Financial Management and Business Data Analytics · Risk and Return

Capital Asset Pricing Model (CAPM) and Beta for CMA Inter

Q: What is the CAPM formula for CMA Intermediate?

Required return = Rf + β × (Rm − Rf). Here Rf is the risk-free rate, β is the security's beta and Rm − Rf is the market risk premium. The result is the minimum return you should expect for the systematic risk taken.

Q: How do I calculate the beta of a portfolio?

Find the weight of each security as its share of total portfolio value. Multiply each weight by that security's beta and add the results. The weights must total 1.

Q: What is the Security Market Line?

It is the graph of CAPM with beta on the X-axis and required return on the Y-axis. It starts at the risk-free rate and has a slope equal to the market risk premium. Fairly priced securities lie on it.

Q: How do I know if a security is undervalued or overvalued using CAPM?

Compute its required return from CAPM and compare it with its expected return. If expected return is higher, the security is undervalued. If it is lower, it is overvalued.

Updated 10 October 2026 · Fact-checked

CAPM says a security's required return equals the risk-free rate plus beta times the market risk premium: Ke = Rf + β × (Rm − Rf). Compute the required return, compare it with the expected return, and if expected is higher the security is undervalued; if lower, it is overvalued.

Understand Capital Asset Pricing Model (CAPM) and Beta

Investors want extra return for taking risk. But not all risk is rewarded. Unsystematic risk is specific to a company and can be removed by diversification. Systematic risk affects the whole market and cannot be diversified away. CAPM says the market pays you only for systematic risk.

Beta (β) measures systematic risk. It shows how much a security's return moves when the market return moves. The market has a beta of 1. A beta of 1.5 means the security tends to move 1.5 times as much as the market. A beta of 0.6 means it moves less. A beta of 1 means it moves in line with the market.

The market risk premium is Rm − Rf, the extra return the market gives over a risk-free investment such as a government security. CAPM multiplies this premium by beta and adds the risk-free rate. The result is the required return, the minimum return the investor should demand for that level of systematic risk.

The Security Market Line (SML) is the graph of CAPM. Beta is on the X-axis and required return is on the Y-axis. The line starts at Rf (where beta is 0) and rises with slope Rm − Rf. It passes through the market point (β = 1, return = Rm). Every fairly priced security lies on the line.

To judge a security, plot its expected return against its beta. If it lies above the SML, it offers more than the required return, so it is undervalued (buy). If it lies below, it offers less, so it is overvalued (sell or avoid). On the line, it is fairly priced.

Key rules to remember

CAPM required return: Ke = Rf + β × (Rm − Rf); Rm − Rf is the market risk premium. Use returns in the same form (all % or all decimals).
Beta of a security: β = Cov(Ri, Rm) ÷ σm² = ρ(i,m) × σi ÷ σm; Use whichever data the question gives: covariance and market variance, or correlation and standard deviations.
Beta of a portfolio: βp = Σ (wi × βi); Weights are market value proportions and must add up to 1. Beta is a weighted average.
Security Market Line: Required return = Rf + (Rm − Rf) × β; Same equation as CAPM, drawn against beta. Intercept Rf, slope Rm − Rf.
Valuation test: Expected return > Required return: undervalued. Expected return < Required return: overvalued.; Equal means fairly priced. Alpha = Expected − Required.
Market risk premium given market return: Premium = Rm − Rf; If the question gives the premium directly, do not subtract Rf again.

How to solve Capital Asset Pricing Model (CAPM) and Beta questions

Use this order for any CAPM question. It keeps your working clear and earns step marks.

1List the data given: Rf, Rm (or market risk premium), beta or the data to find it, and the expected return if any.
2Check whether the question gives Rm or the premium (Rm − Rf). Work out the premium first.
3If beta is not given, compute it using covariance ÷ market variance, or correlation × σi ÷ σm. For a portfolio, take the weighted average of betas.
4Apply Ke = Rf + β × (Rm − Rf). Write the substitution in full.
5Compare the required return with the expected return (or compute expected return from price and dividend if asked).
6State the conclusion in words: undervalued, overvalued or fairly priced, and the action: buy, sell or hold.
7If asked, add a one-line interpretation of beta: aggressive if above 1, defensive if below 1.

Quickest way: Three-line CAPM check

When to use it: Use for MCQs and for the final part of long numericals where you only need the verdict.

Compute premium = Rm − Rf mentally.
Required = Rf + β × premium. Do it in percent, not decimals.
Compare with expected return: higher means buy (undervalued), lower means sell (overvalued).
For portfolio beta, multiply each weight by beta and add. Confirm weights total 100%.

