Capital Asset Pricing Model (CAPM): Formula and Example

The Capital Asset Pricing Model (CAPM) is one of the most influential theories in modern finance. Developed by William Sharpe, John Lintner, and Jan Mossin in the 1960s — building on Harry Markowitz’s portfolio theory — CAPM provides a framework for pricing risky assets and estimating expected returns. This guide covers the CAPM formula, its key assumptions, the Security Market Line, and where the model falls short.

What is the Capital Asset Pricing Model (CAPM)?

The CAPM describes the relationship between systematic risk and expected return for any asset. Its central insight is that investors should only be compensated for bearing risk that cannot be eliminated through diversification — known as systematic (market) risk.

CAPM is widely used across finance for three primary purposes:

• Cost of equity estimation — determining the discount rate for valuation models (DCF analysis)
• Investment evaluation — assessing whether an asset offers sufficient return for its risk level
• Capital budgeting — setting hurdle rates for corporate projects based on their systematic risk

The CAPM Formula

The CAPM expresses expected return as a linear function of beta:

Where:

• E(R_i) — expected return of the asset
• R_f — risk-free rate (typically a government bond yield matched to the investment horizon)
• β_i — the asset’s beta (sensitivity to market movements)
• E(R_m) — expected return of the market portfolio
• E(R_m) – R_f — the equity risk premium (ERP)

The formula’s elegance lies in its simplicity: an asset’s expected return is entirely determined by one factor — its exposure to market risk, measured by beta. All else equal, a stock with a higher beta must offer a higher expected return to compensate investors for the additional systematic risk.

CAPM Assumptions

The CAPM is built on a set of simplifying assumptions about investors and markets. Understanding these assumptions is important because they define the conditions under which the model holds perfectly — and help explain its real-world limitations.

• Rational mean-variance optimizers — all investors make decisions based solely on expected return and variance (risk)
• Homogeneous expectations — all investors share the same forecasts for expected returns, variances, and correlations
• Single-period horizon — all investors plan over the same one-period time frame
• Frictionless markets — no taxes, transaction costs, or restrictions on short selling
• Risk-free borrowing and lending — all investors can borrow and lend unlimited amounts at the risk-free rate
• Perfectly divisible and liquid assets — all assets can be bought and sold in any quantity without affecting prices

Interpreting CAPM: The Three Building Blocks

Every CAPM calculation requires three inputs. Getting each one right is essential for a meaningful result.

The Risk-Free Rate (R_f)

The risk-free rate represents the return an investor can earn with zero default risk. In practice, it is proxied by a government bond yield — but the choice of maturity matters.

Beta (β_i)

Beta measures how sensitive an asset’s returns are to market movements. A beta of 1.0 means the asset moves in lockstep with the market. A beta greater than 1.0 amplifies market moves; a beta less than 1.0 dampens them. For a complete guide to beta — including how to calculate and interpret it — see our Beta in Finance article, or use the Beta Calculator to estimate beta for any stock.

The Market Risk Premium (E(R_m) – R_f)

The equity risk premium (ERP) is the extra return investors expect for holding the risky market portfolio instead of risk-free assets. Estimating the ERP is one of the most debated topics in finance because different methods produce different results:

Note that U.S. ERP estimates are not universal. Emerging markets typically require a country risk premium on top of the base ERP to account for additional political, economic, and liquidity risks. The choice of ERP significantly impacts CAPM output, so transparency about your assumption is critical.

CAPM Example: Calculating Expected Return

Let’s apply the CAPM to two real companies with very different risk profiles to see how beta drives expected returns.

If you expect NVIDIA to return more than 14%, the stock may be underpriced relative to CAPM (positive alpha). If you expect less than 14%, it may be overpriced relative to the model. This concept is formalized in the Security Market Line, covered next.

The Security Market Line (SML)

The Security Market Line is the graphical representation of the CAPM. It plots the relationship between expected return and beta for all assets in the market. Every asset that is fairly priced according to CAPM should lie directly on this line.

How to Read the SML

The SML has a straightforward structure:

• Y-axis: Expected return
• X-axis: Beta (systematic risk)
• Y-intercept: The risk-free rate (R_f) — the return when beta equals zero
• Slope: The equity risk premium [E(R_m) – R_f]
• Market portfolio: Located at β = 1.0 with expected return = E(R_m)

Stocks Above and Below the SML

The SML’s practical power lies in identifying assets that deviate from the line:

• Above the SML — the asset offers a higher expected return than CAPM predicts for its beta level. This implies positive alpha and suggests the asset may be underpriced relative to CAPM.
• Below the SML — the asset offers a lower expected return than CAPM predicts. This implies negative alpha and suggests the asset may be overpriced relative to CAPM.
• On the SML — the asset is fairly priced according to the model. Its expected return exactly compensates for its systematic risk.

SML vs. CML (Capital Market Line)

The Security Market Line and Capital Market Line are related but distinct concepts that are frequently confused. The critical difference is the risk measure on the X-axis.

