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.
Formula
Copy the exact expression or work through it step by step below.
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
Identify the risk-free rate and the expected market return.
Risk-free rate 4%, expected market return 11%.
- 2
Compute the market risk premium as expected market return minus risk-free rate.
11% - 4% = 7%.
- 3
Multiply the market risk premium by the asset's beta.
Beta 1.3 gives 1.3 x 7% = 9.1%.
- 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
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Sources & References
- Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk — William F. Sharpe, Journal of Finance (1964)
- The Valuation of Risk Assets and the Selection of Risky Investments — John Lintner, Review of Economics and Statistics (1965)
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The beta formula: covariance of asset and market returns over market variance. The CAPM regression slope measuring systematic risk, with an example.
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Jensen's alpha formula: realized return minus the CAPM-expected return given beta. The excess return a manager earns beyond market risk.
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.
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