How much return should an investor require from a share? The Capital Asset Pricing Model (CAPM), developed by William Sharpe (1964) and others, gives a simple answer: the risk-free rate plus a reward for the share’s exposure to market risk, measured by beta. The CAPM is used to estimate the cost of equity for valuation and capital budgeting, and to judge whether a fund manager has added value, measured by alpha.
What you will learn
- State the CAPM formula and the meaning of each input
- Calculate beta from returns and interpret it
- Calculate required returns, portfolio beta and Jensen’s alpha
- Understand the security market line and the limitations of the CAPM
The CAPM formula
Capital Asset Pricing Model
E(Ri) = Rf + βi × (E(Rm) − Rf)
- Rf — the risk-free rate, usually a government bond or bill yield.
- βi — the asset’s beta, its sensitivity to market movements.
- E(Rm) − Rf — the market risk premium, the extra return expected from the market portfolio.
The logic comes from modern portfolio theory: since investors can diversify away company-specific risk, only systematic risk — the part that moves with the market — should earn a premium.
Understanding beta
| Beta | Meaning | Typical examples |
|---|---|---|
| β = 1 | Moves in line with the market on average | Broad market index |
| β > 1 | More sensitive than the market | Cyclical and highly leveraged companies |
| 0 < β < 1 | Less sensitive than the market | Utilities, consumer staples |
| β ≈ 0 | Unrelated to market movements | Treasury bills |
| β < 0 | Tends to move against the market | Rare; some hedging assets |
A beta of 1.2 means that, on average, when the market rises 10%, the share tends to rise about 12% — and falls about 12% when the market falls 10%.
Beta
β = Covariance(Ri, Rm) ÷ Variance(Rm)
In practice, beta is estimated by regressing the share’s returns on market returns, usually using two to five years of weekly or monthly data.
Worked example: estimating beta
Over five periods, a share returned 8%, −4%, 12%, 3% and 6%, while the market returned 5%, −2%, 9%, 1% and 4% (illustrative figures; real estimates use many more observations).
- Average returns: share 5.0%, market 3.4%.
- Sample covariance of share and market returns: 24.50.
- Sample variance of market returns: 17.30.
- Beta = 24.50 ÷ 17.30 = 1.42.
The share has tended to move about 1.4 times as much as the market.
Using the CAPM
Worked example: required returns
The risk-free rate is 7% and the expected market return is 13%, so the market risk premium is 6% (illustrative figures).
| Beta | Required return = 7% + β × 6% |
|---|---|
| 0.6 | 10.6% |
| 1.0 | 13.0% |
| 1.2 | 14.2% |
| 1.5 | 16.0% |
A company with a beta of 1.2 has an estimated cost of equity of 14.2% — an input to its WACC. Try the cost of equity calculator.
Portfolio beta is the weighted average of the holdings’ betas. A portfolio with 40% in a share with beta 1.2, 35% with beta 0.8 and 25% with beta 1.5 has a beta of 0.40 × 1.2 + 0.35 × 0.8 + 0.25 × 1.5 = 1.135.
The security market line
Plotting required return against beta gives the security market line (SML), a straight line starting at the risk-free rate with a slope equal to the market risk premium.
The security market line
Show the data
| Series | Beta | Required return |
|---|---|---|
| Security market line | 0 | 7.0% |
| Security market line | 0.5 | 10.0% |
| Security market line | 1 | 13.0% |
| Security market line | 1.5 | 16.0% |
| Security market line | 2 | 19.0% |
According to the CAPM, fairly priced assets lie on the line. An asset expected to earn more than its required return plots above the line and appears undervalued; one below the line appears overvalued.
Alpha
Jensen’s alpha (Jensen, 1968) measures the return earned above what the CAPM predicts for the risk taken:
Jensen’s alpha
α = Actual return − [Rf + β × (Rm − Rf)]
Worked example: did the fund manager add value?
With Rf = 7% and a market return of 13%:
- Share X, beta 1.2, earned 16%. Required: 14.2%. Alpha = +1.8%.
- A fund with beta 1.1 earned 15%. Required: 7% + 1.1 × 6% = 13.6%. Alpha = +1.4%.
Positive alpha suggests performance beyond what market exposure explains — though one period may reflect luck. Persistent positive alpha after fees is rare, as research on market efficiency shows.
Limitations
- Inputs are estimates: betas vary with the period and frequency of data; the market risk premium is uncertain and debated.
- The "market" is unobservable: the theory’s market portfolio includes all assets; a stock index is only a proxy.
- Empirical evidence: research has found that beta alone does not fully explain differences in average returns. Fama and French (1993) added factors for company size and value (book-to-market), and later models add others such as profitability and momentum.
- Simplifying assumptions: a single period, no taxes or transaction costs, unlimited borrowing at the risk-free rate.
- Emerging and less liquid markets: thin trading can distort beta estimates; analysts may use industry betas or adjust for country risk.
Despite these issues, the CAPM remains the most widely used method for estimating the cost of equity because it is simple, transparent and grounded in theory.
Common mistakes
- Using total volatility instead of beta to set required returns.
- Using a beta estimated over too short or unusual a period.
- Mixing currencies — for example, a local-currency risk-free rate with a US-dollar market premium.
- Treating a single period’s alpha as proof of skill.
Key terms
- Beta — the sensitivity of an asset’s returns to market returns.
- Market risk premium — the expected market return minus the risk-free rate.
- Security market line — the CAPM relationship between beta and required return.
- Alpha — the return above that predicted by the CAPM.
- Systematic risk — market-wide risk measured by beta.
Frequently asked questions
Where do I find a company’s beta?
Financial data providers publish betas, or you can estimate one from historical share and index returns. Check the period and index used.
Can beta change over time?
Yes. Changes in a company’s business mix, leverage or market conditions change its beta.
Is a high-beta share a bad investment?
Not necessarily. It carries more market risk and so should offer a higher expected return; whether it suits you depends on your portfolio and tolerance.
Key takeaways
- CAPM: required return = risk-free rate + beta × market risk premium.
- Beta measures sensitivity to market movements and is estimated from returns.
- The security market line shows fair returns for each beta; alpha measures performance above it.
- The CAPM is widely used but relies on uncertain inputs and is supplemented by multi-factor models.
Explore this in ARBIMETRA LAB
Apply these ideas to your own data. Files are analysed in your browser and are not uploaded.
- CAPM: Beta, alpha and expected return.
- Fama-French Three-Factor Model: Market, size and value loadings.
- Treynor Ratio: Excess return per unit of beta.
- Jensen's Alpha: CAPM alpha with inference.