The SML uses beta (systematic risk) and is applicable to any asset — making it the correct tool for evaluating individual stock pricing. The CML uses standard deviation (total risk) and is relevant only for efficient, well-diversified portfolios that combine the risk-free asset with the market portfolio.

CAPM vs. the Fama-French Three-Factor Model

While the CAPM uses a single factor (market risk) to explain expected returns, Eugene Fama and Kenneth French proposed a three-factor model in 1993 that adds two additional factors: size (SMB — Small Minus Big) and value (HML — High Minus Low book-to-market ratio). Here’s how they compare:

The Fama-French model better explains why small-cap and value stocks have historically earned higher returns than CAPM alone would predict. Despite this, CAPM remains the standard in corporate finance and valuation because of its simplicity — estimating cost of equity with one beta is far more practical than running a three-factor regression for every project.

How to Use the CAPM

Applying the CAPM in practice involves five straightforward steps:

1. Determine the risk-free rate — use a government bond yield matched to your investment horizon and currency (e.g., the current 10-year U.S. Treasury yield for long-term U.S. equity analysis)
2. Estimate the equity risk premium — use a long-run historical average, a survey-based estimate, or an implied ERP from current market prices. Be transparent about your choice.
3. Find or calculate beta — use a financial data provider, or calculate it from regression analysis. Our Beta Calculator can estimate beta for any stock.
4. Apply the CAPM formula — plug in R_f, β, and ERP to compute the expected return
5. Compare to your own return forecast — if you expect the asset to return more than the CAPM-predicted return, it may have positive alpha

CAPM in Cost of Equity and WACC

The CAPM’s most common practical application is estimating the cost of equity — the return shareholders require for investing in a company. This cost of equity feeds directly into the Weighted Average Cost of Capital (WACC), which is the discount rate used in discounted cash flow (DCF) valuation. When an analyst says a company’s cost of equity is 11%, they typically arrived at that number using the CAPM formula with the company’s beta.

Learn how to apply CAPM and other asset pricing models step by step in our Portfolio Analytics & Risk Management course.

Common Mistakes When Using CAPM

The CAPM formula is simple, but applying it correctly requires care. Here are the most common errors:

1. Using the Wrong Risk-Free Rate — Mismatching the risk-free rate’s duration with the investment horizon is a frequent mistake. Using a 3-month T-bill rate for long-term equity valuation understates the risk-free rate and distorts the expected return. Similarly, using a U.S. Treasury yield for a stock denominated in euros introduces a currency mismatch.

2. Confusing the SML with the CML — The Security Market Line plots return vs. beta and applies to any asset. The Capital Market Line plots return vs. standard deviation and applies only to efficient portfolios. Using the CML framework to evaluate an individual stock’s pricing is conceptually incorrect — the SML is the right tool.

3. Assuming Beta is Static — Many analysts take a beta estimate from a data provider and treat it as a fixed constant. In reality, beta changes over time as a company’s business model evolves, its financial leverage shifts, or market conditions change. Using a stale beta from a period with different dynamics produces misleading CAPM estimates.

4. Mixing Inconsistent Inputs — All CAPM inputs must be internally consistent. Mixing a nominal risk-free rate with a real (inflation-adjusted) equity risk premium, or using a U.S. risk-free rate with a global market proxy, introduces subtle errors that can materially distort the output. Ensure all inputs share the same currency, inflation basis, and time horizon.

Limitations of the CAPM

Despite its widespread use, the CAPM has well-documented limitations that every practitioner should understand:

1. Single-Factor Model — CAPM assumes that beta alone explains differences in expected returns across assets. Empirical research — most notably by Fama and French (1993) — has shown that additional factors like size and value also drive cross-sectional return patterns. Later work by Carhart (1997) added momentum as a fourth factor. CAPM cannot capture any of these additional dimensions of risk.

2. Unrealistic Assumptions — As discussed in the Assumptions section, the CAPM relies on idealized conditions (frictionless markets, homogeneous expectations, unlimited risk-free borrowing) that do not hold in practice. While the model can still provide useful estimates, its accuracy degrades when real-world frictions are significant.

3. Roll’s Critique — Richard Roll (1977) argued that the CAPM is fundamentally untestable because the true market portfolio — which should include all risky assets (stocks, bonds, real estate, human capital, and more) — is unobservable. Any empirical test of CAPM is actually a joint test of the model and the specific market proxy used, making it impossible to isolate CAPM’s validity.

4. Equity Risk Premium Uncertainty — The expected market return E(R_m) is not directly observable. Historical averages, survey estimates, and implied approaches each produce materially different ERP values, and the choice of method can shift the CAPM output by several percentage points.

5. The Low-Beta Anomaly — Empirical studies have consistently found that low-beta stocks tend to outperform CAPM predictions, while high-beta stocks tend to underperform. This “betting against beta” anomaly has been attributed to leverage constraints, investor lottery preferences, and institutional benchmark mandates — none of which the CAPM accounts for.