Capital Asset Pricing Model (CAPM)

Quick Answer

The Capital Asset Pricing Model computes expected return as the risk-free rate plus beta times the market risk premium (E(R) = Rf + beta x (Rm - Rf)). CAPM is the foundational formula that defines risk-adjusted expected return and serves as the benchmark for computing alpha. It assumes investors are fully diversified and uses beta as the sole risk measure.

Alpha and beta live inside one equation: the Capital Asset Pricing Model (CAPM). CAPM is the foundational risk-return formula named in the Series 6 outline and the basis for computing alpha.

What is the CAPM formula?

E(R) = R_f + \beta \times (R_m - R_f)

Where:

$E(R)$ = expected (required) return on the investment
$R_f$ = risk-free rate (typically a U.S. Treasury bill or note yield)
$\beta$ = beta; systematic risk of the investment relative to the market
$R_m$ = expected market return
$(R_m - R_f)$ = the market risk premium (equity risk premium); the return investors demand for bearing market risk above the risk-free rate

Component	Meaning	Typical Proxy
E(R)	Expected return on the investment	What the investor should demand
R_f	Risk-free rate	U.S. Treasury bill or note yield
β (Beta)	Systematic risk relative to the market	Historical beta vs. the S&P 500
R_m	Expected market return	Long-run market average or forecast
R_m − R_f	Market risk premium	Additional return demanded for market risk

Exam Tip: Gotchas

CAPM starts with the risk-free rate, not zero. Every investor earns at least $R_f$ for lending money (time value of money). The beta term adds compensation for bearing market risk.

Given $R_f = 3\%$ and $R_m = 10\%$ , the market risk premium is 7%, not 10%. The premium is always the market return minus the risk-free rate.

How is CAPM calculated step by step?

Inputs:

Risk-free rate = 3%
Expected market return = 10%
Fund beta = 1.5

Step 1: Market risk premium = $R_m - R_f$ = 10% − 3% = 7%

Step 2: Expected return = 3% + 1.5 × 7% = 3% + 10.5% = 13.5%

Step 3: Compare actual return to the expected return to derive alpha:

If the fund's actual return is 15%, alpha = 15% − 13.5% = +1.5% (positive; outperformed expectation)
If the fund's actual return is 12%, alpha = 12% − 13.5% = −1.5% (negative; underperformed expectation)

Think of it this way: CAPM answers "what return should this fund deliver given its beta?" Alpha answers "did it deliver more or less than that?" The two steps are sequential: compute CAPM expected first, compute alpha second.

Exam Tip: Gotchas

Alpha is measured against CAPM expected return, not against the market return. Two funds with the same raw return can have very different alphas depending on their betas. The exam will give $R_f$ , $R_m$ , beta, and actual return; compute CAPM first, then alpha.

How is CAPM used for investment decisions?

Scenario	Implication
Actual or estimated return greater than CAPM expected return	Investment is undervalued; delivers more return than the beta warrants (positive alpha)
Actual or estimated return equal to CAPM expected return	Investment is fairly valued (zero alpha)
Actual or estimated return less than CAPM expected return	Investment is overvalued; does not compensate for the beta (negative alpha)

Positive alpha signals a manager or security worth holding for the extra return beyond the risk-adjusted expectation
Zero alpha after fees is the typical result for an index fund; the fund is priced exactly for its risk
Negative alpha after fees is the case for switching to a lower-cost alternative with the same beta exposure

What are the assumptions and limitations of CAPM?

Assumes investors are rational and hold fully diversified portfolios (so only systematic risk matters)
Uses beta as the sole risk measure, ignoring factors like size, value, and momentum
Beta is historical: may not predict future sensitivity
Despite limitations, CAPM is the foundational risk-return model named in the Series 6 outline and the basis for interpreting alpha

Exam Tip: Gotchas

CAPM assumes the investor is fully diversified, which is why unsystematic risk is zero in the formula. This is the reason beta (systematic risk) is the only risk measure in the equation. If an investor is not diversified, CAPM understates the actual risk they face.

Beta is historical, but the CAPM forecast is forward-looking. A historical beta of 1.2 does not guarantee a future beta of 1.2. The exam treats beta as a best-available estimate, not a promise.