CAPM

The capital asset pricing model, almost always written CAPM, is a finance model that estimates the return an investor should expect from an asset given the amount of market risk it carries. Its equation is short:

Expected return = risk-free rate + beta × (expected market return − risk-free rate)

The three inputs are a risk-free rate, usually proxied by a short-term government security; the market's expected return above that rate, which is the equity risk premium; and the asset's beta, its sensitivity to the market's movements. The model's central claim is that only the risk an investor cannot diversify away, the part that moves with the market, is compensated. Risk specific to a single company earns nothing in expectation, because a holder could have removed it by diversifying and chose not to.

A note on the name. This page is titled by the acronym rather than the expansion because that is overwhelmingly how the model is searched and written. The two are the same thing and are used interchangeably below. The model is also sometimes called a Sharpe-Lintner model after its authors, which should not be confused with the Sharpe ratio, a separate measure.

Where it came from, and what problem it solved. The Royal Swedish Academy of Sciences awarded the 1990 prize in economic sciences to Harry Markowitz, Merton Miller and William Sharpe, and Sharpe's share was "for his contributions to the theory of price formation for financial assets, the so-called, Capital Asset Pricing Model (CAPM)". The Academy located his achievement in a 1964 essay, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, and described the step it represented: the model took Markowitz's portfolio theory, which explains how one investor should choose, and used it as an explanatory theory of how prices form in the market as a whole. John Lintner reached a closely related result in 1965, and Fama and French's later review names both as the model's authors. Sharpe returned to its assumptions in his own 1990 Prize Lecture, which the Nobel Foundation lists as "Capital Asset Prices with and without Negative Holding".

What the Academy said the model implies, which is the cleanest statement of it. An investor chooses risk exposure by combining borrowing or lending at the risk-free rate with an optimal portfolio of risky securities, and the composition of that risky portfolio does not depend on the investor's own appetite for risk, only on the prospects of the securities. Attitude to risk shows up solely in how much is held in the risky portfolio versus in the risk-free asset. For an investor with no special information there is no reason to hold anything other than the market portfolio. What the Academy calls the "beta value" of a share "indicates its marginal contribution to the risk of the entire market portfolio of risky securities", and in an efficient market "the risk premium and thus also the expected return on an asset, will vary in direct proportion to the beta value".

Two uses, both still ordinary practice. Corporate finance uses CAPM to estimate a company's cost of equity, which then feeds discounted-cash-flow valuations and capital-budgeting decisions. Investment analysis uses it as the benchmark against which a manager's result is measured: run the model, get the return the portfolio's market risk predicted, and the difference between that and the actual return is alpha. Fama and French describe the same two applications, "estimating the cost of equity capital for firms and evaluating the performance of managed portfolios", and note that the model is "the centerpiece, indeed often the only asset pricing model taught in MBA level investment courses".

The honest verdict on how it has held up. Fama and French's review in the Journal of Economic Perspectives is unusually blunt for a peer-reviewed survey. They write that "the attraction of the CAPM is its powerfully simple logic and intuitively pleasing predictions about how to measure risk and about the relation between expected return and risk", and then, in the next sentence, that "perhaps because of its simplicity, the empirical record of the model is poor" and "poor enough to invalidate the way it is used in applications". That judgment coexists with the model's continued teaching and use, which is worth sitting with rather than resolving: CAPM is the reference frame the entire vocabulary of risk-adjusted return is built on, and it is a poor predictor of what returns actually turn out to be. Both are true.

The assumptions that cause the trouble. The model assumes investors care only about the mean and variance of a single period's return, agree about those prospects, can borrow and lend freely at one risk-free rate, and face no taxes or transaction costs. Relaxing any of these changes the result, which is why the literature since has replaced the single market factor with several, adding characteristics such as company size and relative price. That is the lineage the multi-factor approaches descend from, and they are the answer to CAPM's empirical problems rather than a rejection of the risk-and-return framing it established.

What a practical investor should take from it. Three things survive the empirical criticism intact. Diversifiable risk is not rewarded, so bearing more of it is a cost with no expected benefit. Expected return rises with exposure to the risk that cannot be diversified away, whatever the right way to measure that turns out to be. And "expected" is doing real work in both sentences: the model produces an expectation, not a forecast of what any particular year will deliver.

Begin with the three inputs. Suppose short-term government securities yield 3.5%, and the market as a whole is expected to return 9%. The market's expected excess return, the equity risk premium in the model, is therefore 9% − 3.5% = 5.5%. Beta is supplied per asset.

Take an example with three different holdings. A defensive stock with a beta of 0.8 has an expected return of 3.5% + 0.8 × 5.5% = 3.5% + 4.4% = 7.9%. A stock with a beta of 1.1 gives 3.5% + 1.1 × 5.5% = 3.5% + 6.05% = 9.55%. An aggressive stock with a beta of 1.5 gives 3.5% + 1.5 × 5.5% = 3.5% + 8.25% = 11.75%. The pattern is the model's whole content: every extra unit of market sensitivity buys the same extra slice of the market's premium, in either direction.

Now use it the way a company does. If that second business, with a beta of 1.1, is estimating what its shareholders require, CAPM says the number is 9.55%. A project inside the business expected to return 8% therefore destroys value on this measure even though 8% is a positive number, because the capital funding it could have earned 9.55% at the same risk.

And the way an analyst does. If the aggressive stock's fund actually returned 13% over the period, the model predicted 11.75%, so the excess is 13% − 11.75% = 1.25 percentage points. That residual is what gets called alpha. Two cautions belong with that number. It is only as good as the beta estimate and the market return used, both of which are measured with error; and a positive residual over one period is not evidence of skill, since the model produces expectations rather than predictions and the errors are large.

Pros

• It turns "how much return should this deserve?" into an arithmetic question with three named inputs, which is why it became the standard teaching model.
• It makes the case for diversification precisely rather than by slogan: risk that can be diversified away is not expected to pay.
• It gives the cost of equity a defensible number, which capital-budgeting and valuation both need.
• It supplies the benchmark that makes performance comparable across portfolios with different levels of market exposure.

Cons

• Its empirical record is weak. Fama and French describe it as "poor enough to invalidate the way it is used in applications".
• Every input is estimated. The risk-free rate has to be chosen, the market return forecast, and beta measured from past data that may not describe the future.
• The assumptions are unrealistic in ways that matter, including a single period, a single risk-free borrowing rate, and no taxes or transaction costs.
• A single market factor misses characteristics that later research links to returns, which is why multi-factor models exist.