Strategic Financial Management · Asset Pricing Theories

Capital Asset Pricing Model (CAPM): Formula, Assumptions and Numericals

Q: What are the main assumptions of CAPM?

Investors are rational, risk-averse and hold diversified portfolios over a single period. They share the same expectations and can borrow and lend at the risk-free rate. Markets are perfect, with no taxes or transaction costs.

Q: How do I calculate expected return using CAPM?

Subtract the risk-free rate from the market return to get the premium. Multiply it by beta and add the risk-free rate. For example, with Rf 5%, Rm 11% and beta 1.5, the return is 5% + 1.5 × 6% = 14%.

Q: What are the limitations of CAPM?

It relies on unrealistic assumptions such as perfect markets and unlimited borrowing at the risk-free rate. Beta is estimated from past data and may not hold in future. The true market portfolio cannot be observed, and a single factor may not explain all returns.

Q: What is the difference between CAPM and the Security Market Line?

CAPM is the equation that gives the required return. The Security Market Line is its graph, with beta on the x-axis and expected return on the y-axis. Securities above the line are underpriced and those below are overpriced.

Updated 11 October 2026 · Fact-checked

CAPM gives the return an investor should expect from a security given its systematic risk. Use Ke = Rf + β × (Rm − Rf). Find the risk-free rate, beta and market return, subtract Rf from Rm to get the market premium, multiply by beta, then add Rf.

Understand Capital Asset Pricing Model (CAPM)

Investors are paid for waiting and for bearing risk. The risk-free rate pays for waiting. Extra return is the reward for risk. CAPM says only one kind of risk earns that reward.

Total risk has two parts. Unsystematic risk is specific to a firm, such as a strike or a product failure. You can remove it by holding a well-diversified portfolio. Systematic risk comes from the whole market, such as interest rates, inflation or a recession. It cannot be diversified away. CAPM therefore rewards only systematic risk.

Beta (β) measures how sensitive a security is to market movements. A beta of 1 means the security moves in line with the market. A beta above 1 means it moves more than the market. A beta below 1 means it moves less. The market itself has a beta of 1, and a risk-free asset has a beta of 0.

The market risk premium is Rm − Rf, the extra return the market gives over the risk-free rate. The required return of a security is the risk-free rate plus beta times this premium. Plotted against beta, this gives a straight line called the Security Market Line.

CAPM rests on assumptions: investors are rational and risk-averse, they hold diversified portfolios and use the same single-period horizon, all have the same expectations, they can borrow and lend at the risk-free rate, markets are perfect with no taxes or transaction costs, and assets are infinitely divisible. These are simplifications, and that is the source of the model's limitations.

Key rules to remember

CAPM expected return: E(Ri) = Rf + βi × (Rm − Rf); Gives the required return for the security. Use the same basis (annual, in %) for all inputs.
Market risk premium: Market risk premium = Rm − Rf; If the question gives the premium directly, do not subtract Rf again.
Beta: β = Cov(Ri, Rm) ÷ σm² = ρim × σi ÷ σm; Use when covariance, correlation or standard deviations are given.
Portfolio beta: βp = Σ (wi × βi); Weights are the proportion of portfolio value in each security and should add to 1.
Security Market Line test: Expected return > CAPM return: underpriced (buy). Expected return < CAPM return: overpriced (sell).; Compare the return you expect from the security with the CAPM required return.
Alpha (excess return): α = Expected return − CAPM required return; A positive alpha means the security plots above the SML.

How to solve Capital Asset Pricing Model (CAPM) questions

Follow the same sequence for every CAPM question. It keeps your working clean and earns step marks even if one input is misread.

1Read the question and list Rf, Rm (or the market premium), and beta. Note if beta must be computed.
2If beta is not given, compute it from covariance ÷ variance of market, or correlation × σi ÷ σm.
3Find the market premium: Rm − Rf. If the question gives the premium, use it as it is.
4Apply E(R) = Rf + β × premium and show the substitution.
5For a portfolio, compute portfolio beta as the weighted average of betas and then apply CAPM, or compute each return and weight them. Both give the same result.
6If asked to judge a security, compare the expected or actual return with the CAPM return and state overpriced, underpriced or fairly priced.
7If the question asks for a share price or cost of equity use, take the CAPM return as Ke and continue with the valuation.
8State the final answer in %, with a one-line conclusion.

Quickest way: Premium-first shortcut

When to use it: Use in the objective section and for short numerical parts where inputs are given directly.

