Capital Asset Pricing Model (CAPM) formula and how to use it

The capital asset pricing model (CAPM) shows whether an investment’s expected return justifies its risk. The CAPM formula links return to systematic risk using the risk-free rate, beta, and the market risk premium.

Finance teams use CAPM to calculate cost of equity, set hurdle rates, and benchmark investments on a consistent, risk-adjusted basis.

What is the capital asset pricing model (CAPM)?

The capital asset pricing model (CAPM) calculates an investment’s expected return based on its systematic risk relative to the overall market. It shows the return investors should require given that level of market risk, compared with a risk-free rate such as a US Treasury security.

CAPM focuses only on systematic risk, which you can’t eliminate through diversification. Broad forces like economic shifts, interest rate changes, and geopolitical events affect the entire market, so the model assumes company-specific risk has already been diversified away.

Because it provides a consistent link between risk and return, CAPM is a cornerstone of modern portfolio theory. Finance teams use the CAPM formula in valuation, capital budgeting, and portfolio management to decide whether an opportunity’s expected return justifies its level of risk.

The CAPM formula and equation

The CAPM formula quantifies the relationship between systematic risk and expected return. It shows the minimum return you should require to justify taking on market risk.

Expected return (CAPM) = Risk-free rate + Beta * (Expected market return – Risk-free rate)

In notation form:

E(Rᵢ) = Rf + βᵢ * (E(Rₘ) – Rf)

The CAPM formula calculates expected return by adding the risk-free rate to beta multiplied by the market risk premium.

Where:

• E(Rᵢ) = Expected return on the investment
• Rf = Risk-free rate of return
• βᵢ = Beta, a measure of the asset’s systematic risk relative to the market
• E(Rₘ) = Expected market return
• E(Rₘ) – Rf = Market risk premium

The output, expected return, represents the minimum annual return you should demand to compensate for the asset’s systematic risk. Finance teams use the CAPM formula to estimate cost of equity, set hurdle rates, and compare investment opportunities on a risk-adjusted basis.

Components of the CAPM formula

The CAPM formula relies on four inputs to estimate expected return. Each variable translates market data into a practical cost of equity calculation.

Risk-free rate

The risk-free rate is the baseline return on an investment with virtually no default risk. Most analysts use the 10-year US Treasury bond yield for long-term equity valuation and shorter-term Treasury bills for near-term analysis.

This rate anchors all return expectations in corporate finance and valuation. Because it moves with interest rates and monetary policy, you should update it regularly to keep your CAPM calculations accurate.

Beta coefficient

Beta measures how much an asset’s returns move relative to the overall market. It’s the sole risk variable in the CAPM formula.

• Beta = 1.0: The asset moves in line with the market
• Beta > 1.0: The asset is more volatile than the market
• Beta < 1.0: The asset is less volatile than the market

A higher beta implies higher systematic risk and therefore a higher required return. Analysts typically estimate beta using regression analysis of historical returns or pull it from data providers such as Bloomberg or Yahoo Finance.

Expected market return

The expected market return represents the anticipated return of the overall market, often proxied by a broad index such as the S&P 500. Many analysts reference a long-term range of 8–10% for US equities, based on historical averages or forward-looking estimates.

The appropriate figure depends on your time horizon, economic outlook, and methodology. Use a consistent approach across your analysis to avoid introducing bias.

Market risk premium

The market risk premium equals the expected market return minus the risk-free rate. It represents the additional return investors demand for holding risky assets instead of government bonds.

• Calculated as: E(Rₘ) – Rf
• Often estimated in the 4–7% range in the US, depending on time period and assumptions
• Used to estimate cost of equity and discount rates in valuation, including net present value calculations

Because there’s no single agreed-upon risk premium, even small changes in assumptions can materially affect your CAPM output.

How to calculate CAPM step by step

Calculating the CAPM formula turns market inputs into a required rate of return. Follow these four steps to estimate expected return.

Step 1. Find the current risk-free rate

Look up the yield on a US Treasury security that matches your investment horizon. For long-term equity valuation or capital projects, use the 10-year Treasury bond yield. For short-term analysis, a 3-month or 1-year Treasury bill may be more appropriate.

Aligning the maturity with your time horizon reduces distortion in your expected return estimate.

Step 2. Determine the asset’s beta

Find the asset’s beta using a financial data provider such as Bloomberg, Yahoo Finance, or your brokerage platform. Most public companies have a published beta based on historical returns.

You can also calculate beta by running a regression of the asset’s historical returns against a market index. In practice, most finance teams rely on published or adjusted betas rather than building the regression from scratch.

