NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory

CAPM, Beta and Security Market Line Explained

Updated 11 October 2026 · Fact-checked

CAPM says a security's required return equals the risk-free rate plus beta times the market risk premium: E(Ri) = Rf + β × (Rm − Rf). Beta measures systematic risk. The Security Market Line plots this required return against beta. To solve, identify Rf, β and Rm, then substitute.

Understand CAPM, Beta and Security Market Line

Total risk of a security has two parts. Unsystematic risk is specific to a company or industry and can be removed by diversification. Systematic risk comes from the whole market, such as interest rate moves or recessions, and cannot be diversified away. The market rewards only systematic risk.

Beta (β) measures how sensitive a security's return is to the market's return. The market portfolio has a beta of 1. A beta above 1 means the security tends to move more than the market. A beta below 1 means it moves less. A risk-free asset has a beta of 0. Beta is calculated as Covariance(security, market) ÷ Variance(market).

The Capital Asset Pricing Model (CAPM) converts beta into a required return. You start with the risk-free rate. You add a premium for taking market risk. That premium is beta times the market risk premium, which is the market return minus the risk-free rate.

The Security Market Line (SML) is the graph of CAPM. Beta is on the x-axis and expected or required return is on the y-axis. The intercept is Rf and the slope is the market risk premium (Rm − Rf). It applies to individual securities and to portfolios, since it uses beta.

The SML is not the Capital Market Line (CML). The CML uses standard deviation (total risk) on the x-axis and applies only to efficient portfolios. If a security's expected return is above the SML, it is undervalued (positive alpha). If it is below the SML, it is overvalued (negative alpha).

Key formulas to remember

CAPM required return: E(Ri) = Rf + βi × (Rm − Rf); Rf is the risk-free rate, Rm the expected market return. Use the same period for all rates, usually annual.
Market risk premium: MRP = Rm − Rf; This is the slope of the Security Market Line.
Beta: β = Cov(Ri, Rm) ÷ Var(Rm); Also equals correlation × (σi ÷ σm).
Portfolio beta: βp = Σ (wi × βi); Weighted average of individual betas. Weights are market value proportions and sum to 1.
Alpha (Jensen's): α = Actual or expected return − CAPM required return; Positive alpha means above the SML. Negative means below the SML.
SML versus CML: SML: risk = beta. CML: risk = standard deviation; SML prices any security. CML covers only efficient portfolios of the risk-free asset and the market portfolio.

How to solve CAPM, Beta and Security Market Line questions

Use this method for any CAPM, beta or SML question.

1Read what is asked: required return, beta, portfolio beta, or whether a security is over or undervalued.
2List the inputs: Rf, Rm (or market risk premium), and beta. Note if the question gives the premium directly.
3If Rm is given, compute the premium as Rm − Rf first.
4Multiply beta by the premium, then add Rf.
5For a portfolio, find the weighted average beta first, then apply CAPM.
6For valuation, compare expected return with the required return. Higher expected return means undervalued.
7Check that the answer is sensible: beta 1 gives Rm, beta 0 gives Rf.

Quickest way: Premium first, then beta

When to use it: Use for any numerical CAPM question where options are close together.

Compute Rm − Rf mentally.
Multiply by beta.
Add Rf last.
Eliminate options with a quick check: beta above 1 must give a return above Rm; beta below 1 must give a return below Rm but above Rf.

Common mistakes in CAPM, Beta and Security Market Line

Using Rm instead of (Rm − Rf) as the multiplier of beta.
Students remember 'beta times market return' and skip the subtraction.
Fix: Always bracket (Rm − Rf) first. Beta multiplies only the premium.
Confusing the SML with the CML.
Both are straight lines starting at the risk-free rate.
Fix: Check the x-axis. Beta means SML. Standard deviation means CML.
Treating beta as total risk.
Beta is called a risk measure, so it feels like overall risk.
Fix: Beta measures only systematic risk. Standard deviation measures total risk.
Saying a security with high beta is always a better investment.
Higher beta gives a higher required return.
Fix: High beta means higher required return and more market risk. It is not automatically better.
Judging mispricing by comparing the return with the market return.
Students forget that the benchmark is the security's own CAPM return.
Fix: Compare expected return with the CAPM required return for that beta.
Averaging portfolio beta with equal weights.
Students ignore the amounts invested.
Fix: Weight each beta by its share of portfolio value.

Worked examples

Example 1

The risk-free rate is 6%, the expected market return is 12% and a stock has a beta of 1.5. What is the required return?

Show the solution

Market risk premium = 12% − 6% = 6%.
Beta × premium = 1.5 × 6% = 9%.
Required return = 6% + 9% = 15%.

Answer: 15%

Example 2

A stock is expected to return 13%. Rf is 7%, Rm is 11% and the stock's beta is 1.25. Is it undervalued or overvalued, and what is its alpha?

Show the solution

Premium = 11% − 7% = 4%.
Required return = 7% + 1.25 × 4% = 7% + 5% = 12%.
Expected return 13% is above required 12%, so the stock plots above the SML.
Alpha = 13% − 12% = 1%.

Answer: Undervalued, with a positive alpha of 1%

Exam tips

Expect direct substitution questions. Write Rf, Rm and beta clearly before calculating.
Know the SML versus CML difference cold: beta versus standard deviation, and all securities versus efficient portfolios.
Remember the beta anchors: market 1, risk-free asset 0.
Questions on diversification often ask what it removes. The answer is unsystematic risk, not systematic risk.
On caselets worth 2 marks, a wrong answer costs more, so compute rather than guess.

Practice questions from Introduction to Modern 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 is the CAPM formula?

E(Ri) = Rf + β × (Rm − Rf). It gives the return an investor should require for the systematic risk of a security.

What is the difference between the Security Market Line and the Capital Market Line?

The SML plots required return against beta and applies to any security or portfolio. The CML plots return against standard deviation and applies only to efficient portfolios that combine the risk-free asset and the market portfolio.

What does a beta of 1.2 mean?

The security tends to move 1.2 times as much as the market. It has more systematic risk than the market and a higher required return.

Can beta be negative?

Yes. A negative beta means the security tends to move opposite to the market. It is rare in practice.