Price on Value

Free Money and the Capital Asset Pricing Model

John Price,  Ph.D.

You are probably thinking that I wrote ‘free money’ in the title just to get your attention. More, even if you have heard of the capital asset pricing model for stock prices, it is likely you think of it as a bit of academic stodge and certainly not able to supply free money.

Okay, so now the challenge for me is to prove otherwise on both counts in the remaining 800 words. Of course there are catches, two, to be precise. The first is that the capital asset pricing model CAPM has to be valid. The second is that the money is not exactly free; to get it you need to take on a bit more risk.

In the CAPM, risk is defined using the concept of beta. This is that mysterious number that gets quoted on a lot of financial web sites. It is the ratio of the movements of an individual stock relative to the movements of the overall market portfolio or a proxy such as the S&P500 index. It is calculated using daily, weekly or monthly historical data taken over a year or more. Once beta is calculated, it is assumed to be a predictor of future market behavior. If the stock market goes up (or down) by a particular percentage, the theory is that there is a tendency for the stock itself to go up (or down) by the same percentage multiplied by beta.

This is why stocks with a beta greater than 1 are considered riskier; however the market fluctuates, the high-beta stocks fluctuate even more. If the beta is negative, the tendency of the stock is to move in the opposite direction to that of the market.

For the statistically minded, beta is defined as the covariance of the returns of the stock and the market divided by the variance of the returns of the market. These returns are plotted for the past 15 months for the S&P500 index and Gillette on the following chart. The thing to notice is that swings of Gillette are more pronounced than those of the index.

Using this data gives Gillette a beta of 1.37.

The CAPM is a simple formula that says that E(R), the expected rate of return on a stock, satisfies the following formula

E(R) = r + ERP ´ beta,

where r is the risk-free interest rate and ERP is the equity risk premium for the overall market portfolio. To be fair, Sharpe, Lintner and Mossin, the developers of the CAPM, did not just pull this formula out of the air. It is a logical extension of mean-variance theory.

The risk-free interest rate is usually based on one or other of the government treasuries. We’ll take it as 5%. The ERP is a measure of how much better the market portfolio has performed relative to the risk-free rate. In today’s market, the equity risk premium is commonly taken to be in the order of 5-6 per cent. Call it 5.5%.

Consider Gillette with a beta of 1.37. The formula says that your expected return from a purchase Gillette is 5 + 5.5 ´ 1.37 = 12.54%.

On the other hand, if you choose a stock such as Charles Schwab with a beta of 1.85 the expected return is 5 + 5.5 ´ 1.85 = 15.17%. So here is your free money—just invest in stocks with a high beta. The ride might be bumpy, but if you are in for the long run, perhaps it will be worth it.

The question is, do you really believe in CAPM? Does anyone? Firstly, it does not say anything about the company. It is only some simple calculations using historical data of market and stock prices. As Warren Buffett has written, one company might make Barbie dolls and the other pet rocks; if they have the same beta, then CAPM says that one is as good as the other.

With the Efficient Market Hypothesis, stock prices are assumed to follow paths that can be described by tosses of a coin.

Secondly, it does not say anything about the price you pay for the stock. Current stock prices do not appear in the CAPM. (This is not quite true. They may have a small effect on the calculations of the beta.) The reason for this is that the CAPM depends on the notion that the market is efficient. This is a wonderful idea since it simplifies things enormously. (Never mind the fact that only a few diehards continue to believe in it.) There are a number of versions of it but they all end up at the same point. Whatever is the current price of a stock, this is what you should buy, or sell, it for. No amount of analysis will enable you to outperform this strategy, says EMH, the efficient market hypothesis.

The proponents of EMH argue that the same information is available to everyone and that no one is consistently better than anyone else in using this for their stock transactions. That’s like saying that all the hockey players on the ice had the same information regarding the positions and movements of the others and that every player was just as good as Wayne Gretzky in anticipating the next moves.

Here’s another bizarre consequence of the CAPM. Suppose that instead of 59.4375, Gillette closed on March 31 at 50. Then its beta would have been 1.31. Further, if it closed at 70 its beta would have been 1.44. In other words, the higher the stock price the higher the beta. So if you want a high beta portfolio, buy Gillette at a higher price.

Now suppose that the S&P500 closed at 1230 instead of 1286.37 on March 31. Now the beta runs in the opposite direction, from 1.37 down to 1.19. A higher price means a lower beta. This is displayed in the next chart.

Much as I might love the mathematics in different models, the capital asset pricing model is so extreme that I have only one thing to say, "Pass me the next annual report."