Capital Asset Pricing Model (CAPM)

A model that links an asset's expected return to its market beta and the market risk premium.

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).

Knowledge Check

### In CAPM, investors are compensated for which type of risk? - [ ] Idiosyncratic (asset-specific) risk - [x] Systematic (market) risk - [ ] Accounting risk - [ ] Legal risk > **Explanation:** CAPM's core claim is that only market-wide risk that cannot be diversified away is priced. ### Beta (\\(\\beta\\)) is commonly computed as: - [ ] \\(\\operatorname{Var}(R_i) / \\operatorname{Var}(R_m)\\) - [x] \\(\\operatorname{Cov}(R_i, R_m) / \\operatorname{Var}(R_m)\\) - [ ] \\(E(R_i) - R_f\\) - [ ] \\(R_f / E(R_m)\\) > **Explanation:** Beta measures co-movement with the market; covariance captures co-movement and is scaled by market variance. ### In CAPM, the market risk premium is: - [x] \\(E(R_m) - R_f\\) - [ ] \\(E(R_i) - E(R_m)\\) - [ ] \\(R_f - E(R_m)\\) - [ ] \\(\\beta_i - 1\\) > **Explanation:** It is the extra expected return investors demand for holding the market portfolio instead of the risk-free asset. ### Suppose \\(R_f=2\\%\\), \\(E(R_m)=7\\%\\), and \\(\\beta_i=1.5\\). What does CAPM imply for \\(E(R_i)\\)? - [ ] 4.5% - [ ] 7.0% - [x] 9.5% - [ ] 12.0% > **Explanation:** \\(E(R_i)=2\\%+1.5\\times(7\\%-2\\%)=2\\%+7.5\\%=9.5\\%\\).