The CAPM assumes investors are rational, single-period planners who agree on a common input list from security analysis and seek mean-variance optimal portfolios.
The CAPM assumes ideal security markets in the sense that: (a) markets are large and investors are price takers, (b) there are no taxes or transaction costs, (c) all risky assets are publicly traded, and (d) any amount can be borrowed and lent at a fixed, risk-free rate. These assumptions mean that all investors will hold identical risky portfolios. The CAPM implies that, in equilibrium, the market portfolio is the unique mean-variance efficient tangency portfolio, which indicates that a passive strategy is efficient.
The market portfolio is a value-weighted portfolio. Each security is held in a proportion equal to its market value divided by the total market value of all securities. The risk premium on the market portfolio is proportional to its variance, σ2M, and to the risk aversion of the average investor.
The CAPM implies that the risk premium on any individual asset or portfolio is the product of the risk premium of the market portfolio and the asset's beta. The security market line shows the return demanded by investors as a function of the beta of their investment. This expected return is a benchmark for evaluating investment performance.
In a single-index security market, once an index is specified, a security beta can be estimated from a regression of the security's excess return on the index's excess return. This regression line is called the security characteristic line (SCL). The intercept of the SCL, called alpha, represents the average excess return on the security when the index excess return is zero. The CAPM implies that alphas should be zero.
The CAPM and the security market line can be used to establish benchmarks for evaluation of investment performance or to determine appropriate discount rates for capital budgeting applications. They are also used in regulatory proceedings concerning the "fair" rate of return for regulated industries.
The CAPM is usually implemented as a single-factor model, with all systematic risk summarized by the return on a broad market index. However, multifactor generalizations of the basic model may be specified to accommodate multiple sources of systematic risk. In such multifactor extensions of the CAPM, the risk premium of any security is determined by its sensitivity to each systematic risk factor as well as the risk premium associated with that source of risk.
There are two general approaches to finding extra-market systematic risk factors. One is characteristics based and looks for factors that are empirically associated with high average returns and so may be proxies for relevant measures of systematic risk. The other focuses on factors that are plausibly important sources of risk to wide segments of investors and may thus command risk premiums.
An arbitrage opportunity arises when the disparity between two or more security prices enables investors to construct a zero net investment portfolio that will yield a sure profit. The presence of arbitrage opportunities and the resulting volume of trades will create pressure on security prices that will persist until prices reach levels that preclude arbitrage. Only a few investors need to become aware of arbitrage opportunities to trigger this process because of the large volume of trades in which they will engage.
When securities are priced so that there are no arbitrage opportunities, the market satisfies the no-arbitrage condition. Price relationships that satisfy the no-arbitrage condition are important because we expect them to hold in real-world markets.
Portfolios are called well diversified if they include a large number of securities in such proportions that the residual or diversifiable risk of the portfolio is negligible.
In a single-factor security market, all well-diversified portfolios must satisfy the expected return-beta relationship of the SML in order to satisfy the no-arbitrage condition. If all well-diversified portfolios satisfy the expected return-beta relationship, then all but a small number of securities also must satisfy this relationship.
The APT implies the same expected return-beta relationship as the CAPM, yet does not require that all investors be mean-variance optimizers. The price of this generality is that the APT does not guarantee this relationship for all securities at all times.
A multifactor APT generalizes the single-factor model to accommodate several sources of systematic risk.