Write Rf and Rm − Rf on the margin.
Multiply beta by the premium mentally.
Add Rf to the result.
For a beta of 1 the answer is Rm. For a beta of 0 the answer is Rf. Use these to check your result.
If beta is above 1 the answer must exceed Rm. If below 1 it must lie between Rf and Rm.

Common mistakes in Capital Asset Pricing Model (CAPM)

Multiplying beta by Rm instead of by (Rm − Rf).
Students remember 'beta times market return' and skip the premium step.
Fix: Always compute the premium first. Then check: beta 1 must give Rm.
Subtracting Rf again when the question already gives the market risk premium.
Mechanical use of the formula without reading the data.
Fix: Underline the words 'premium' or 'excess return' in the question. A premium is already Rm − Rf.
Taking the weighted average of the returns of securities using wrong weights for portfolio beta.
Students use number of shares or amounts invested instead of proportions.
Fix: Divide each investment by total portfolio value to get weights that add to 1.
Confusing total risk (standard deviation) with beta.
Both are called 'risk' in the chapter.
Fix: CAPM uses only beta. Standard deviation appears only inside the beta formula or in the Capital Market Line.
Calling a security overpriced when its expected return is higher than the CAPM return.
Mixing up the price view with the return view.
Fix: Higher expected return than required means the price is low, so it is underpriced. Lower means overpriced.
Listing limitations as assumptions or giving only one-word points in theory answers.
Rushing the descriptive part.
Fix: Give each point with a short reason, such as 'beta is based on past data and may change'.

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. (a) Calculate the expected return on Kaveri Ltd shares. (b) Analysts expect the share to return 16%. Is it underpriced or overpriced?

Show the solution

Market risk premium = 13% − 7% = 6%.
Expected return = 7% + 1.4 × 6% = 7% + 8.4% = 15.4%.
Analysts' expected return is 16%, which is higher than the required 15.4%.
Alpha = 16% − 15.4% = +0.6%.

Answer: (a) The CAPM expected return is 15.4%. (b) Because the expected return of 16% is above the required 15.4%, the share plots above the SML and is underpriced. It is a buy.

Example 2

Mr. Iyer holds a portfolio of ₹10,00,000 invested as: ₹4,00,000 in Stock A (beta 0.8), ₹3,00,000 in Stock B (beta 1.2) and ₹3,00,000 in Stock 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.
Portfolio beta = (0.4 × 0.8) + (0.3 × 1.2) + (0.3 × 1.5) = 0.32 + 0.36 + 0.45 = 1.13.
Market premium = 12% − 6% = 6%.
Required return = 6% + 1.13 × 6% = 6% + 6.78% = 12.78%.
Check by weights: A = 6 + 0.8 × 6 = 10.8%; B = 6 + 1.2 × 6 = 13.2%; C = 6 + 1.5 × 6 = 15%. Weighted = 0.4 × 10.8 + 0.3 × 13.2 + 0.3 × 15 = 4.32 + 3.96 + 4.5 = 12.78%.

Answer: Portfolio beta is 1.13 and the required portfolio return is 12.78%.

Exam tips

In Section A, expect a direct substitution question or a test of the meaning of beta. Do the arithmetic carefully because each MCQ carries 2 marks and there is no negative marking.
In the 14-mark questions CAPM is usually a part of a larger problem such as cost of equity, share valuation or a buy-sell decision. Show the CAPM line clearly, since the later steps depend on it.
Write the formula before substituting. Step marks are given for the formula and the premium.
For theory parts, prepare five assumptions and five limitations in crisp one-line points with reasons.
Always end a security evaluation with a clear recommendation: buy if underpriced, sell or avoid if overpriced.

Practice questions from Asset Pricing Theories

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

What are the main assumptions of CAPM?

Investors are rational, risk-averse and hold diversified portfolios over a single period. They share the same expectations and can borrow and lend at the risk-free rate. Markets are perfect, with no taxes or transaction costs.

How do I calculate expected return using CAPM?

Subtract the risk-free rate from the market return to get the premium. Multiply it by beta and add the risk-free rate. For example, with Rf 5%, Rm 11% and beta 1.5, the return is 5% + 1.5 × 6% = 14%.

What are the limitations of CAPM?

It relies on unrealistic assumptions such as perfect markets and unlimited borrowing at the risk-free rate. Beta is estimated from past data and may not hold in future. The true market portfolio cannot be observed, and a single factor may not explain all returns.

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

CAPM is the equation that gives the required return. The Security Market Line is its graph, with beta on the x-axis and expected return on the y-axis. Securities above the line are underpriced and those below are overpriced.