What Is the Capital Asset Pricing Model (CAPM)? Formula and Assumptions

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The capital asset pricing model (CAPM) is a model that estimates the return an investor should require from an asset given its exposure to systematic risk, the market-wide risk that diversification cannot remove. It expresses that required return as the risk-free rate plus a premium scaled by the asset’s beta, its sensitivity to movements in the overall market. In corporate finance and valuation, CAPM is the standard starting point for estimating a company’s cost of equity, the discount rate applied to its future cash flows.

What the Capital Asset Pricing Model Says

CAPM describes a linear relationship between risk and required return: investors are compensated for the time value of money and for systematic risk. An asset’s own volatility matters only to the extent that it moves with the market.

The reasoning starts with diversification. A single stock carries two kinds of risk. Unsystematic risk comes from events specific to the company: a failed product launch, a lawsuit, a management change. Systematic risk comes from forces that affect nearly all assets at once: recessions, interest rate changes, broad shifts in investor sentiment. Holding many stocks dilutes unsystematic risk because the company-specific surprises tend to offset each other. Systematic risk remains no matter how many stocks a portfolio holds.

Because unsystematic risk can be eliminated cheaply by diversifying, CAPM argues the market will not pay investors for bearing it. The only risk that commands a premium is the part an asset contributes to a fully diversified portfolio, and beta measures that contribution.

The CAPM Formula

The CAPM equation is:

E(Ri) = Rf + βi × (E(Rm) − Rf)

where:

• E(Ri) is the expected (required) return on asset i
• Rf is the risk-free rate
• βi is the beta of asset i
• E(Rm) is the expected return on the market portfolio
• E(Rm) − Rf is the market risk premium, sometimes called the equity risk premium when the market is an equity index

The risk-free rate compensates for the time value of money. An investor who ties up capital in any asset gives up the return available with no default risk, so every risky asset must offer at least that much. In U.S. practice, analysts typically use the yield on Treasury bills or, for long-lived valuations, a longer-dated Treasury yield matched to the horizon of the cash flows being discounted. The choice matters: when short and long rates differ, the same company can produce a noticeably different cost of equity depending on which maturity is used.

The market risk premium is the extra return investors demand for holding the market as a whole instead of the risk-free asset. It is a single number applied to every asset in the same market.

Beta scales that premium for the specific asset. A beta of 1.0 receives the full market premium; a beta of 0.5 receives half; a beta of 1.5 receives one and a half times the premium.

The structure means the formula is a straight line. Doubling beta doubles the risk premium portion of the required return, though not the total return, because the risk-free rate is added on top.

How Beta Fits In

Beta measures how much an asset’s returns move in relation to the market’s returns. It is calculated as:

β = Cov(Ri, Rm) / Var(Rm)

An equivalent form is the correlation between the asset and the market multiplied by the ratio of their standard deviations:

β = ρ(i,m) × (σi / σm)

The second form shows why a highly volatile stock does not automatically have a high beta. If its swings are largely unrelated to the market (low correlation), most of its volatility is unsystematic and does not raise its beta much.

Hypothetical example: a stock has an annual standard deviation of 30%, the market’s is 15%, and their correlation is 0.6. Beta = 0.6 × (30% / 15%) = 1.2.

Interpreting beta values:

• β = 1.0: the asset tends to move in line with the market.
• β > 1.0: the asset tends to amplify market moves and carries more systematic risk than the market.
• 0 < β < 1.0: the asset tends to move with the market but less sharply; adding it lowers a portfolio’s market sensitivity.
• β = 0: no linear relationship with the market. Under CAPM, such an asset should return only the risk-free rate.
• β < 0: the asset tends to move against the market. CAPM assigns it a required return below the risk-free rate, because it acts as a hedge. Persistently negative betas are uncommon among individual stocks.

In practice, beta is estimated by regressing the asset’s historical returns against the returns of a market proxy over the same period, using daily, weekly or monthly data. This regression is often called the market model, and it differs from CAPM in purpose. The market model is a statistical description of past co-movement; CAPM is an equilibrium theory about what returns should be. CAPM borrows the slope of the market model as its beta input.

Calculating CAPM: A Worked Example

Hypothetical assumptions:

• Risk-free rate: 4%
• Expected market return: 9%
• Stock’s beta: 1.2

Step 1: Market risk premium. 9% − 4% = 5%

Step 2: Scale by beta. 1.2 × 5% = 6%

Step 3: Add the risk-free rate. 4% + 6% = 10%

The stock’s required return is 10% per year.

