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 If you're interested in trying to project the expected return from a common stock - or any type of asset - one of the models you can use is the capital asset pricing model or CAPM. In general, the capital asset pricing model describes the relationship between the risk of a particular asset or stock, its market price, and the expected return to the investor.
The Capital Asset Pricing Model
The capital asset pricing model states that the price of a stock is tied to two variables - the time value of money and the risk of the stock itself. When we look at some of the formulas used in the CAPM later on, we'll see that the time value of money is represented by the risk-free rate of interest or rf.
When measuring the risk of the stock itself, the capital asset pricing model explains that risk in terms relative to the overall stock market risk. Thankfully, we've already got a measure of individual stock risk relative to market risk - that's called a stock's beta.
So to figure out the expected rate of return of a particular stock, the CAPM formula states we only need to understand three variables:
- rf = which is equal to the risk-free rate of an investment
- rm = which is equal to the overall stock market risk
- ß = which is equal to the stock's beta
Using CAPM to Calculate Stock Returns
We've already discussed in our publication on Calculating Stock Prices how the price of a common stock is equal to the discounted value of the expected dividend stream and the end-of-period stock price. The CAPM helps investors to figure out the expected return on a particular investment.
CAPM Formula
The way CAPM helps investors calculate their return is by using a simple formula which explains the relationship between expected return and risk:
Expected Rate of Return = r = rf + ß (rm - rf)
Where:
- rf = The risk-free interest rate is the interest rate the investor would expect to receive from a risk-free investment. Typically, US Treasury Bills are used for US dollars and German Government bills are used for the Euro.
- ß = A stock beta is used to mathematically describe the relationship between the movements of an individual stock versus the market itself. Investors can use a stock's beta to measure the risk of a security versus the market.
- rm = The expected market return is the return the investor would expect to receive from a broad stock market indicator such as the S&P 500 Index. For example, over the last 17 years or so, the S&P 500 has yielded investors an average annual return of around 8.10%.
So what exactly is this CAPM formula telling us? The formula states that the expected return of a stock is equal to the risk-free rate of interest plus the risk associated with all common stocks (market premium risk) adjusted for the risk of the common stock we're examining.
This means the investor can expect a rate of return on this asset that compensates them for both the risk-free rate of interest, the stock market's risk and this particular stock's risk - it all makes sense.
Calculating Expected Returns Using CAPM
If you're interested in running through some calculations using the CAPM approach, we've got a Capital Asset Pricing Model Calculator. That calculator provides you with some guidance on where you can find a stock's beta online as well as some information on the risk free rate of interest and the expected market return.
By using the above mentioned information, the calculator can figure out the expected stock market premium as well as the expected rate of return on the capital assets (a share of common stock in this example).
CAPM versus Arbitrage Pricing Theory
With the advent of modern computers and the complex relationships they can examine, it is surprising there has not been more interest in the Arbitrage Pricing Theory or APT. The approach was first outlined by Stephen Ross in his publication The Arbitrage Theory of Capital Asset Pricing, which appeared in the Journal of Economics in December 1976.
While the CAPM builds on the concept of investors constructing efficient portfolios, the arbitrage pricing theory attempts to explain the expected return on a stock in terms of other factors. APT differs from CAPM in that it assumes that a stock's return depends on multiple factors as explained by the APT formula below:
Expected Return = rf + b1 x (factor 1) + b2 x (factor 2)... + bn x (factor n)
Where:
- b = the sensitivity of the stock to each factor
- factor = the risk premium associated with each factor
The APT is different than CAPM in that it doesn't attempt to identify what each of the factors is for a given stock. For example, the price of oil might be one factor that applies to ExxonMobil but not to Colgate Palmolive.
And while the entire APT approach provides a great deal of analytical "leeway," it is this same lack of specificity that makes the CAPM approach a bit easier to understand and calculate.
About the Author - Capital Asset Pricing Model or CAPM
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