The Capital Asset Pricing Model describes the relationship between risk and the expected rate of return on an investment.

Expected return on the investment, r.
The CAPM calculates the expected return on an investment, taking into account the average return on the market as a whole, and the systematic risk of the investment itself.

Return on a riskfree investment, R_{f}.
This is the value of the return on an investment which has a beta, or systematic risk, of zero. This is normally based on the arithmetic average of historical riskfree rates of return.

Average return of the market as a whole, R_{m}.
This is the expected return on the market as a whole. It is usually estimated by measuring the geometric average of the historical returns on a market portfolio.

Beta, ß.
Beta is a measurement of systematic risk, or the sensitivity of an investment to movements in the market as a whole. The price of an investment with a beta of 1.0 will move in exactly the same way as the market. The price of an investment with a beta of 0.5 will move by 0.5% for every 1% movement in the market. Hence the greater the measure of beta, the greater the volatility of the investment.
The CAPM enables the plotting of the security market line (SML), which demonstrates that the expected return on an investment,
$r$, is directly proportional to its volatility,
$\xdf$. The gradient of the SML,
$\mathrm{\xdf\hspace{0.5em}}\left({R}_{m}{R}_{f}\right)$, gives the risk premium, which is the difference between the expected market rate of return and the riskfree rate of return, in relation to the volatility of the individual investment. The point at which the SML cuts the yaxis is the value of the return on a riskfree investment, ie when the systematic risk,
$\xdf$, is zero. The point at which
$\xdf=1.0$ gives the value of the expected rate of return for the market as a whole.
Example
If the expected rate of return on a riskfree investment, such as a government bond, is 3%, the expected return in the stock market as a whole is 8% and the ß of the investment in question is 0.8, we can use the CAPM to determine the expected rate of return on the investment:

$r={R}_{f}+\xdf\hspace{0.5em}\left({R}_{m}{R}_{f}\right)$

$r=3+\mathrm{0.8\hspace{0.5em}}\left(83\right)$

$r=7\%$
Points to consider
It is important to remember that CAPM was developed as a predictive model to provide the expected return on an investment; it does not have the benefit of hindsight. Many of the criticisms levelled at CAPM arise from actual observed figures calculated after the event. There are many reasons why an investment may not meet its expected return; some alternatives to CAPM have been developed in an attempt to take these factors into account:

Arbitrage pricing theory.
This theory takes into account macroeconomic factors and possible market imperfections. It uses individual risk calculations for each identified factor that may affect the investment’s expected return.

The threefactor model.
This model takes into account the return on assets in the market as a whole, the size of the investment and the effect of differing booktomarket ratios.
Another weakness is that the CAPM is theoretical; it assumes, for example, that trade is conducted taxfree and without transaction costs, and that all investors agree upon the beta of an investment.