Using the result to value a stock

The CAPM return becomes the discount rate for the stock’s expected cash flows. Suppose, under the same assumptions, the stock is expected to pay a $2.00 dividend next year, and dividends are expected to grow 4% per year indefinitely. The constant-growth (Gordon) dividend discount model gives:

Value = D1 / (r − g) = $2.00 / (0.10 − 0.04) = $33.33

If the stock trades at $30, this calculation suggests it is undervalued relative to its risk; at $40, overvalued. The conclusion is only as good as the dividend forecast, the growth assumption and the CAPM inputs. Raise the required return to 11% and the value drops to $28.57, which shows how sensitive valuations are to small changes in beta or the risk premium.

Can CAPM give you a growth rate?

Not on its own. CAPM produces a required return, not a growth rate, but combined with the constant-growth model it can back out the growth rate the market price implies: g = r − D1 / P. With a 10% CAPM return, a $2.00 expected dividend and a $40 price, the implied growth rate is 10% − 5% = 5%. An analyst can then ask whether 5% perpetual growth is plausible for the business.

Using the result in WACC

Companies use the CAPM figure as the cost of equity component of the weighted average cost of capital (WACC). Hypothetical example: a firm is financed 60% by equity and 40% by debt, its CAPM cost of equity is 10%, its pretax cost of debt is 6% and its tax rate is 25%.

• After-tax cost of debt: 6% × (1 − 0.25) = 4.5%
• WACC: (0.60 × 10%) + (0.40 × 4.5%) = 6.0% + 1.8% = 7.8%

A project with risk similar to the firm’s existing business would need to earn more than 7.8% to add value under these assumptions.

How CAPM Is Used

Cost of equity and capital budgeting. Equity has no stated interest rate, so its cost must be estimated. CAPM provides a consistent method that ties the estimate to observable inputs, which is why it appears in corporate valuation, fairness opinions and regulatory rate-setting.

Discount rates for valuation. Discounted cash flow and dividend discount models need a rate that reflects risk. CAPM supplies it, as in the example above.

Performance evaluation. CAPM defines what return a portfolio should have earned for its beta. The difference between the actual return and that benchmark is Jensen’s alpha:

α = Ri − [Rf + βi × (Rm − Rf)]

Here the realized market return is used instead of the expected one. Hypothetical example: with a 4% risk-free rate, a realized market return of 11% and a beta of 1.2, the benchmark return is 4% + 1.2 × 7% = 12.4%. A portfolio that returned 14% produced an alpha of 1.6 percentage points. A portfolio that returned 12% beat the market’s 11% but still had negative alpha, because its higher beta called for more. See alpha in finance for more; the Sharpe ratio is a related measure that uses total volatility instead of beta.

Reasonableness checks. Even skeptics use CAPM to test assumptions. If an investment is justified with a 13% expected return while the company and its peers have historically earned 9% to 10%, CAPM helps frame whether the gap reflects higher systematic risk or simple optimism.

Indexing. CAPM’s message that higher expected returns come only from bearing more market risk supported holding the market portfolio itself, contributing to the growth of low-cost index funds and ETFs that track broad benchmarks.

CAPM, the Efficient Frontier and the Security Market Line

CAPM grew out of modern portfolio theory, and its graphs come from the same framework.

The efficient frontier and the capital market line

Plot every possible portfolio of risky assets by expected return (vertical axis) and standard deviation (horizontal axis). The upper-left edge of that cloud is the efficient frontier: the portfolios with the highest expected return for each level of risk. Anything below or to the right of it is inferior.

Introducing a risk-free asset changes the picture. A straight line drawn from the risk-free rate tangent to the frontier is the capital market line (CML). The tangency point is the market portfolio. Combinations of the risk-free asset and the market portfolio, including borrowing at the risk-free rate to hold more than 100% of the market, lie on this line and dominate every other risky portfolio. The slope of the CML is the market’s reward per unit of total risk.

The security market line

The security market line (SML) is the graph of the CAPM equation itself. It plots expected return against beta instead of standard deviation. Its intercept is the risk-free rate, and its slope is the market risk premium. At β = 1.0, the line passes through the expected market return.

The SML and CML are easy to confuse, but they answer different questions:

The SML gives CAPM its practical use as a pricing test. An asset whose expected return plots above the line offers more return than its beta requires, which suggests it is underpriced. An asset plotting below the line offers too little, which suggests overpricing. Under the model’s equilibrium, buying and selling should push every asset back onto the line.

The Assumptions Behind CAPM

CAPM is derived from a stylized market. The main assumptions are:

• Investors are rational, risk-averse and seek to maximize expected utility from returns.
• All investors evaluate investments over the same single period.
• Investors share the same expectations about returns, volatilities and correlations.
• Everyone can borrow and lend unlimited amounts at the risk-free rate.
• Assets can be divided into any size, and all assets are traded.
• There are no taxes, inflation or transaction costs.
• Markets are competitive and efficient: information spreads quickly and is absorbed into prices, and no single investor can move prices.
• Risk and return are linearly related.

