The Capital Asset Pricing Model (CAPM) holds that an asset's expected return is set by its systematic risk — risk that diversification cannot eliminate. Sharpe (1964) derived this in "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," published in the Journal of Finance. The paper extends the Markowitz mean-variance framework to full market equilibrium. Assets unaffected by economic activity return the pure interest rate P; assets that move with the economy earn proportionally higher returns. Beta — Big = rig·σRi / σRg — is the single relevant risk measure.
What the Study Found
Sharpe (1964) derived that in equilibrium all efficient portfolios lie on the capital market line, where σR = S(ER − P). An asset's expected return follows ERi = P + Big × (ERg − P): the risk-free rate plus beta times the market excess return. An asset with Big = 0 earns only P; an asset with Big = 1 earns the market return. All efficient combinations in equilibrium are perfectly positively correlated (rab = +1). Unsystematic risk — the component uncorrelated with the market — earns no return premium because diversification eliminates it at no cost.
Methodology
Sharpe (1964) built on the Markowitz mean-variance portfolio selection model and Tobin's two-fund separation theorem to construct a market equilibrium theory. The model assumes a common pure interest rate with all investors able to borrow and lend on equal terms. Investors are assumed to hold homogeneous expectations — identical views on expected values, standard deviations, and correlations. No empirical dataset was used; the paper derives equilibrium conditions analytically.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Investor utility function | U = f(Ew, σw) = g(ER, σR) | Utility depends only on expected return and standard deviation; foundational mean-variance assumption |
| Portfolio standard deviation | σRc = √[a²σRa² + (1−a)²σRb² + 2rab·a(1−a)·σRa·σRb] | Risk of a two-asset combination; rab captures diversification benefit |
| Riskless asset combination | σRc = (1 − a)σRa | When σRp = 0, combination standard deviation reduces to this form |
| Capital Market Line | σR = S(ER − P) | All efficient portfolios lie on this line; S = slope; P = pure interest rate |
| Security Market Line (CAPM) | ERi = P + Big × (ERg − P) | Linear relationship between expected return and systematic risk |
| Beta | Big = rig·σRi / σRg | Sensitivity of asset i's return to efficient combination g; sole relevant risk measure |
| Equilibrium correlation | rab = +1 for all efficient combinations | All portfolios on the capital market line are perfectly positively correlated |
Why This Matters
CAPM gave practitioners a single-number risk measure — beta — for pricing any asset against a common benchmark. Portfolio managers use the Security Market Line to set required returns on equity. Corporate finance practitioners use it to evaluate whether a security is priced fairly relative to its market risk. The model set the terms for all subsequent asset pricing debates. Every multi-factor model that followed, including Fama-French, is structured as an extension or rejection of Sharpe's (1964) equilibrium conditions.