Economic Modelling · Mean-variance portfolio theory

CAPM, Beta and the Security Market Line Explained

Updated 11 October 2026 · Fact-checked

The Capital Asset Pricing Model says a security's expected return equals the risk-free rate plus beta times the market risk premium: E(Ri) = rf + βi [E(Rm) − rf]. Beta measures systematic risk. Plot this line against beta and you get the security market line. To solve questions, find beta, then substitute.

Understand CAPM, Beta and Security Market Line

Start with diversification. If you hold many assets, the risk that is specific to one company largely cancels out. What remains is systematic risk, the risk that moves with the whole market. Specific risk is also called unsystematic or diversifiable risk.

The Capital Asset Pricing Model (CAPM) builds on mean-variance portfolio theory. If all investors hold efficient portfolios, then in equilibrium everyone holds some mix of the risk-free asset and the same market portfolio. Since only systematic risk cannot be diversified away, the market pays a reward only for systematic risk. Investors are not paid extra for bearing specific risk.

Beta measures how much a security moves with the market. Beta = Cov(Ri, Rm) ÷ Var(Rm). A beta of 1 means the security moves with the market on average. A beta above 1 means it amplifies market moves. A beta below 1 means it dampens them. The market portfolio has beta 1 and the risk-free asset has beta 0.

The security market line (SML) plots expected return against beta. It is a straight line with intercept rf and slope E(Rm) − rf. Every correctly priced security lies on it. A security above the line has a higher expected return than required (underpriced). One below the line is overpriced.

Do not confuse the SML with the capital market line (CML). The CML plots expected return against standard deviation and applies only to efficient portfolios. The SML plots against beta and applies to every security and every portfolio, efficient or not.

The main assumptions are: investors care only about mean and variance of return over a single period; they are rational and risk averse; all investors have the same (homogeneous) expectations; they can borrow and lend at the risk-free rate without limit; markets are frictionless, with no taxes or transaction costs; assets are infinitely divisible; and investors are price takers.

Key rules to remember

CAPM: E(Ri) = rf + βi [E(Rm) − rf]; E(Rm) − rf is the market risk premium. Use the same time unit for all rates.
Beta of a security: βi = Cov(Ri, Rm) ÷ Var(Rm) = ρim σi ÷ σm; ρim is the correlation between the security and the market. σ values are standard deviations.
Beta of a portfolio: βp = Σ wi βi; Weights wi are market-value proportions and sum to 1. Include the risk-free asset with beta 0.
Systematic and specific variance: σi² = βi² σm² + σ²(εi); Total variance splits into systematic and specific parts. Specific variance can be diversified away.
Capital market line: E(Rp) = rf + [(E(Rm) − rf) ÷ σm] σp; Applies to efficient portfolios only. The slope is the market price of risk.
Security market line: E(Ri) = rf + βi [E(Rm) − rf]; Applies to all assets and portfolios. Beta is on the horizontal axis.
Alpha (Jensen): αi = actual E(Ri) − [rf + βi (E(Rm) − rf)]; Positive alpha means above the SML; zero in CAPM equilibrium.

How to solve CAPM, Beta and Security Market Line questions

Use this method for any CAPM, beta or SML question. Write the notation first so your working is easy to mark.

1List the givens: rf, E(Rm), σm, and any covariances, correlations or betas. Check that all are in the same period, such as annual.
2If beta is not given, calculate it as Cov(Ri, Rm) ÷ Var(Rm), or as ρ σi ÷ σm. Square σm to get the variance.
3For a portfolio, find each asset's beta and weight. Compute βp = Σ wi βi. Treat the risk-free asset as beta 0.
4Compute the market risk premium E(Rm) − rf.
5Substitute into E(Ri) = rf + βi × premium. Show each number.
6If asked whether a security is mispriced, compare its forecast return with the CAPM required return. Higher forecast means underpriced and a buy; lower means overpriced.
7If asked for CML versus SML, check whether the risk measure is σ (CML) or β (SML), and whether the asset is efficient.
8State the answer with units and a one-line interpretation.

Quickest way: Required return in three lines

When to use it: Use it for MCQs and short numerical questions where rf, the market return and a beta or beta inputs are given.

Write premium = E(Rm) − rf.
Write beta as ρσi ÷ σm or Cov ÷ σm² if not given.
Compute rf + beta × premium. Sense-check: beta above 1 must give a return above E(Rm), and beta below 1 must give a return between rf and E(Rm).