Under these conditions, every investor holds the same market portfolio of risky assets, combined with borrowing or lending at the risk-free rate, and asset prices adjust until expected returns line up with beta. Several of the model’s practical problems trace directly to these unrealistic assumptions.

Limitations of CAPM

Beta’s weak empirical record

The most serious challenge is evidence. When Fama and French examined returns on NYSE, AMEX and Nasdaq stocks, they found that differences in beta over long periods did not explain differences in performance. The beta-return relationship was flatter than CAPM predicts, and company size and value (book-to-market ratio) explained returns that beta missed. The linear link between beta and individual stock returns also breaks down over shorter periods.

Beta treats upside and downside the same

Beta is built from variance and covariance, which weigh gains and losses symmetrically. Investors do not experience them symmetrically. Two stocks can share the same beta while one suffers frequent sharp drops and the other moves more evenly, and CAPM assigns them the same required return. Stock returns also are not normally distributed, so measures built on variance can understate the risk of extreme moves.

Estimation choices change the answer

Beta depends on the look-back period, the data frequency and the index used as the market. None of these is standardized, and a company’s measured beta can shift as its business, leverage or industry conditions change. Historical beta is a backward-looking estimate applied to a forward-looking question.

The market portfolio cannot be observed

In theory, the market portfolio contains every risky asset: stocks, bonds, real estate, private businesses, even human capital. That portfolio cannot be bought or measured. Analysts substitute a major stock index such as the S&P 500, which is an imperfect stand-in. Because the theory is about the true market portfolio, tests using a proxy cannot fully confirm or reject it.

Estimating the market risk premium

The market risk premium is an expectation, not an observable number. Analysts estimate it from long-run historical returns, from premiums implied by current prices and forecast cash flows, or from surveys of practitioners. Each method relies on judgment: the historical period chosen, whether averages are arithmetic or geometric, and which risk-free maturity is subtracted. Reasonable estimates can differ by a percentage point or more, and with a beta of 1.2, every point of difference in the premium moves the required return by 1.2 points.

A constant risk-free rate

The model treats the risk-free rate as fixed over the discounting period, but rates move. In the earlier example, if Treasury yields rose from 4% to 6% during a long holding period, the required return and cost of capital would rise too, and a stock that looked fairly priced at the start could look overvalued.

Cash flow forecasts

CAPM supplies the discount rate, but valuation still depends on forecasting future cash flows, which is often the larger source of error.

None of these problems has displaced CAPM from practice. Its inputs are simple and its logic is transparent, which makes it useful as a baseline, a comparison tool and a check on assumptions, provided it is not the only method used to value a security.

Who Developed CAPM

CAPM was developed in the early 1960s by William Sharpe, Jack Treynor, John Lintner and Jan Mossin, working largely independently. Their work extended Harry Markowitz’s portfolio selection theory from the 1950s, which showed how diversification reduces risk and introduced the efficient frontier. Sharpe shared the 1990 Nobel Memorial Prize in Economic Sciences with Markowitz and Merton Miller, in part for his contribution to CAPM.

Alternatives and Extensions

Arbitrage pricing theory (APT). Developed by Stephen Ross, APT allows expected returns to depend on multiple risk factors, which may be macroeconomic (inflation, interest rates, industrial production) or company-specific. It relies on the absence of arbitrage instead of a full market equilibrium and does not require identifying the market portfolio, though it does not specify which factors to use.

Fama-French three-factor model. This model adds two factors to the market factor: size (small companies versus large) and value (high book-to-market versus low). It was built to capture the return patterns that beta failed to explain.

Fama-French five-factor model. In 2015, Fama and French added profitability, reflecting evidence that more profitable firms earned higher stock returns, and investment, reflecting evidence that firms investing aggressively in growth earned lower returns than those investing conservatively.

International CAPM. The international capital asset pricing model applies CAPM principles to cross-border investing. It adds compensation for direct and indirect exposure to foreign currency risk alongside the time value of money and market risk.

CAPM Compared With Related Terms

CAPM vs. portfolio theory. Modern portfolio theory tells an individual investor how to build an efficient portfolio. CAPM goes a step further and asks what happens to prices when every investor behaves that way.

CAPM vs. realized return. CAPM gives a forward-looking required return. Measures such as return on investment or CAGR describe what an investment actually earned. Comparing the two, after adjusting for beta, is the logic behind alpha.

FAQs

The Bottom Line

CAPM matters most to analysts, corporate finance teams and investors who need a cost of equity or a discount rate for valuation, capital budgeting or performance review. Its simple inputs and transparent logic make it a sound baseline. Its weak empirical record, unobservable market portfolio and judgment-heavy premium estimates mean results should be stress-tested and paired with other methods rather than relied on alone.