Common mistakes in Capital Asset Pricing Model (CAPM) and Beta

Using Rm instead of (Rm − Rf) as the multiplier of beta.
Students remember 'beta times market return' and skip the subtraction.
Fix: Write the formula first, then substitute. Always compute the premium on its own line.
Subtracting Rf again when the question already gives the market risk premium.
The words 'market premium' and 'market return' look alike.
Fix: Read the wording. 'Market return' = Rm. 'Risk premium' = Rm − Rf already.
Taking a simple average of betas for a portfolio when weights differ.
Weights are ignored when investment amounts are given in rupees.
Fix: Convert amounts into proportions of total investment, then compute Σ wi × βi.
Reversing the verdict: calling a security with higher expected return overvalued.
Confusing return with price. A higher return for a given risk means the price is too low.
Fix: Remember: expected above required means price is low, so undervalued, so buy.
Treating beta as total risk.
Beta is confused with standard deviation.
Fix: Beta measures only systematic risk. Standard deviation measures total risk. Say this in theory answers.
Mixing percent and decimals in one calculation.
Beta is a decimal while returns are given in percent.
Fix: Keep returns in percent throughout. Beta is just a multiplier, so the answer stays in percent.

Worked examples

Example 1

The risk-free rate is 7% and the expected market return is 13%. Shares of Kaveri Ltd have a beta of 1.4 and an expected return of 16%. Shares of Narmada Ltd have a beta of 0.8 and an expected return of 11%. Using CAPM, find the required return of each share and state whether each is undervalued or overvalued.

Show the solution

Market risk premium = Rm − Rf = 13% − 7% = 6%.
Kaveri: Required return = 7% + 1.4 × 6% = 7% + 8.4% = 15.4%.
Kaveri: Expected return 16% > Required return 15.4%. It plots above the SML, so it is undervalued.
Narmada: Required return = 7% + 0.8 × 6% = 7% + 4.8% = 11.8%.
Narmada: Expected return 11% < Required return 11.8%. It plots below the SML, so it is overvalued.

Answer: Kaveri Ltd: required return 15.4%, undervalued (buy). Narmada Ltd: required return 11.8%, overvalued (sell or avoid).

Example 2

Mr. Rao holds a portfolio of ₹10,00,000 in three shares: ₹4,00,000 in A (beta 1.2), ₹3,00,000 in B (beta 0.9) and ₹3,00,000 in C (beta 1.5). The risk-free rate is 6% and the market return is 12%. Find the portfolio beta and the required return of the portfolio.

Show the solution

Weights: A = 4,00,000 ÷ 10,00,000 = 0.4; B = 0.3; C = 0.3. Total = 1.0.
Portfolio beta = 0.4 × 1.2 + 0.3 × 0.9 + 0.3 × 1.5.
= 0.48 + 0.27 + 0.45 = 1.20.
Market risk premium = 12% − 6% = 6%.
Required return = 6% + 1.20 × 6% = 6% + 7.2% = 13.2%.
Interpretation: beta above 1 means the portfolio is more volatile than the market.

Answer: Portfolio beta = 1.20; required return = 13.2%.

Exam tips

In the MCQ section, expect a direct substitution into Ke = Rf + β × (Rm − Rf). Do it in percent and check whether the premium or the market return is given.
In written answers, show the premium, the substitution and the verdict as separate lines. Step marks come from these.
Always end a valuation question with a clear statement: undervalued or overvalued, and buy or sell.
For portfolio beta questions, convert rupee amounts to weights first and check they add to 1.
If asked to explain the SML, state the intercept (Rf), the slope (Rm − Rf) and that securities above the line are undervalued.

Practice questions from Risk and Return

Capital Asset Pricing Model (CAPM) and Beta in other exams

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

Capital Asset Pricing Model (CAPM) and Beta: frequently asked questions

What is the CAPM formula for CMA Intermediate?

Required return = Rf + β × (Rm − Rf). Here Rf is the risk-free rate, β is the security's beta and Rm − Rf is the market risk premium. The result is the minimum return you should expect for the systematic risk taken.

How do I calculate the beta of a portfolio?

Find the weight of each security as its share of total portfolio value. Multiply each weight by that security's beta and add the results. The weights must total 1.

What is the Security Market Line?

It is the graph of CAPM with beta on the X-axis and required return on the Y-axis. It starts at the risk-free rate and has a slope equal to the market risk premium. Fairly priced securities lie on it.

How do I know if a security is undervalued or overvalued using CAPM?

Compute its required return from CAPM and compare it with its expected return. If expected return is higher, the security is undervalued. If it is lower, it is overvalued.