Common mistakes in CAPM, Beta and Security Market Line

Using E(Rm) instead of E(Rm) − rf as the multiplier of beta.
The formula looks like a plain weighted average of returns.
Fix: Always compute the premium first, then multiply by beta, then add rf.
Dividing covariance by σm instead of σm².
Students mix up beta with correlation or with the CML slope.
Fix: Beta divides by the variance of the market. Remember β = Cov ÷ Var.
Using the SML for risk measured by standard deviation, or the CML for an individual security.
Both lines look alike and both start at rf.
Fix: CML: efficient portfolios, σ on the axis. SML: any asset, β on the axis.
Leaving out the risk-free asset when finding a portfolio beta, or using weights that do not sum to 1.
Students only list the risky holdings.
Fix: Include cash or borrowing as beta 0, and borrowing as a negative weight. Check the weights add to 1.
Saying a high-beta security has high total risk, or that a low-σ security has low beta.
Beta and standard deviation are treated as the same thing.
Fix: Beta measures only systematic risk. Total risk also includes specific risk, so a low σ asset can have a high beta if it is highly correlated with the market.
Claiming CAPM is proven by data or that it must hold in practice.
Its clean result looks like a fact.
Fix: Describe it as an equilibrium model resting on strong assumptions, and name criticisms such as unobservable market portfolio and unstable betas.

Worked examples

Example 1

The risk-free rate is 6% a year and the expected return on the market is 12%. A share has covariance 0.045 with the market return, and the market variance is 0.030. (a) Find the share's beta. (b) Find its required return under CAPM. (c) An analyst forecasts a 14% return. Is the share underpriced or overpriced?

Show the solution

(a) β = Cov ÷ Var(Rm) = 0.045 ÷ 0.030 = 1.5.
(b) Market risk premium = 12% − 6% = 6%.
Required return = 6% + 1.5 × 6% = 6% + 9% = 15%.
(c) Forecast return 14% is below the required 15%.
Alpha = 14% − 15% = −1%. The share lies below the SML.

Answer: Beta is 1.5 and the required return is 15%. The forecast is 14%, so the share is overpriced relative to CAPM.

Example 2

A portfolio has 50% in Share A (beta 1.2), 30% in Share B (beta 0.8) and 20% in risk-free government securities. The risk-free rate is 5% and the expected market return is 11%. Find the portfolio beta and its expected return.

Show the solution

Risk-free asset has beta 0.
βp = 0.5 × 1.2 + 0.3 × 0.8 + 0.2 × 0 = 0.60 + 0.24 + 0 = 0.84.
Market risk premium = 11% − 5% = 6%.
E(Rp) = 5% + 0.84 × 6% = 5% + 5.04% = 10.04%.
Check: beta below 1 gives a return between 5% and 11%. It does.

Answer: Portfolio beta is 0.84 and its expected return is 10.04% a year.

Exam tips

Write E(Ri) = rf + βi[E(Rm) − rf] at the top of your answer, then substitute. Marks are given for the method even if the arithmetic slips.
In written questions on assumptions, give each assumption with a short reason it matters, such as homogeneous expectations leading to one market portfolio.
For CML versus SML questions, state what is on each axis, which assets each applies to, and where each is used. This is a very common comparison.
When asked about limitations, cover unobservable market portfolio, unrealistic assumptions, single period, unstable betas and poor empirical support. Link each to its effect.
In Paper B style work, show the formula for beta as a covariance divided by variance. Compute it from the data, then apply CAPM.

Practice questions from Mean-variance portfolio theory

CAPM, Beta and Security Market Line in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CAPM, Beta and Security Market Line: frequently asked questions

What are the main assumptions of CAPM?

Investors are rational, risk averse and care only about mean and variance over one period. They share the same expectations, can borrow and lend at the risk-free rate, and face no taxes or transaction costs. Assets are divisible and investors are price takers.

What is the difference between the CML and the SML?

The CML plots expected return against standard deviation and holds only for efficient portfolios. The SML plots expected return against beta and holds for every asset and portfolio in equilibrium. Both start at the risk-free rate on the vertical axis.

How do I calculate the beta of a portfolio?

Multiply each asset's beta by its weight and add them up. Treat the risk-free asset as beta 0. Weights are proportions of total portfolio value and sum to 1.

What are the main criticisms of CAPM?

The true market portfolio cannot be observed. Betas change over time and are estimated with error. The assumptions, such as unlimited risk-free borrowing and identical expectations, are unrealistic. Empirical tests find returns related to factors other than beta.

Can beta be negative?

Yes. A negative beta means the asset tends to move opposite to the market. CAPM then gives an expected return below the risk-free rate, because the asset reduces portfolio risk.