Step 3. Estimate the expected market return

Estimate the expected return of the overall market using one consistent methodology:

• Historical average: Use the long-term average annual return of a broad index like the S&P 500
• Forward-looking estimate: Use analyst consensus forecasts or an implied equity risk premium model

Whichever method you choose, apply it consistently across projects and valuations.

Step 4. Apply the CAPM equation

Plug your inputs into the formula. First calculate the market risk premium, then multiply it by beta, and finally add back the risk-free rate.

E(Rᵢ) = Rf + βᵢ * (E(Rₘ) – Rf)

For example:

E(Rᵢ) = 4% + 1.2 * (10% – 4%) = 11.2%

This 11.2% represents the minimum annual return required to justify the investment’s systematic risk. If your projected return exceeds this rate, the investment may create value. If it falls short, the risk-adjusted return may not be sufficient.

CAPM calculation example

A worked example makes the CAPM formula easier to apply. Suppose you’re evaluating an investment in TechCorp and have gathered the following inputs:

• Risk-free rate (Rf): 4.5%, based on the 10-year Treasury yield
• Beta (βᵢ): 1.35
• Expected market return (E(Rₘ)): 11%

First, calculate the market risk premium:

E(Rₘ) – Rf = 11% – 4.5% = 6.5%

Next, apply the CAPM formula:

E(Rᵢ) = Rf + βᵢ * (E(Rₘ) – Rf)

E(Rᵢ) = 4.5% + 1.35 * 6.5% = 13.28%

TechCorp must generate at least 13.28% in annual returns to compensate for its systematic risk. If your financial projections estimate a 15% return, the investment exceeds the required rate and may create value. If projected returns are 12%, the risk-adjusted return falls short of the CAPM threshold.

This calculation gives you a clear hurdle rate to compare TechCorp against other opportunities with similar risk profiles.

How to calculate CAPM in Excel

You can build a simple CAPM calculator in Excel using just a few cells. Set up your inputs first.

• Cell A1: Risk-free rate → Cell B1: Enter the rate (e.g., 0.045 for 4.5%)
• Cell A2: Beta → Cell B2: Enter the beta value (e.g., 1.35)
• Cell A3: Expected market return → Cell B3: Enter the rate (e.g., 0.11 for 11%)

Next, calculate the expected return.

• Cell A5: Expected return (CAPM)
• Cell B5: =B1+B2*(B3-B1)

Format cell B5 as a percentage to display the result. Using the TechCorp example, the output will be 13.28%.

To run sensitivity analysis, vary beta or the market risk premium across a range of values and use Excel’s Data Table feature to calculate multiple outcomes at once. This helps you see how changes in assumptions affect required return.

If you need to calculate beta from historical data, use Excel’s =SLOPE() function. Enter the asset’s historical returns in one column and the market index returns in another, then use =SLOPE(asset_returns, market_returns) to estimate beta.

Key assumptions of the CAPM model

The CAPM model relies on simplified assumptions about how markets and investors behave. Understanding these assumptions helps you evaluate when the CAPM formula may be less reliable.

• Efficient markets: All investors have access to the same information, and asset prices reflect all available data
• Single-period investment horizon: Investors evaluate opportunities over the same time frame
• Risk-free borrowing and lending: Investors can borrow and lend unlimited amounts at the risk-free rate
• No taxes or transaction costs: Trading occurs without fees, capital gains taxes, or bid-ask spreads
• Rational, risk-averse investors: Investors seek to maximize return for a given level of risk
• Fully diversified portfolios: Company-specific (unsystematic) risk is eliminated through diversification

In reality, markets have frictions, investors have different time horizons, and access to capital varies. That’s why CAPM works best as a benchmark rather than a precise predictor of future returns.

Limitations of the CAPM

The CAPM formula is simple and widely used, but it has meaningful limitations. Finance teams should treat it as a benchmark, not a definitive valuation tool.

• Beta instability: CAPM assumes beta is stable, but a company’s risk profile can change due to leverage, strategy shifts, or market conditions. Historical betas may not reflect future risk.
• Single-factor model: CAPM only accounts for market risk. It ignores other drivers of returns, such as company size, value characteristics, and profitability.
• Unrealistic assumptions: Real markets include taxes, transaction costs, and information asymmetry, which create gaps between theoretical and achievable returns
• Risk premium uncertainty: There’s no universally accepted market risk premium. Different data sets and time periods can produce materially different required returns.
• Market proxy limitations: CAPM assumes a true market portfolio of all assets exists, but in practice, analysts use broad indexes as imperfect proxies
• Behavioral factors: Investors aren’t always rational. Behavioral biases and liquidity constraints can cause returns to deviate from CAPM predictions

Because of these limitations, experienced finance teams use CAPM alongside other valuation and risk assessment tools rather than relying on it in isolation.

