The CAPM equation, from the capital asset pricing model, sets the return required on an asset equal to the risk-free rate plus the asset’s beta multiplied by the equity risk premium, where the equity risk premium is the expected return on the market less the risk-free rate. Applied to a company’s own stock it produces the cost of equity, the return equity holders require for leaving money in that business rather than putting it somewhere of the same risk. It prices one kind of risk only, the kind an investor cannot diversify away.
The Formula and Its Terms
The equation puts the asset’s expected return on the left and two components on the right.
Ra = Rf + Ba x (Rm - Rf)
Ra the return the asset's risk requires, its expected return under the model.
Written Re when the asset is a company's own equity, where it is the cost
of equity
Rf the risk-free rate, the return on an asset treated as carrying no default risk
Ba the asset's beta, its sensitivity to movements in the market as a whole
Rm the expected return on the market as a whole
Rm - Rf the equity risk premium, also called the market risk premium: the extra return
expected for holding market risk instead of the risk-free assetRa is the output, and it is the only term the equation solves for. Rf is the input closest to observable, because it is read off government debt of a chosen maturity rather than estimated. Rm is an expectation rather than an observation, which is why the pair Rm minus Rf is normally estimated as a single quantity, the equity risk premium, instead of estimating each side and subtracting. Ba is the only term specific to the asset, since everything else in the equation is the same for every asset priced on the same day. When the asset is a company’s own equity the output is written Re and called the cost of equity, and that is the form a valuation reaches for.
What Beta Measures
Beta measures systematic risk, the part of an asset’s variability that moves with the market and cannot be removed by holding other assets alongside it. A beta of 1 moves with the market. A beta between 0 and 1 damps the market’s moves, a beta above 1 amplifies them, a beta of 0 leaves the asset priced at the risk-free rate, and a negative beta moves against the market.
Risk that belongs to one company alone, such as a lost client or a lawsuit, is diversifiable, so the model pays nothing for bearing it. That is why the equation carries one risk term rather than two, and why a company can swing hard on its own news without that showing up in its beta.
A Worked Example
The inputs below are stated for the example rather than read from a market.
Rf risk-free rate 4.0% stated input
Ba beta 1.2 stated input
Rm expected market return 10.0% stated input
Equity risk premium = 10.0% - 4.0% = 6.0%
Ra = 4.0% + (1.2 x 6.0%)
= 4.0% + 7.2% = 11.2%Beta and the equity risk premium are both estimates, so the output is only as defensible as the work behind them.
Where a CPA Firm Meets It
A firm rarely meets CAPM as an answer. It meets it as an input, buried inside a rate somebody else has to accept.
In a valuation engagement the output feeds the equity leg. Re is one of the two legs blended into the weighted average cost of capital, which cost of capital sets out in full, including the appraiser’s step of matching the rate to the benefit stream. That rate does its work inside the income approach, one of the three approaches set out in valuation. Where the subject is an accounting practice, the factors that actually move the number are worked through in how to value a CPA firm.
On the audit side the rate stops being a conclusion and becomes something to test. PCAOB standards are the ones registered firms follow in preparing audit reports for public companies and other issuers, and for broker-dealers (PCAOB, Auditing Standards). In that setting AS 2501 tells the auditor to identify which of the assumptions used by the company are significant assumptions to the accounting estimate, that is, the assumptions that are important to the recognition or measurement of the accounting estimate in the financial statements. Its examples include assumptions that are sensitive to variation, such that minor changes in the assumption can cause significant changes in the estimate, and assumptions that involve unobservable data or company adjustments of observable data (paragraph .15, PCAOB, AS 2501).
A cost of equity built from CAPM sits in both of those examples, because beta and the equity risk premium are estimated rather than observed. The standard never names CAPM. It requires the reasonableness of the significant assumptions to be evaluated both individually and in combination, including whether they are consistent with existing market information (paragraph .16, PCAOB, AS 2501).
What CAPM Is Not
The Weighted Average Cost of Capital
CAPM prices equity, and only equity. The weighted average cost of capital is the blend of that number with the after-tax cost of debt in the proportions that actually fund the business, so CAPM supplies one of two inputs rather than the finished rate. Using a CAPM output as the discount rate for a business that carries debt prices every borrowed dollar as though it were equity, which normally pushes the rate too high.
Total Volatility
Beta is the part of an asset’s movement that tracks the market, not the size of its movement. A company’s stock can be far more volatile than the market and still carry a modest beta, if most of that movement is its own.
A Return Forecast
The equation answers what return the risk requires, not what return will arrive. Two analysts using the same beta and the same premium are agreeing on what the risk has to be compensated for, not on what the asset will do.
Common Questions
No. The two coincide only where a business carries no debt at all, because the equity leg then carries the whole weight of the blend. Anywhere else, a CAPM result is an input to the weighted average and never the weighted average itself.
Beta is estimated statistically, by regressing the asset’s returns against the returns of a market index over a chosen window, so the same company yields different betas depending on the index, the return interval and the length of the period used. A private company has no traded return series at all, so its beta is commonly built from public companies in comparable businesses and then adjusted for the difference in borrowing between those companies and the subject.
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