CAPM
Also written Capital Asset Pricing Model
A model that prices the return an investor should demand from a share: the risk-free rate plus beta times the market risk premium.
In plain language
CAPM answers: what return should I demand for owning this particular share?
Start with what a government security pays, since that is available without risk. Then add compensation for taking equity risk — but only for the part of the risk that cannot be diversified away. Beta measures how much of that undiversifiable risk this share carries. A share that swings twice as hard as the index earns twice the premium.
The answer is the cost of equity: the discount rate for an equity valuation, and the hurdle a company must beat to be creating value.
How it works
The workbook builds CAPM from three components (Chapter 10, section 10.5):
- Risk-free rate (Rf) — the return available without taking risk.
- Expected market return (Rm) — the return expected on a stock market portfolio. Subtract Rf and you have the market risk premium (MRP).
- Beta (β) — a proxy for the firm's systematic risk, reflecting both its business and its financial risk. It is the sensitivity of the stock's return to the market's return.
Beta scales the premium. Chapter 12 (section 12.5) shows what the number means. With a beta of 1, a 10% market return gives the share 1 × 10% = 10%. With a beta of 1.2, a 15% rise in the market return gives 1.2 × 15% = 18%. A beta below 1 means the share is less volatile than the market.
The product β × (Rm − Rf) is the equity risk premium: what the investor must be paid over and above the risk-free rate. Add Rf back and you have the cost of equity, Ke.
Ke then does three jobs in the workbook:
The formula
Cost of equity = Rf + β × (Rm − Rf)
Rf risk-free rate — the yield on a government security
β beta, the share's sensitivity to the index
Rm − Rf market risk premium, the extra return equities pay over the risk-free rate
A worked example
Valuing an Indian private bank (illustrative figures — not from the workbook):
- Risk-free rate: 10-year government security yield, 6.9%
- Beta: 1.25 (the bank moves 25% harder than the Nifty)
- Market risk premium: 6.0%
Cost of equity = 6.9% + 1.25 × 6.0% = 6.9% + 7.5% = 14.4%
Every rupee of the bank's future cash flow must be discounted at 14.4%. A rupee ten years out is worth 26 paise today.
Now take a consumer staples company with a beta of 0.65:
Cost of equity = 6.9% + 0.65 × 6.0% = 10.8%
A rupee ten years out is worth 36 paise — nearly 40% more. The same cash flow is worth substantially more when it is more predictable, and that is the entire economic content of the model.
Why NISM asks about it
Chapter 10 introduces CAPM as the source of the discount rate for equity valuation, and Chapter 12 supplies the risk concepts behind it. Numerical questions usually give three of the four quantities and ask for the fourth.
Common exam traps
- The market risk premium is
Rm − Rf, notRm. Multiplying beta by the whole market return is the classic mistake and every option list contains the answer it produces. - CAPM prices systematic risk only. Company-specific risk is assumed diversified away and earns no premium — which is why a single risky stock in a portfolio of one is not compensated for that concentration.
- A beta above 1 raises the cost of equity and therefore lowers the valuation. Higher demanded return, lower present value.
- Beta is measured from past prices. It describes how a share has behaved, not how it must behave.
Check yourself
1.An investor has placed a significant portion of his wealth in one particular investment and has not adequately diversified. Which risk-adjusted return measure is appropriate for appraising that investment?
- a)Treynor ratio
- b)Sharpe ratio
- c)Jensen's Alpha
- d)Modified duration
Show the answer
Answer: (b) Sharpe ratio
The workbook assigns the two ratios to two different investors, and the exam tests exactly this split.
Sharpe Ratio is appropriate for appraising the investment performance of individuals who have invested a significant portion of their wealth in a particular investment, and have not adequately diversified.
Treynor Ratio is appropriate for individuals who have adequately diversified their wealth into multiple asset classes.
The logic is worth carrying rather than memorising. Sharpe divides by standard deviation, which measures total risk — and an undiversified investor still carries unsystematic risk, so total risk is what matters to him. Treynor divides by beta, which measures only systematic risk — appropriate once diversification has removed the rest.
Option C measures excess return over the CAPM expectation, which does not depend on how the investor's own wealth is arranged. Option D is a bond interest-rate sensitivity measure, not a risk-adjusted return measure at all.
2.A portfolio returned 18%. The risk-free rate is 6.5%, the market return is 12%, and the portfolio beta is 1.30. What is Jensen's Alpha?
- a)+4.35%
- b)+6.00%
- c)+11.50%
- d)−1.30%
Show the answer
Answer: (a) +4.35%
Jensen's Alpha = Return on portfolio − (Risk free rate + β × market risk premium)
The step candidates skip is computing the market risk premium, which is the market return minus the risk-free rate:
12% − 6.5% = 5.5%
CAPM expected return = 6.5 + (1.30 × 5.5) = 6.5 + 7.15 = 13.65%
Jensen's Alpha = 18 − 13.65 = +4.35%
Option B is 18 − 12 — the crude "beat the market by 6 points" answer, which ignores beta and the risk-free rate entirely. Option C is simply the risk premium, 18 − 6.5, with no risk adjustment at all. Option D has no basis.
The error that produces a genuinely wrong working is using the market return (12%) where the formula says market risk premium (5.5%): 18 − (6.5 + 1.30 × 12) = −4.1%. A premium is always measured over the risk-free rate.
