# Capital Asset Pricing Model (CAPM)

One of the models that can be used to project the expected return from a common stock, or any type of asset, 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

CAPM states 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, 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 that are relative to the overall stock market risk. Fortunately, this is exactly what a stock's beta measures.

To figure out the expected rate of return of a particular stock, the CAPM formula only requires three variables:

• rf = which is equal to the risk-free rate of an investment
• rm = which is equal to the overall stock market risk
• B = which is equal to the stock's beta

### Using CAPM to Calculate Stock Returns

We've already discussed in our article, 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 calculation provided by the CAPM helps investors determine their return by using a formula that explains the relationship between expected return and risk:

Expected Rate of Return = r = rf + B (rm - rf)

Where:

• rf = The risk-free interest rate is what an investor would expect to receive from a risk-free investment.  Typically, U.S. Treasury Bills are used when examining U.S. dollars, and German Government bills are used for the Euro.
• B = A stock beta is used to mathematically describe the relationship between the movements of an individual stock versus the entire market.  Investors can then use a stock's beta to measure the risk of a security.
• 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 does the CAPM formula tell us?  The formula states 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 being examined.  In other words, the investor can expect a rate of return on an asset that compensates them for both the risk-free rate of interest, the stock market's risk, and the stock's individual risk.

### Calculating Expected Returns

Individuals interested in running through calculations using the CAPM approach, can use our Capital Asset Pricing Model Calculator.  That calculator provides guidance on finding a stock's beta online, information on the risk-free rate of interest, as well as the expected market return. By using the above-mentioned information, the calculator can figure out the expected stock market premium, in addition to the expected rate of return for a capital asset (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 hasn't 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 variable

The APT is different than CAPM in that it doesn't attempt to identify each of the factors for a given stock.  For example, the price of oil might be one factor that applies to ExxonMobil but not to Colgate Palmolive.

While the entire APT approach provides a great deal of analytical "leeway," it is this same lack of specificity that makes the CAPM approach easier to understand and calculate.

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