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Formula, in Risk & Portfolio Construction

CAPM Formula

The Capital Asset Pricing Model states that the expected return on an asset equals the risk-free rate plus its beta times the market risk premium. It says investors are compensated only for systematic risk that cannot be diversified away, not for idiosyncratic risk, and it provides the benchmark return against which alpha is measured.

4 variables. Published May 26, 2026. By AI Fin Hub Research.

Formula
E[R_i] = R_f + beta_i x (E[R_m] - R_f)

Variables

E[R_i]

Expected asset return

The return the model predicts the asset should earn in equilibrium given only its systematic risk.

R_f

Risk-free rate

Return on a riskless asset, the baseline every investor can earn without taking market risk.

beta_i

Asset beta

Sensitivity of the asset to market movements, equal to covariance with the market over market variance. It is the only asset-specific input CAPM rewards.

E[R_m] - R_f

Market risk premium

Expected excess return of the market over the risk-free rate, the price of one unit of systematic risk. Multiplied by beta it gives the asset's risk premium.

Step by step

  1. 1

    Identify the risk-free rate and the expected market return.

    Risk-free rate 4%, expected market return 11%.

  2. 2

    Compute the market risk premium as expected market return minus risk-free rate.

    11% - 4% = 7%.

  3. 3

    Multiply the market risk premium by the asset's beta.

    Beta 1.3 gives 1.3 x 7% = 9.1%.

  4. 4

    Add the risk-free rate to obtain the CAPM expected return.

    4% + 9.1% = 13.1%.

Worked example

Required return for a high-beta growth stock

Risk-free rate

4%

Expected market return

11%

Beta

1.3

Market risk premium = 0.11 - 0.04 = 0.07. Beta-scaled premium = 1.3 x 0.07 = 0.091. Expected return = 0.04 + 0.091 = 0.131 = 13.1%.

CAPM expected return of 13.1%. An investor should require at least 13.1% from this stock to be fairly paid for its systematic risk. If a valuation model projects only 11%, the stock is unattractive on a risk-adjusted basis; if it projects 15%, the 1.9-point gap is positive alpha.

Common variations

Fama-French three-factor model: adds size and value premiums to the single market factor.
Carhart four-factor model: extends Fama-French with a momentum factor.
Arbitrage Pricing Theory: replaces the single market factor with an arbitrary set of macro risk factors, each with its own beta and premium.

Run the numbers next

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    Paste a multi-asset returns CSV. See the Markowitz mean-variance frontier, the minimum-variance portfolio, the max-Sharpe (tangency) portfolio.

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    Paste a multi-asset returns CSV. See the Pearson correlation heatmap, condition number, average absolute correlation, and eigenvalue concentration.

Sources

  1. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk , William F. Sharpe, Journal of Finance (1964)
  2. The Valuation of Risk Assets and the Selection of Risky Investments , John Lintner, Review of Economics and Statistics (1965)

Keep the topic connected

  • Formula Beta Formula

    The beta formula: covariance of asset and market returns over market variance. The CAPM regression slope measuring systematic risk, with an example.

  • Formula Jensen's Alpha Formula

    Jensen's alpha formula: realized return minus the CAPM-expected return given beta. The excess return a manager earns beyond market risk.

  • Formula Treynor Ratio Formula

    The Treynor ratio formula: excess return over the risk-free rate divided by beta. Reward per unit of systematic market risk, with a worked example.

  • Learn Alpha

    Alpha as risk-adjusted excess return: definition, the beta-adjustment math, and why most claimed alpha disappears once you adjust for the right factors.