Capital Asset Pricing Model
The capital asset pricing model (CAPM) is a foundational model in financial economics that relates the expected return on an asset to its systematic risk. Developed in the 1960s by William Sharpe, John Lintner, and Jan Mossin, building on the earlier work of Harry Markowitz on portfolio theory, CAPM provides a framework for pricing risky securities and for estimating the cost of capital. Sharpe received the Nobel Memorial Prize in Economic Sciences in 1990 for his contribution.
The model
CAPM expresses the expected return on an asset as the risk-free rate plus a risk premium proportional to the asset's systematic risk:
- E(Ri) = Rf + βi · (E(Rm) − Rf)
where E(Ri) is the expected return on asset i, Rf is the risk-free rate of return, E(Rm) is the expected return on the market portfolio, and βi (beta) measures the asset's sensitivity to movements in the market.
The term (E(Rm) − Rf) is the market risk premium, the additional return investors require to hold the market portfolio rather than a risk-free asset.
Assumptions
CAPM rests on a set of simplifying assumptions:
Investors are risk averse and seek to maximise expected utility. Markets are perfectly competitive, with no individual able to influence prices. Investors have homogeneous expectations about the distribution of returns. There are no transaction costs or taxes. Investors can borrow and lend unlimited amounts at the risk-free rate. All assets are marketable and divisible. Investors hold well-diversified portfolios and care only about systematic risk.
These assumptions are strong and are not satisfied in reality, which is a principal source of criticism of the model. Nonetheless, CAPM provides a useful benchmark and remains widely used.
Systematic versus unsystematic risk
CAPM's central insight is the distinction between two types of risk.
Unsystematic risk (also called idiosyncratic or specific risk) is risk unique to a particular firm or industry, such as the risk that a company's product will fail or that a factory will be struck by a disaster. This risk can be eliminated through diversification, by holding a portfolio of many assets.
Systematic risk (also called market risk or non-diversifiable risk) is risk that affects the entire market, such as changes in interest rates, inflation, or economic conditions. Because it affects all assets, it cannot be eliminated through diversification. Investors must be compensated for bearing systematic risk, and CAPM measures this exposure through beta.
Beta and the security market line
Beta measures the responsiveness of an asset's return to changes in the market return. The market portfolio itself has a beta of one. A beta greater than one indicates that the asset is more volatile than the market (an "aggressive" asset); a beta less than one indicates that the asset is less volatile (a "defensive" asset). A beta of zero corresponds to the risk-free asset.
Beta is calculated as:
- βi = Cov(Ri, Rm) / Var(Rm)
The security market line plots the relationship between expected return and beta as specified by CAPM. Assets that plot above the line are undervalued (offering more return than their risk warrants); assets below the line are overvalued.
Applications
CAPM is widely applied in finance.
Cost of equity capital is estimated using CAPM, providing an input to corporate capital budgeting and to the weighted average cost of capital.
Performance evaluation uses CAPM to compute risk-adjusted measures such as the Sharpe ratio, the Treynor ratio, and Jensen's alpha, which assess whether a portfolio manager has generated returns in excess of those justified by the risk taken.
Portfolio construction uses CAPM to determine the expected return on assets and to construct efficient portfolios.
Regulatory purposes employ CAPM in the estimation of the cost of capital for regulated utilities.
Criticisms and extensions
CAPM has been extensively tested empirically, and the results have been mixed. Early tests appeared to support the model, but later research identified anomalies that CAPM could not explain, including the small-firm effect (small firms earn higher returns than beta would predict), the value premium (value stocks outperform growth stocks), and momentum (past winners continue to outperform).
The Fama–French three-factor model extends CAPM by adding size and value factors, and the Carhart four-factor model adds momentum. Other extensions address the effects of liquidity, macroeconomic factors, and investor behaviour.
Critics point to the difficulty of measuring the market portfolio, the instability of beta estimates, and the violation of the model's assumptions in practice. Defenders argue that, despite these limitations, CAPM provides a valuable framework for thinking about risk and return, and that its simplicity and tractability make it useful despite its imperfections.