Capital Asset Pricing Model (CAPM)
You now understand beta (systematic risk) and alpha (excess return). CAPM is the formula that ties them together - it calculates the return an investor should expect for taking on a given level of market risk.
The CAPM Formula
Expected Return = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)
Or in shorthand: E(R) = Rf + B(Rm - Rf)
| Component | Meaning | Typical Proxy |
|---|---|---|
| E(R) | Expected (required) return on the security | What the investor should demand |
| Rf | Risk-free rate | Yield on U.S. Treasury bills or 10-year Treasury notes |
| B (Beta) | Systematic risk of the security relative to the market | Calculated from historical price data |
| Rm | Expected return of the overall market | Historical average market return or forecast |
| Rm - Rf | Market risk premium (equity risk premium) | Additional return demanded for investing in equities over risk-free assets |
Key insight: CAPM says that an investor always earns at least the risk-free rate (the time value of money). The beta component adds compensation for taking on market risk above that baseline.
CAPM Calculation Example
- Risk-free rate (Rf) = 3%
- Expected market return (Rm) = 10%
- Stock beta (B) = 1.5
- Market risk premium = 10% - 3% = 7%
Calculation:
Expected return = 3% + 1.5(10% - 3%) = 3% + 1.5(7%) = 3% + 10.5% = 13.5%
This means an investor should demand at least a 13.5% return to justify holding this stock, given its level of systematic risk.
Using CAPM for Investment Decisions
Once you calculate the expected return from CAPM, compare it to the security's actual or estimated return:
| Scenario | Implication | Action |
|---|---|---|
| Actual/estimated return > CAPM expected return | Security is undervalued (positive alpha) | Buy - offers more return than the risk warrants |
| Actual/estimated return = CAPM expected return | Security is fairly valued (zero alpha) | Hold - priced correctly for its risk |
| Actual/estimated return < CAPM expected return | Security is overvalued (negative alpha) | Sell - does not compensate for the risk taken |
This connects directly to alpha: The difference between the actual return and the CAPM expected return IS alpha. CAPM provides the benchmark; alpha measures performance against that benchmark.
Exam Tip: Gotchas
- Returning MORE than CAPM expected = undervalued (buy), not overvalued. Students often reverse the logic. If a stock earns more than CAPM says it should, you're getting a bargain (positive alpha). If it earns less, you're overpaying for the risk (negative alpha, sell).
CAPM Assumptions and Limitations
- CAPM assumes investors are rational, markets are efficient, and beta is the sole measure of risk
- Beta is calculated from historical data and may not predict future volatility
- CAPM does not account for unsystematic risk (it assumes investors are fully diversified)
- Despite its limitations, CAPM is the foundational model for understanding the risk-return tradeoff on the Series 7
Putting It All Together: A Full Calculation
Problem: A stock has a beta of 1.3. The risk-free rate is 2% and the expected market return is 9%. The stock actually returned 12% over the past year. Did the manager add value?
Step 1 - Calculate CAPM expected return:
- E(R) = 2% + 1.3(9% - 2%) = 2% + 1.3(7%) = 2% + 9.1% = 11.1%
Step 2 - Calculate alpha:
- Alpha = Actual return - Expected return = 12% - 11.1% = +0.9%
Conclusion: Positive alpha of 0.9%. The manager generated returns slightly above what the risk level predicted; the manager added modest value.
Exam Tip: Gotchas
- CAPM uses the risk-free rate, not zero, as the starting point. The market risk premium is NOT the market return; it is the market return MINUS the risk-free rate. If a question gives Rf = 3% and Rm = 10%, the market risk premium is 7%, not 10%.