Chapter 21
Capital asset pricing model
The capital asset pricing model (or CAPM, as it is universally known) estimates the expected return for a firm’s stock. The calculation uses the prevailing risk-free rate, the stock’s trading history and the return that investors are expecting from owning shares.
When to use it
- To estimate the price you should pay for a security, such as a share in a company.
- To understand the trade-off between risk and return for an investor.
Origins
CAPM was developed by William Sharpe. In 1960, Sharpe introduced himself to Harry Markowitz, inventor of ‘modern portfolio theory’, in search of a doctoral dissertation topic. Sharpe decided to investigate portfolio theory, and this led him to a novel way of thinking about the riskiness of individual securities, and ultimately to a way of estimating the value of these assets. The CAPM model, as it became known, had a dramatic impact on the entire financial community – both investment professionals and corporate financial officers. In 1990, Sharpe won the Nobel Prize in Economics alongside Markowitz and Merton Miller.
What it is
Investors want to earn returns based on the time-value of money and the risk they are taking. The CAPM model accounts for both of these in its formula. First, the risk-free rate, or ‘Rf’, represents the time-value of money. This is the return earned simply by buying the risk-free asset – the current yield on a 10-year US government bond, for example. Second, the asset’s risk profile is estimated based on how much its historical return has deviated from the market’s return. Given that the market has a beta of 1.0 (denoted by βa), an asset whose returns match the market (for example, the shares in a large diversified company) would have a beta close to 1.0. In contrast, an asset whose returns fluctuate with greater amplitude (for example, a high-technology stock) would have a beta higher than 1.0. A defensive stock (for example, a dividend-paying utility) might have a beta lower than 1.0, suggesting its shares are less risky than the market as a whole.
Sharpe developed a simple formula linking these ideas together:
Where:
- Ra = the required return for the asset.
- Rf = the risk-free rate.
- βa = the beta of the asset.
- Rm = the expected market return.
The CAPM indicates that the expected return for a stock is the sum of the risk-free rate, Rf, and the risk premium, or βa (Rm – Rf). The risk premium is the product of the security’s beta and the market’s excess return. Consider a simple example. Assume the risk-free rate of return is 3 per cent (this would typically be the current yield on a US 10-year government bond). If the beta of the stock is 2.0 (it’s a technology stock) and the expected market return over the period is 6 per cent, the stock would be expected to return 9.0 per cent. The calculation is as follows: 3 per cent + 2.0 (6.0 per cent – 3.0 per cent).
As should be clear from this example, the key part of the story is ‘beta’, which is an indicator of how risky a particular stock is. For every stock being analysed, the risk-free rate and the market return do not change.
How to use it
Estimating the risk-free rate is easy because the current yield for a 10-year US government bond is readily available. Estimating the market return is more challenging, because it rises and falls in unpredictable ways. Historically, the market return has averaged somewhere in the region of 5–7 per cent, but it is sometimes much higher or much lower. If the current 10-year US government bond yield is, say, 2.6 per cent, then the market’s excess return is between 2.4 per cent and 4.4 per cent.
A stock’s beta can be found on major financial sites, such as Bloomberg. It is possible to calculate beta on your own by downloading, to a spreadsheet program, a stock’s two- or five-year weekly or monthly history, and the corresponding data for the ‘market’, which is usually the S&P 500.
Top practical tip
CAPM has come to dominate modern financial theory, and a large number of investors use it as a way of making their investment choices. It is a simple model that delivers a simple result — which is attractive, but can lead to a false sense of security.
If you are an investor, the most important practical tip is, first, to understand CAPM so that you can make sense of how securities are often priced, and then to be clear on the limitations of the model. Remember, the beta of a stock is defined by its historical volatility, so if you are able to develop a point of view on the future volatility of that stock — whether it becomes more or less volatile than in the past — you can potentially price that stock more accurately. Think of General Electric’s shares in the 1990s, when its highly predictable earnings growth allowed it to outpace the market, versus the early 2000s when its earnings became more volatile. Had you relied on GE’s beta in the 1990s as an indicator of how well the stock might perform in the future, you would have lost a lot of money after 2000.
Top pitfall
Does CAPM really work? Like many theories in the world of business it is approximately right, but with a very large unexplained component in terms of how much individual stocks are worth. Academic studies have come up with mixed results. For example, Eugene Fama and Kenneth French reviewed share returns in the USA between 1963 and 1990, and they found that there were at least two factors other than beta that accounted for stock returns: whether a firm was small or large, and whether the firm had a high or low book-to-market ratio. The relationship between beta and stock prices, over a short period of time, may not hold.
Further reading
Black, F., Jensen, M.C. and Scholes, M. (1972) ‘The capital asset pricing model: Some empirical tests’, in Jensen, M. (ed.), Studies in the Theory of Capital Markets (pp. 79–121). New York: Praeger Publishers.
Fama, E.F. and French, K.R. (2004) ‘The capital asset pricing model: Theory and evidence’, Journal of Economic Perspectives, 18(3): 25–46.
Sharpe, W.F. (1964) ‘Capital asset prices: A theory of market equilibrium under conditions of risk’, Journal of Finance, 19(3): 425–442.