CFA Program Level I

CAPM and the security market line: CFA Level I explained

The CAPM says an asset's expected return equals the risk-free rate plus beta times the market risk premium: E(Ri) = Rf + beta x [E(Rm) - Rf]. The security market line plots that required return against beta for every asset. An asset whose forecast return is above the line has a positive alpha and is underpriced; one below it is overpriced.

The formula and what beta measures

E(Ri) = Rf + beta_i x [E(Rm) - Rf]. The bracket is the market risk premium.

Beta = covariance of the asset's returns with the market's returns / variance of the market's returns. A beta of 1 means the asset moves with the market in the same direction and by the same magnitude on average.

Only market (systematic) risk is rewarded. The CAPM assumes firm-specific risk can be removed by diversification, so it earns no extra expected return.

Worked example: required return

Risk-free rate 2.5%, market risk premium 6.0%, beta 1.2.

E(R) = 2.5% + 1.2 x 6.0% = 2.5% + 7.2% = 9.7%.

If you are given the expected market return instead of the premium, subtract the risk-free rate first. With E(Rm) = 8.5%, the premium is 8.5% - 2.5% = 6.0%.

Reading the security market line

The SML is the set of equilibrium expected returns for each beta when the CAPM holds. Federal Reserve research defines an asset's alpha as its deviation from that line; an investor using the CAPM identifies a positive-alpha asset as underpriced.

Example: the SML gives a stock 9.7% for its beta of 1.2. An analyst forecasts 11.0%. Alpha = 11.0% - 9.7% = +1.3%. The stock plots above the SML and is underpriced. A forecast of 8.0% would give -1.7% and an overpriced stock.

Black, Jensen and Scholes (1972), cited in the same research, found that from 1926 to 1966 low-beta US stocks earned more than the CAPM predicts and high-beta stocks less: the observed SML is flatter than the model's.

Jensen's alpha for a fund

Jensen's alpha = Rp - [Rf + beta_p x (Rm - Rf)]. It is the return above what the CAPM requires for the market risk taken.

Example: a fund returned 10.0%, the market returned 9.0%, the risk-free rate was 2.0% and the fund's beta was 1.3. Required = 2.0% + 1.3 x 7.0% = 11.1%. Alpha = 10.0% - 11.1% = -1.1%. The fund beat the market but fell short for its risk.

Like the Treynor ratio, Jensen's alpha counts market risk only and depends on which index is used as the market.

Where the exam catches people

Believing a stock above the SML is overpriced: a forecast return above the line means positive alpha and an underpriced stock.
Multiplying beta by the market return instead of the market risk premium: beta scales E(Rm) - Rf.
Believing a more volatile stock must have a higher CAPM return: only beta matters; extra firm-specific volatility earns nothing.
Believing a fund that beat the market has positive Jensen's alpha: a high-beta fund must beat its CAPM required return, not the market return.
Believing Jensen's alpha is independent of the benchmark: it depends on the market index chosen.

Written from CFA Institute's documentation

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

An analyst uses the capital asset pricing model to estimate the required return on Corvane Logistics shares. The risk-free rate is 3.0%, the expected market risk premium (the expected market return minus the risk-free rate) is 5.0%, and Corvane's beta is 1.4. The expected return on Corvane shares is closest to:
Right. In the game that’s Renown for your Portfolio Construction building.
Not that one: C is right. In the game your Portfolio Construction building would lose a little Renown, and this question would come back later.
Your answerA.7.0%This stops at the premium for systematic risk, 1.4 × 5.0% = 7.0%, and forgets to add the 3.0% risk-free rate that every CAPM expected return starts from.Your answerB.8.0%This treats the shares as if their beta were 1.0: 3.0% + 5.0% = 8.0% is the market's expected return. With a beta of 1.4 the shares carry more systematic risk and earn 1.4 times the premium.The answerC.10.0%The CAPM gives E(Ri) = Rf + βi[E(Rm) − Rf]. The bracketed term is the market risk premium, already given as 5.0%, so E(Ri) = 3.0% + 1.4 × 5.0% = 3.0% + 7.0% = 10.0%.
Written from www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/portfolio-risk-return-part-2
Using the capital asset pricing model, an analyst finds that the security market line gives Ternby Mining shares an equilibrium expected return of 9% for their beta. The analyst's own forecast return for the shares is 12%. Under the CAPM, Ternby shares are most likely:
Right. In the game that’s Renown for your Portfolio Construction building.
Not that one: C is right. In the game your Portfolio Construction building would lose a little Renown, and this question would come back later.
Your answerA.OverpricedAn overpriced share would offer less than its equilibrium return and plot below the security market line. Ternby's 12% forecast is above the 9% the SML requires, a positive alpha.Your answerB.Fairly pricedA fairly priced share has a forecast return equal to its security market line return, an alpha of zero. Ternby's forecast exceeds the SML return by 3 percentage points.The answerC.UnderpricedThe security market line gives the equilibrium expected return for each beta when the CAPM holds. Ternby's forecast return of 12% sits above its SML return of 9%, so its alpha is 12% − 9% = +3%.
Show the full explanation and doc quotes
An asset with a positive alpha plots above the SML and is identified as underpriced: its price is low enough to offer more than the return its systematic risk requires.
Written from www.federalreserve.gov/pubs/feds/2014/201401/index.html
Over the past year, a fund returned 8.4% while its benchmark market index returned 11.0% and the risk-free rate was 3.0%. The fund's beta relative to that index was 0.5. The fund's Jensen's alpha for the year is closest to:
Right. In the game that’s Renown for your Portfolio Construction building.
Not that one: C is right. In the game your Portfolio Construction building would lose a little Renown, and this question would come back later.
Your answerA.−2.6%Subtracting the index return, 8.4% − 11.0% = −2.6%, treats the fund as if its beta were 1. With a beta of 0.5 the fund took half the market's risk, so the CAPM asks only 7.0% of it, and it beat that.Your answerB.−0.1%This applies beta to the full 11.0% index return: 3.0% + 0.5 × 11.0% = 8.5%, and 8.4% − 8.5% = −0.1%. Beta scales only the market's excess return over the risk-free rate, 11.0% − 3.0% = 8.0%.The answerC.1.4%Jensen's alpha = Rp − [rf + βp(Rm − rf)], the fund's return minus the CAPM return required for its market risk. Required return = 3.0% + 0.5 × (11.0% − 3.0%) = 3.0% + 4.0% = 7.0%. Alpha = 8.4% − 7.0% = 1.4%, a positive alpha.
Written from rpc.cfainstitute.org/sites/default/files/-/media/documents/code/gips/measures-risk-adjusted-return.pdf