Capital Asset Pricing Model (CAPM)

The capital asset pricing model (CAPM) is a theory of how financial assets should be priced in equilibrium. It states that the expected return on any stock or other risky asset equals the risk-free rate plus a reward for bearing market-wide risk, and that the size of that reward depends only on the asset's beta: how strongly its returns move with the market as a whole. Companies use CAPM to estimate their cost of equity, analysts use it to set discount rates, and fund managers use it as a yardstick for performance.

CAPM was developed independently in the early 1960s by William Sharpe (published 1964), John Lintner (1965) and Jan Mossin (1966), with related unpublished work by Jack Treynor. It builds on Harry Markowitz's 1952 portfolio theory. Sharpe and Markowitz shared the 1990 Nobel Memorial Prize in Economic Sciences with Merton Miller. The model's key insight is that only systematic risk is rewarded, because other risks can be removed by diversification.

Imagine a group of friends sharing umbrellas on a walk. Some rain falls only on one person, say from a dripping balcony, and that can be avoided by stepping aside. A downpour soaks everyone, and nobody escapes it by moving around. Nobody pays you extra for getting wet under a balcony you could have avoided; people will pay you for standing in the downpour.

CAPM says investments work like this. Problems specific to one company can be cancelled out by owning many companies, so the market does not reward you for them. What it rewards is exposure to the shared storm, the ups and downs of the whole market. Beta measures how much of that storm an investment catches.

The model's central equation, known as the security market line, is:

• $E(R_i)$ is the expected return on asset $i$.
• $R_f$ is the risk-free rate, usually a government bill or bond yield.
• $\beta_i$ is the asset's beta: the covariance of its returns with the market divided by the variance of market returns.
• $E(R_m) - R_f$ is the market risk premium, the extra return expected from the whole market over the risk-free rate.

Worked example: with a risk-free rate of 4%, an expected market return of 9% and a beta of 1.2, the required return is $4\% + 1.2 \times (9\% - 4\%) = 10\%$. A defensive share with a beta of 0.6 would need only $4\% + 0.6 \times 5\% = 7\%$. The 10% figure could then serve as the discount rate in a dividend discount model or a net present value calculation.

CAPM rests on deliberately simple assumptions:

• Investors care only about expected return and variance, measured by standard deviation.
• Everyone can borrow and lend unlimited amounts at the risk-free rate.
• Investors share the same expectations and the same one-period horizon.
• There are no taxes or trading costs, and all assets can be traded.

Under these conditions every investor holds a mix of the risk-free asset and the same market portfolio of all risky assets, an idea that helped inspire index funds and passive management.

A 2001 survey of US chief financial officers by John Graham and Campbell Harvey found that about three-quarters used CAPM to estimate the cost of equity, making it the most common method. Utility and telecom regulators use it to set allowed returns. In performance measurement, CAPM supplies the benchmark for alpha, the return above what beta alone would predict, and for the Treynor ratio, a risk-adjusted return measure that divides excess return by beta. It also sits behind the risk–return trade-off taught in most finance courses.

• Weak empirical fit. Studies since the 1970s found the relation between beta and average return flatter than the model predicts: low-beta stocks earned more, and high-beta stocks less, than CAPM implies. Eugene Fama and Kenneth French reported in 1992 that beta explained little of the cross-section of US returns once company size and book-to-market ratio were considered.
• Untestable market portfolio. Richard Roll argued in 1977 that the true market portfolio includes every asset, including property and human capital, so tests using a stock market index such as the S&P 500 cannot confirm or reject the theory.
• Unstable inputs. Beta estimates change with the period and frequency of data, and the market risk premium is itself disputed.
• Alternatives. Multifactor models add factors such as size, value, profitability, investment and momentum; Fama and French published three-factor (1993) and five-factor (2015) versions. Stephen Ross's arbitrage pricing theory (1976) allows several sources of systematic risk. Each of these still keeps CAPM's core idea that only undiversifiable risk earns a premium.

The model's predictions also depend on markets pricing information correctly, which links it to debates over the efficient market hypothesis and to findings in behavioral economics.

• The Nobel Prize: 1990 Prize in Economic Sciences press release (Markowitz, Miller, Sharpe)
• Investor.gov (US SEC): Beta