# The Capital Asset Pricing Model: Sharpe's Theory of Risk and Return

Cite as: Gorak, R. (2026). The Capital Asset Pricing Model: Sharpe's Theory of Risk and Return. Tradicted. https://www.tradicted.com/research/sharpe-capm-1964/
Paper: William F. Sharpe — *Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk*
Published in: Journal of Finance (1964)
Original: https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1964.tb02865.x
DOI: 10.1111/j.1540-6261.1964.tb02865.x

Key finding: In equilibrium, expected asset returns are linearly related to their systematic risk (beta), with assets that move with the market promising higher returns than those unaffected by economic activity.

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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.

## FAQ

### What is beta in the CAPM and how is it calculated?

Beta equals rig·σRi divided by σRg — the correlation between asset i and the market combination, scaled by the ratio of their standard deviations. An asset with beta above 1 moves more than the market; below 1, less. Sharpe (1964) showed beta is the only undiversifiable risk component. It is therefore the only component that earns a return premium above the pure interest rate P.

### What does the Capital Market Line represent in Sharpe's model?

The Capital Market Line is σR = S(ER − P), where P is the pure interest rate and S is the slope. Every efficient portfolio in Sharpe's (1964) equilibrium lies on this line. Investors who lend at the risk-free rate hold combinations below the tangency point. Those who borrow hold combinations above it on the extended line.

### Why does unsystematic risk earn no return premium in CAPM?

Big = rig·σRi / σRg is the only risk measure that commands a return above the pure interest rate P. Sharpe (1964) showed that diversification eliminates all risk uncorrelated with the market combination. Because unsystematic risk is avoidable at no cost, equilibrium prices it at zero. Only Big — systematic risk — remains.

### How does CAPM extend the Markowitz efficient frontier?

σR = S(ER − P) — the capital market line — replaces the curved efficient frontier once a risk-free rate is introduced. Sharpe (1964) added a common pure interest rate P and homogeneous expectations to the Markowitz mean-variance framework. All investors then select the same optimal risky portfolio — the tangency point. Each combines it with the risk-free asset to reach their preferred position on σR = S(ER − P).

## Source

Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. *Journal of Finance*, XIX(3), 425–442.

[Read the full paper →](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1964.tb02865.x)