When to use CAPM in finance

The CAPM formula is most useful when you need a market-based required rate of return. It provides a consistent framework for linking risk and return across corporate finance and investment decisions.

Cost of equity estimation

CAPM is the most common method for estimating cost of equity, which represents the return shareholders expect for investing in your company. This figure feeds directly into your weighted average cost of capital (WACC) and shapes capital allocation decisions.

By applying your company’s beta in the CAPM formula, you get a market-driven estimate of the return equity investors require. That makes your discount rate more objective and defensible.

Capital budgeting decisions

Finance teams use the CAPM-derived cost of equity to set hurdle rates for new projects. If a project’s projected return exceeds the CAPM rate, it’s expected to create value. If it falls short, the return may not justify the risk.

This approach introduces consistency into capital budgeting. Instead of relying on intuition, you evaluate each project against a risk-adjusted benchmark tied to market data.

Investment performance analysis

Comparing actual returns with CAPM-expected returns shows whether an investment generated alpha. Positive alpha indicates outperformance relative to risk, while negative alpha signals underperformance.

Portfolio managers use this framework, along with the security market line (SML), to assess whether returns appropriately compensate for systematic risk.

Portfolio risk assessment

CAPM helps you evaluate how each holding contributes to overall portfolio risk. By analyzing beta and expected return across positions, you can assess whether your portfolio’s risk-return profile aligns with your targets.

This is particularly useful when rebalancing or adding new positions. If an asset’s expected return doesn’t exceed the CAPM-required rate for its beta, it may dilute risk-adjusted performance.

CAPM vs. other valuation models

CAPM isn’t the only way to estimate expected return. Several alternative models incorporate additional risk factors or use different methodologies, depending on your use case.

Arbitrage pricing theory

Arbitrage pricing theory (APT) allows multiple economic factors to influence expected returns. Each factor has its own beta coefficient, which measures sensitivity to variables such as inflation, GDP growth, or interest rate changes.

Unlike CAPM, APT doesn’t prescribe a single market factor. That flexibility makes it adaptable, but it also increases complexity because you must determine which factors are relevant.

Fama-French 3-factor model

The Fama-French model expands on CAPM by adding size and book-to-market (value) factors to market risk. Later versions add profitability and investment factors.

These multi-factor models better explain historical stock returns, but they require more data and are less commonly used in day-to-day corporate finance decisions.

Build-up method

The build-up method starts with the risk-free rate and layers on additional risk premiums, such as an equity risk premium, size premium, industry premium, and company-specific premium. It does not rely on beta.

This approach is common in private company valuations, where there’s no observable stock price to calculate beta. Instead of deriving risk from market covariance, you construct the required return from published risk premiums and professional judgment.

Tips for applying the CAPM model effectively

The CAPM formula is simple, but small input changes can materially affect your result. These best practices help you produce more reliable required return estimates.

Match your risk-free rate to your investment horizon

Use a Treasury maturity that aligns with your analysis. For a 10-year capital project, reference the 10-year Treasury yield. For a short-term investment decision, a 3-month T-bill may be more appropriate. Mismatched time horizons introduce avoidable error into your expected return calculation.

Use adjusted beta for forward-looking analysis

Raw historical beta can be volatile, and research shows betas tend to revert toward 1.0 over time. Bloomberg’s adjusted beta formula—(2/3 * raw beta) + (1/3 * 1.0)—accounts for this mean reversion and often produces more stable forward-looking estimates.

If you’re setting a hurdle rate or estimating cost of equity, an adjusted beta may better reflect long-term risk.

Apply sensitivity analysis to key inputs

Don’t rely on a single CAPM output. Test a range of assumptions for beta and the market risk premium to see how sensitive your required return is to each variable. If small changes materially shift your result, document those ranges in your investment memo. That transparency strengthens decision-making.

Use CAPM alongside other valuation tools

CAPM works best as one input in a broader analysis. Cross-check your required return against other approaches, such as a build-up method or multi-factor model. If multiple methods point to a similar result, you can have more confidence in your cost of equity estimate.

Putting CAPM to work with Ramp

The capital asset pricing model gives you a structured way to set required returns and evaluate investments on a risk-adjusted basis. When you apply the CAPM formula consistently, your capital budgeting and valuation decisions become more defensible and data-driven.

Modern finance teams extend that discipline with better systems. Ramp’s accounting automation software helps you reduce manual data entry, improve reporting accuracy, and maintain real-time visibility into financial performance. Instead of chasing spreadsheets, your team can focus on modeling scenarios, pressure-testing assumptions, and making informed decisions.

If you want to streamline your financial workflows and strengthen decision-making, you can explore Ramp’s capabilities through an interactive product demo.