Based on the behavior of risk-averse investors, there is an implied equilibrium relationship between risk and expected return for each security. In market equilibrium, a security is supposed to provide an expected return commensurate with its systematic risk - the risk that cannot be avoided by diversification. The greater the systematic risk of a security, the greater the return that investors will expect from the security. The relationship between expected return and systematic risk, and the valuation of securities that follows, is the essence of Nobel laureate William Sharpe's capital-asset pricing model (CAPM). This model was developed in the 1960s, and it has had important implications for finance ever since. Though other models also attempt to capture market behavior, the CAPM is simple in concept and has real-world applicability.
Like any model, this one is a simplification of reality. Nevertheless, it allows us to draw certain inferences about risk and the size of the risk premium necessary to compensate for bearing risk. We shall concentrate on the general aspects of the model and its important implications. Certain corners have been cut in the interest of simplicity.
As with any model, there are assumptions to be made. First, we assume that capital markets are efficient in that investors are well informed, transactions costs are low, there are negligible restrictions on investment, and no investor is large enough to affect the market price of a stock. We also assume that investors are in general agreement about the likely performance of individual securities and that their expectations are based on a common holding period, say one year. There are two types of investment opportunities with which we will be concerned. The first is a risk-free security whose return over the holding period is known with certainty. Frequently, the rate on short- to intermediate-term Treasury securities is used as a surrogate for the risk-free rate. The second is the market portfolio of common stocks. It is represented by all available common stocks and weighted according to their total aggregate market values outstanding. As the market portfolio is a somewhat unwieldy thing with which to work, most are often used to gauge the performance of the overall market, as with an index such as the S&P 500. Other indexes are smaller, or more focused, perhaps containing just small companies or pharmaceutical companies or Latin American companies.
Indexes aren't things you invest in, though. To meet the needs of people interested in investing in various indexes, index mutual funds were created. If you want to invest in a certain index, for example, you would invest in an index fund based on it.