CAPM Calculator
Enter a risk-free rate, a market return (or market risk premium) and a beta, and get the CAPM expected return, the asset's risk premium and a security market line. Or paste paired asset and market returns and the calculator estimates beta by regression, with alpha, R², a confidence interval and a scatter plot. Runs in your browser. Free, no sign-up.
Your inputs
CAPM: expected return = risk-free rate + beta × (market return − risk-free rate). Rates are annual and in percent; beta has no unit. Entering the market risk premium instead of the market return gives the same result.
Expected return (CAPM)
9%
Expected return
5%
Market risk premium
6%
Asset risk premium (β × premium)
1.2
Beta used
The working
Expected return = Rf + β × (Rm − Rf) = 3% + 1.2 × (8% − 3%) = 9%
Required return at other betas
| Beta | Expected return |
|---|---|
| 0 | 3% |
| 0.5 | 5.5% |
| 1 | 8% |
| 1.5 | 10.5% |
| 2 | 13% |
How to Use the CAPM Calculator
- 1. Enter the risk-free rate. The annual return on a risk-free asset, usually a government bond yield matched to your time horizon.
- 2. Enter the market input. Either the expected annual return on the market or the market risk premium (market return minus risk-free rate). They give the same answer.
- 3. Give a beta. Type one you know, or switch to "Estimate beta from returns" and paste one line per period with the asset's return and the market's return, in percent.
- 4. Read the expected return. You get the CAPM return, the asset's risk premium and the security market line, with your asset marked on it. When beta is estimated, you also see alpha, R², the standard error and a 95% interval, plus a scatter plot with the fitted line.
The CAPM Formula
The Capital Asset Pricing Model says an asset's expected return is the risk-free rate plus a reward for the market risk it carries: E(R) = Rf + β × (Rm − Rf). Rf is the risk-free rate, Rm the expected market return, and Rm − Rf the market risk premium. Beta (β) measures how much the asset moves with the market. Only that systematic risk is rewarded in the model; the rest can be diversified away.
- β = 1 — the asset moves with the market and the model's expected return equals the market return.
- β > 1 — the asset amplifies market moves, so it needs a higher expected return.
- 0 < β < 1 — it is less sensitive than the market, so its required return is lower.
- β = 0 — no market risk, so the expected return is the risk-free rate. A negative beta, such as some hedging assets, gives an expected return below the risk-free rate.
The result is often used as the cost of equity: the return shareholders require. It is the input to the equity part of the WACC Calculator, and the discount rate for the NPV and IRR Calculator when the cash flows have the risk of equity.
Estimating Beta From Returns
Beta is the slope of a regression of the asset's returns on the market's: β = Cov(asset, market) ÷ Var(market). The intercept is alpha — the average return the asset earned beyond what its beta explains. If you subtract the risk-free return per period from both series first, the regression uses excess returns and the intercept is Jensen's alpha. The slope barely changes, which is why most beta estimates use raw returns. R² shows how much of the asset's variation the market explains, and the standard error and 95% interval show how precise the estimate is. The adjusted beta, ⅔β + ⅓, is the Blume adjustment, which pulls the estimate towards 1 on the observation that betas tend to drift towards the market average.
Worked Examples
A risk-free rate of 3%, a market return of 8% and a beta of 1.2 give a market risk premium of 5%, an asset risk premium of 1.2 × 5% = 6% and an expected return of 3% + 6% = 9%. At betas of 0, 0.5, 1, 1.5 and 2 the same market gives 3%, 5.5%, 8%, 10.5% and 13%. A beta of −0.5 gives 3% − 2.5% = 0.5%.
For the beta example, the calculator starts with 12 invented monthly returns. Regressing them gives a beta of 1.5206, alpha of −0.0238% a month, R² of 0.8839 (correlation 0.9402), a standard error of 0.1743 and a 95% interval of 1.1323 to 1.9088. The adjusted beta is 1.3471. Used in the CAPM with a 3% risk-free rate and an 8% market return, that beta gives 3% + 1.5206 × 5% = 10.6029%. The wide interval is the point: twelve months is too few for a reliable beta.
What CAPM does not do
CAPM is a one-factor model with strong assumptions — investors hold diversified portfolios, borrow and lend at the risk-free rate, and care only about mean and variance. Estimated betas depend on the market index, the return interval and the period. Treat the output as a textbook estimate of the required return, not a forecast, and not investment advice.
Frequently Asked Questions
- What is the CAPM formula?
- Expected return = risk-free rate + beta × (expected market return − risk-free rate). With a 3% risk-free rate, a beta of 1.2 and an 8% expected market return, the expected return is 3% + 1.2 × 5% = 9%.
- What risk-free rate should I use?
- The yield on a government bond in the same currency, with a maturity close to your investment horizon — a 10-year government yield is a common choice for long-term valuations. It should be an annual rate in the same units as the market return.
- What is a market risk premium?
- The extra return investors expect from the market portfolio over the risk-free rate (Rm − Rf). Estimates differ by method, country and date, so published figures vary; use a source you can cite and state it.
- How is beta calculated?
- As the covariance of the asset's returns with the market's divided by the variance of the market's returns, which is also the slope of the regression line of asset returns on market returns. Use the same interval (for example monthly) and the same period for both series.
- How many data points do I need for beta?
- There is no fixed rule, but more is better: the 95% interval shows the uncertainty directly. Five years of monthly returns (60 points) or two years of weekly returns are common conventions. With about a dozen points the interval is very wide.
- What is the difference between CAPM and WACC?
- CAPM gives the cost of equity — what shareholders require. WACC blends the cost of equity with the after-tax cost of debt, weighted by how the firm is financed, to give the overall cost of capital.