The Capital Asset Pricing Model (CAPM) is a linear model that describes the relationship between risk and expected return of a risky asset. The CAPM formula states that the return on each risky security or portfolio is simple the risk free rate plus some risk premium for investing in the risky security (the risk premium can be thought of as compensation for taking on the additional risk above the risk free investment). The risk premium is the return provided by the "market" less the risk free return. In other words, it is the amount of extra return on top the of the risk free rate that you should be compensated for for exposing yourself to securities riskier than the risk free asset. Beta, often referred to as non-diversifiable risk, systemic risk, or market risk, represents the sensitivity of the security's returns to the market's returns. That is, the market risk premium measures the amount of extra return you should earn for holding risky assets, and the beta measures the amount of riskiness of each security. The formula for CAPM is as follows:
The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. For example, if Security A has an expected return of 5%, but based on the CAPM the expected return should be 6%, then you should not buy Security A because for the same level of risk you can find other investments with an expected return of 6%.
Using the CAPM model and the following assumptions, we can compute the expected return of a stock: if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17% (3%+2(10%-3%)).