Higher Jensen's Alpha is better. But note it uses beta, so it says nothing about the portfolio's total risk — a fund can have a strong alpha and still be an unsuitable holding for an undiversified investor.
Where this is taught
- Series XXI-B · Chapter 3: Investing in Stocksintroduced here
- Series XV · Chapter 10: Valuation Principlesintroduced here
- Series XXI-A · Chapter 3: Investing in Stocksintroduced here
Related terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Discounted Cash FlowA valuation method that estimates the cash a business will generate in future years and converts each year back to what it is worth today.
- Intrinsic valueWhat an asset is actually worth — the present value of the cash it will generate over its remaining life, as against whatever price the market is quoting today.
- Systematic riskThe part of an investment's risk that comes from economy-wide forces moving every asset at once — it cannot be diversified away, and it is the only risk the market pays you to carry.
- AlphaThe return a fund earned above what its beta and the benchmark say it should have earned — the slice of performance left over once the market has been given credit for its share.
- Arbitrage Pricing TheoryA multifactor alternative to CAPM, developed by Stephen Ross, in which expected return depends on several risk factors — each with its own beta — instead of the market alone.
- Market anomalyA pattern of returns that departs from what an asset's fundamentals and risk — as measured by CAPM or another pricing model — say it should earn, and so contradicts market efficiency.
- Size AnomalyThe finding that small firms, measured by total market value, have consistently earned larger risk-adjusted returns than large firms — contradicting market efficiency.
- Market ProxyA practical stand-in for the theoretical market portfolio — usually a broad-based equity index. The choice matters: an incorrect proxy distorts beta and the security market line.
- Single-factor modelThe workbook's own term for CAPM: a model that explains an asset's return using just one risk factor, market risk, unlike the several factors used in APT and other multifactor models.
- Undervalued securityUnder CAPM, a security whose estimated return plots above the Security Market Line — earning more than its systematic risk (beta) warrants under market equilibrium.
- Lending portfolioAny mix of the risk-free asset and the market portfolio that uses only the investor's own money — it plots on the Capital Market Line between the risk-free rate and M, and lending means buying the risk-free asset.
- Overvalued securityUnder CAPM, a security whose estimated return plots below the Security Market Line — it is expected to earn less than its systematic risk warrants under market equilibrium.
- Regression of beta toward the meanAn empirical finding in the tests of CAPM: high-beta portfolios tend to drift down towards 1.00 over time, and low-beta portfolios tend to drift up towards 1.00.
- Risk premiumThe extra return an investor demands over the nominal risk-free rate as compensation for uncertainty about future cash flows — the last and largest block in the required rate of return.
- Modern Portfolio TheoryMarkowitz's framework for building portfolios on expected return and risk together, in which the co-movement between holdings — not their individual riskiness — decides the risk of the whole.
- Capital Market LineThe straight line from the risk-free rate tangent to the efficient frontier at the market portfolio — with a risk-free asset available, it is the efficient frontier, priced in standard deviation.
- Security Market LineThe graph of CAPM: expected return plotted against beta. In equilibrium every asset lies on it — a security plotting above is undervalued, one plotting below is overvalued.
- Return on Capital EmployedOperating profit as a percentage of all the capital in the business, equity and debt together — the return the enterprise earns before any question of how it was funded or taxed.
- Dividend Discount ModelA valuation that treats a share as worth the present value of every dividend it will ever pay, discounted at the return an equity investor demands for holding it.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Capital Market TheoryThe extension of Modern Portfolio Theory that adds a risk-free asset and builds a model for pricing all risky assets, giving the Capital Market Line, the market portfolio and CAPM.
- WACCThe blended after-tax rate a company pays on all its capital, equity and debt weighted by how much of each it uses — and therefore the discount rate for free cash flow to the firm.
- Country Risk PremiumThe extra return an investor demands for putting money into one country rather than another, added to the required rate of return to pay for that country's political and macroeconomic risk.
- Portfolio betaThe weighted average of the betas of the holdings in a portfolio — the measure of its systematic, non-diversifiable risk used in CAPM, the Treynor ratio and market-neutral strategies.
- Expected Portfolio ReturnThe weighted average of the expected returns of the holdings in a portfolio, each weight being that asset's share of portfolio value — the return half of Modern Portfolio Theory.
- Variance of a SecurityThe probability-weighted average of the squared gaps between a security's possible returns and its expected return — the forward-looking measure of a single asset's risk in Modern Portfolio Theory.
- Opportunity CostThe benefit given up on the next-best alternative when money is committed to one investment instead of another — the yardstick an AIF return has to beat before it counts as a good return.
- Specific Company Risk PremiumAn extra slice added to the discount rate for one particular company, on top of beta and the market risk premium, to price the unsystematic risk that the CAPM does not capture.
- Unsystematic riskThe part of an investment's risk that belongs to one company or one issuer — a strike, a fraud, a downgrade — and which diversification can remove, unlike market-wide systematic risk.
- Treynor ratioRisk premium per unit of market risk — the return a scheme earned above the risk-free rate, divided by its beta rather than by its standard deviation.
- Beta returnUnder the CAPM, the part of a portfolio's return that comes purely from taking on market (systematic) risk, calculated as beta multiplied by the market's excess return over the risk-free rate.