The Capital Asset Pricing Model (CAPM) is an asset-pricing model that says the expected return on an asset is determined by the risk-free rate plus compensation for systematic risk (market risk) as measured by the asset’s beta.
The CAPM Equation
The model is usually written as:
\[ E(R_i) = R_f + \beta_i\big(E(R_m) - R_f\big) \]
where:
- \(R_f\) is the risk-free rate,
- \(E(R_m) - R_f\) is the market risk premium,
- \(\beta_i\) measures how much the asset’s returns co-move with the market.
Intuition: if you hold a diversified portfolio, the idiosyncratic (asset-specific) risk washes out; the only risk you are paid for is the risk that moves with the market.
What Beta Measures
One common definition is:
\[ \beta_i = \frac{\operatorname{Cov}(R_i, R_m)}{\operatorname{Var}(R_m)} \]
So:
- \(\beta > 1\): the asset tends to move more than the market (higher systematic risk),
- \(\beta < 1\): the asset tends to move less than the market,
- \(\beta \approx 0\): little co-movement with the market.
What CAPM Is Used For
CAPM shows up in both investment analysis and corporate finance:
- Cost of equity / discount rates: a common input in valuation and capital budgeting.
- Performance attribution: comparing realized returns to CAPM-implied expected returns (often discussed as “alpha” versus “beta”).
- Risk communication: a compact way to describe market exposure, even when the model fits imperfectly.
A Quick Numerical Example
If \(R_f = 3\%\), \(E(R_m)=8\%\), and \(\beta_i=1.2\), then:
\[ E(R_i) = 3\% + 1.2\times(8\%-3\%) = 9\% \]
Key Assumptions (And Why They Matter)
CAPM’s clean prediction depends on strong assumptions, such as frictionless trading, mean-variance optimization, and investors holding (some version of) the market portfolio. In practice:
- beta estimates can be unstable over time,
- borrowing/lending at a true risk-free rate is unrealistic for many investors,
- multiple systematic risk factors may be priced (so a single-beta model is incomplete).
Related Terms
- Beta Coefficient
- Systematic Risk
- Idiosyncratic Risk
- Risk-Free Asset
- Risk Premium
- Portfolio Theory
- Efficient Markets Hypothesis
- Cost of Capital