CAPM Formula
Reference for the CAPM formula: E(R) = Rf + beta*(Rm - Rf).
Calculates expected return from risk-free rate, beta, and market premium for stock valuation.
The Formula
E(R) = R_f + β × (R_m - R_f)
CAPM calculates the expected return an investor should demand for taking on a specific level of risk. Higher risk (higher beta) means higher expected return.
Variables
| Symbol | Meaning |
|---|---|
| E(R) | Expected return of the investment |
| R_f | Risk-free rate (e.g., government bond yield) |
| β | Beta — measure of the investment's volatility relative to the market |
| R_m | Expected return of the overall market |
| R_m - R_f | Market risk premium |
Example 1
Risk-free rate = 3%, market return = 10%, stock beta = 1.5
E(R) = 3% + 1.5 × (10% - 3%)
E(R) = 3% + 1.5 × 7%
E(R) = 13.5% (higher risk demands higher return)
Example 2
A utility stock with beta = 0.6. Risk-free = 4%, market = 9%.
E(R) = 4% + 0.6 × (9% - 4%)
E(R) = 4% + 3%
E(R) = 7% (lower risk = lower expected return)
When to Use It
Use the CAPM formula when:
- Estimating the required return for a stock or portfolio
- Determining the cost of equity capital for a company
- Evaluating whether an investment is fairly priced for its risk
- Setting discount rates for NPV calculations
Key Notes
- Beta interpretation: β > 1 means the stock is more volatile than the market; β < 1 means less volatile; β = 1 is the market itself; β < 0 (rare) means the asset tends to rise when the market falls — sometimes seen with gold or inverse ETFs
- CAPM is a single-factor model — it only prices systematic (market) risk; firm-specific risks are assumed to be diversified away in a large portfolio and carry no expected premium in theory
- Empirical studies show that CAPM alphas (actual returns above CAPM prediction) persist in practice — small-cap and value stocks historically outperformed CAPM predictions, motivating the Fama-French three-factor model that adds size and value factors
- The risk-free rate R_f is usually the current yield on short-term government bills (3-month T-bills in the US) — it changes daily, so the CAPM expected return changes even when beta stays constant