# Capital Asset Pricing Model (CAPM)

## What it is:

The **capital asset pricing model (CAPM)** is used to calculate the required rate of return for any risky asset. Your required rate of return is the increase in value you should expect to see based on the inherent risk level of the asset.

## How it works (Example):

As an analyst, you could use CAPM to decide what price you should pay for a particular stock. If Stock A is riskier than Stock B, the price of Stock A should be lower to compensate investors for taking on the increased risk.

The *CAPM formula* is:

r_{a} = r_{rf }+ B_{a} (r_{m}-r_{rf})

where:

r_{rf }= the rate of return for a risk-free security

r_{m} = the broad market's expected rate of return

CAPM can be best explained by looking at an example.

Assume the following for Asset XYZ:

r_{rf} = 3%

r_{m} = 10%

B_{a} = 0.75

By using CAPM, we calculate that you should demand the following rate of return to invest in Asset XYZ: r_{a} = 0.03 + [0.75 * (0.10 - 0.03)] = 0.0825 = 8.25%

The inputs for r_{rf} , r_{m} and B_{a} are determined by the analyst and are open to interpretation.

Beta (B_{a}) -- Most investors use a beta calculated by a third party, whether it's an analyst, broker or Yahoo! Finance.

You can calculate beta yourself by running a straight-line statistical regression on data points showing price changes of a broad market index versus price changes in your risky asset. Note that beta can be different depending on what time frame you pull your data from. Beta calculated with 10 years of data is different from beta calculated with 10 months of data. Neither is right or wrong – it depends totally on the rationale of the analyst.

Market return (r_{m}) – Your input of market rate of return, r_{m}, can be based on past returns or projected future returns. Economist Peter Bernstein famously calculated that over the last 200 years, the stock market has returned an average of 9.6% per year. Whether or not you want to use this as your projection of future stock market returns is up to you as an analyst.

Risk-free return (r_{rf}): U.S. Treasury bills and bonds are most often used as the proxy for the risk-free rate. Most analysts try to match the duration of the bond with the projection horizon of the investment. For example, if you're using CAPM to estimate Stock XYZ's required rate of return over a 10 year time horizon, you'll want to use the 10-year U.S. Treasury bond rate as your measure of r_{rf}.

## Why it Matters:

CAPM is most often used to determine what the fair price of an investment should be. When you calculate the risky asset's rate of return using CAPM, that rate can then be used to discount the investment's future cash flows to their present value and thus arrive at the investment's fair value.

By extension, once you've calculated the investment's fair value, you can then compare it to its market price. If your price estimate is higher than the market's, you could consider the stock a bargain. If your price estimate is lower, you could consider the stock to be overvalued.