should I use? Is it the rate on short-term treasury bills or long-term government bonds? Let's say we go with treasury bills. That's fine. But, which government's treasury are you actually referring to? Presumably, and to mangle a quote, attributed to the renowned author, George Orwell, some countries debt securities are more risk-free than others. Continuing on with specification issues. The next element of the CAPM equation is the asset's beta. Now to measure beta we need to observe the way in which the asset's returns covary with the returns of the market portfolio. Theory tells us that the market portfolio is a valuated portfolio that consists of all risky assets in existence. Now obviously it's impossible to precisely define the constituents of such a portfolio, let alone observe the returns in it. But, let's say you could. Let's say you could identify the returns from a portfolio consisting of all risky assets. In order to estimate any individual asset's beta, we need to observe how the returns of the asset move relative to the market portfolio. But the theory is silent on the issue of the estimation period you should employ to calculate beta. Should you estimate it over the last ten years, ten months, or ten days? Even if you were sure of your estimation period, it's still not clear what return interval is optimal for better estimation. Should you be measuring standard deviation on the correlations coefficient using monthly, weekly, daily, hourly, or minute-by-minute returns? Now, many, many years ago, back when I was a newly mentored academic. It was standard to estimate betas using five years of monthly returns. Nowadays, it's much more common to use shorter estimation periods and smaller return intervals. So where does that leave us? Well firstly, to get around the problem of not being able to accurately observe expectations of the returns of different assets, we make an assumption that whatever the expectations are they're unbiased. Now what that means is that the realized returns that we observe in the market should on average match the unbiased expectations of investors. If the CAPM is an accurate model of expectations, then it follows that we should find that high beta stocks should earn high returns on average than low beta stocks. Indeed if the CAPM is the correct model of expected returns, then no other variable but beta should accurately explain variability in the realized returns of assets across the market. Now this leads us to one of the most famous pieces of research in finance in the last 30 years. Back in 1992, Eugene Farmer and Kenny French published a paper entitled <i>The Cross-Section of Expected Stock Returns</i>. In this paper they tested whether the variability in stock returns observed between 1964 and 1990 could be explained by a mix of variables including beta, size as measured by the firm's market capitalization, and the ratio of the Book Value firm's equity to its Market Value of Equity. This book to market ratio is most often interpreted as a measure of the growth prospects of the firm. With high book to market ratios implying that the firm is a low growth firm which we also refer to as a value firm. While low book to market firms are those with high growth prospects. And not surprisingly are referred to as growth firms. So, what do they find? Well, here's what they did. At the beginning of each year, they sorted firms into groups or portfolios, based upon their identifying characteristic of interest. They then measured returns for each portfolio, to see if there was a relationship between the characteristic of interest, and subsequent return behavior. This first chart provides the evidence with respect to beta portfolios. Now if the CAPM was the correct model of expectations, and if our beta estimate was an accurate measure of the true beta of the companies in the sample, then we would expect higher beta stocks to earn higher returns than low beta stocks. That is on this graph, we would expect to see the columns getting higher as we move from the left hand side to the right hand side of the graph. As you can see, there's no such relationship documented. Now what about the other characteristics of interest? The next thing the researchers did was group firms together according to their market capitalization. Now you'll recall that the market capitalization for a firm is simply the total market value of all of the firm's equity, so it's a size proxy. As you can see from this graph there is a definite size affect. In that the portfolios made up of smaller firms earn higher returns than the portfolios consisting of larger firms. So what about book to market ratios? Say here. The authors formed their portfolios of sample firms on the basis of book to market ratio. So as we move from the left to the right, we are moving from growth firms, firms like Facebook and Trip Advisor, to value firms, which traditionally include consumer staple firms like Kellogg's and Kraft. What do we find? Well similarly to the results for size, we find that the ratio of book to market values do have a strong relationship with future returns. Specifically, we see that value firms earn much higher returns than growth firms. Finally, the authors run a series of statistical tests to check that the initial results weren't due to the specific methodology that that employed. They report, “In a nutshell, market beta seems to have no role in explaining the average returns on NYSE, AMEX and NASDAQ stocks for the period between 1963-1190, while size and book-to-market equity capture the cross sectional variation in average stock returns…” They conclude by suggesting that “if there is any role for beta in explaining variability in stock returns, it would only be as part of a multifactor model…” That is a model that includes factors other than beta such as size and book-to-market ratios. To summarize. In this session, we've highlighted the challenges that researchers face in attempting to test the Capital Asset Pricing Model. We've also looked at the key findings of Fama and French's 1992 article, which documented no discernible relationship between returns and beta, but did find evidence of a relationship between returns and size and returns in book-to-market ratios. The next questions that we need to answer are, firstly, have multi-factor models been developed in light of the Fama and French evidence? And then secondly, let's put academics to the side for a moment and ask the managers, what do they actually do when hunting around for a discount rate? That will be the topic of our next session together.
