Portfolio & Asset Pricingadvanced

The CAPM and the SML

The Capital Asset Pricing Model (CAPM) states that the expected return on an asset rises with its beta, the sensitivity of its return to the market. Because diversification removes idiosyncratic risk, only systematic risk is priced, and beta measures exactly that systematic exposure. Plotting expected return against beta gives the Security Market Line (SML), along which every fairly priced asset lies. The SML is not the CML. The CML uses total risk $\sigma$ and applies to efficient portfolios, while the SML uses systematic risk $\beta$ and applies to any asset, fairly priced or not.

Try it yourself

CAPM & the Security Market Line

The CAPM prices an asset by its systematic risk β: E(R_i) = R_f + β_i·(E(R_m) − R_f). Plotted against β this is the Security Market Line, from R_f at β = 0 through the market at β = 1. An asset above the line is under-valued and one below it is over-valued. The gap is its alpha.

CAPM required return at β = 1.109.6%

Market risk premium E(R_m) − R_f 6.0%

Risk-free rate R_f3.0%

Market return E(R_m)9.0%

Asset beta β1.10

Show actual expected return (reveals alpha)

Try this

At β = 1.10 the CAPM requires 9.6%: the risk-free 3.0% plus β times the 6.0% market risk premium. Tick the box above to compare an actual return and read off alpha.

SML vs CML. This is the SML: it uses β and prices every asset, fairly priced or not. The CML uses total risk σ and applies only to efficient portfolios. Same market point, different risk axis.

Discuss: if a stock plots above the SML, what should buying pressure do to its price, and where does the point move as it re-prices?

Why it matters

The market pays you for risk you cannot avoid, and beta is the yardstick of that unavoidable, market-linked risk. A beta of one moves with the market, a beta of two amplifies it, and a beta below one cushions it. The CAPM turns this into a price for risk. Start at the risk-free rate and add beta times the market risk premium. The crucial exam distinction is the axis. The CML measures risk on the total-volatility axis and only efficient portfolios sit on it, whereas the SML measures risk on the beta axis and every security, well diversified or not, should sit on it if priced correctly. Confusing the two is the classic error.

Formulas

CAPM expected return

E(R_i) = R_f + \beta_i\!\left(E(R_m) - R_f\right)

Risk-free rate plus beta times the market risk premium

E(R_m)-R_f

. This equation is the Security Market Line.

Beta

\beta_i = \dfrac{\mathrm{Cov}(R_i, R_m)}{\sigma_m^2} = \rho_{im}\,\dfrac{\sigma_i}{\sigma_m}

Systematic risk, the covariance of the asset with the market scaled by market variance. The market itself has

\beta=1

Worked examples

Scenario

The risk-free rate is 4%, the expected market return is 10%, and a stock has a beta of 1.3. What return does the CAPM require?

Solution

The market risk premium is 10% minus 4%, or 6%. The required return is $R_f+\beta(E(R_m)-R_f)=4\%+1.3(6\%)=11.8\%$ . Because the stock is more sensitive to the market than average, it must offer more than the 10% market return to compensate for its higher systematic risk.

Scenario

A stock plots above the Security Market Line given its beta. What does that imply?

Solution

It offers a higher expected return than the CAPM requires for its systematic risk, so it appears underpriced and attractive. Buying pressure should push its price up and its expected return down until it falls back onto the SML. Points on the line are fairly priced, points above are bargains, and points below are overpriced.

Common mistakes

✗The CML and the SML are the same line. The CML plots return against total risk $\sigma$ for efficient portfolios, while the SML plots return against systematic risk $\beta$ for any asset.
✗A higher-beta stock always earns a higher return. The CAPM predicts a higher expected return for higher beta, but realised returns vary widely, so a high-beta stock can and often does underperform in any given period.
✗Beta measures the total risk of a stock. Beta captures only the systematic, market-linked portion, so a stock with huge idiosyncratic volatility can still have a modest beta.
✗The CAPM rewards firm-specific risk. Only systematic risk earns a premium, because idiosyncratic risk can be diversified away at no cost and so commands no reward.

Revision bullets

•CAPM: required return is the risk-free rate plus beta times the market risk premium
•Beta is systematic risk, the asset covariance with the market over market variance
•Only systematic risk is priced because idiosyncratic risk diversifies away
•The SML plots required return against beta, the CAPM as a line
•CML uses total risk for efficient portfolios, SML uses beta for any asset

Quick check

According to the CAPM, the expected return on an asset depends on

The key distinction between the Security Market Line and the Capital Market Line is that

Connected topics

Diversification Efficient Frontier Capital Allocation Factor Models Performance Eval

Sources

Sharpe (1964)
Sharpe, W. F. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, 19(3), 425-442, 1964.
Derives the CAPM, beta as the priced risk, and the Security Market Line.
Brailsford, Heaney & Bilson (2015), Ch. 9
Brailsford, T., Heaney, R., & Bilson, C. Investments: Concepts and Applications. 5th ed. Cengage Learning Australia, 2015.
Presents the CAPM, beta, the SML, and the contrast with the CML.

How to cite this page

Dr. Phil's Quant Lab. (2026). The CAPM and the SML. Derivatives Atlas. https://phucnguyenvan.com/concept/im-capm

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