CAPM Calculator — Beta, Expected Return & Alpha
Compute CAPM beta from volatility and market correlation, expected return on the Security Market Line, alpha, and the Treynor ratio for up to four assets.
CAPM Asset Pricing
| Asset | Beta | CAPM return | Expected return | Alpha | Treynor |
|---|---|---|---|---|---|
| Asset A | 0.7624 | 8.07% | 11.20% | 3.13% | 0.1010 |
| Asset B | 1.2565 | 11.04% | 15.10% | 4.06% | 0.0923 |
| Asset C | 0.4518 | 6.21% | 7.40% | 1.19% | 0.0863 |
| Asset D | 1.7141 | 13.78% | 18.80% | 5.02% | 0.0893 |
A clear path from inputs to results.
For investors and analysts who want to sanity-check an asset against its market risk, or estimate a cost of equity. Enter each asset’s volatility, correlation with the market, and your own return forecast; the calculator derives beta, the CAPM expected return, alpha, and the Treynor ratio, and plots every asset against the Security Market Line. It turns a return hunch into a structured statement about how much risk that hunch implies you are not being paid for.
How to use
- Set the risk-free rate, the expected market return, and the market volatility — these fix the market risk premium E[R_m] - R_f and the denominator of every beta.
- For each of the four asset cards, name the asset and enter its annualized volatility.
- Enter each asset’s correlation with the market between -1 and 1; beta is computed as rho x sigma_i / sigma_m.
- Enter your own expected return for each asset; alpha is the gap between your forecast and the CAPM prediction.
- Read the equilibrium matrix: beta, CAPM return, alpha, and Treynor ratio per asset, with mean beta and mean alpha as an aggregate check.
- Use the Security Market Line chart to see which assets plot above or below the line, and the characteristic-line and 3D plane views for the regression-style picture of the same equilibrium.
The formula
Reference: Sharpe (1964), "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk"; Lintner (1965); Mossin (1966); textbook treatment in Hull, Options, Futures, and Other Derivatives.
Worked example
Asset A: 18% volatility, 0.72 correlation with the market
- Risk-free rate 3.5%; expected market return 9.5% (market risk premium 6.0%); market volatility 17%. Asset volatility 18%, correlation with market 0.72, your expected return 11.2%.
- 1
Beta is rho x sigma_i / sigma_m = 0.72 x 0.18 / 0.17 = 0.7624, so the asset carries about three-quarters of the market’s risk. The CAPM return is 3.5% + 0.7624 x 6.0% = 8.07%. Alpha is the gap to your expected return: 11.2% - 8.07% = +3.13%. The Treynor ratio, excess return per unit of beta, is (11.2% - 3.5%) / 0.7624 = 0.1010.
Beta 0.7624; CAPM expected return 8.07%; alpha +3.13% relative to the 11.2% expected-return estimate; Treynor ratio 0.101.
Interpreting the result
If an asset plots above the Security Market Line, it offers more return than CAPM requires for its beta — positive alpha — and below the line means less. That alpha is entirely relative to your expected-return estimate and to the CAPM inputs you chose, so it scores your disagreement with the model rather than proving a mispricing. The Treynor ratio restates the same information per unit of beta and is directly comparable across assets with different betas.
Assumptions & limitations
- Single-period mean-variance equilibrium with a common risk-free lending and borrowing rate; no taxes or transaction costs.
- Beta is built from your volatility and correlation inputs rather than estimated from a return regression; the two are algebraically equivalent but only as good as the numbers you supply.
- The market portfolio is proxied by a single market volatility input, and idiosyncratic volatility is assumed to be diversified away.
- Alpha is measured relative to CAPM, so it reflects deviation from the model’s pricing, not a guaranteed arbitrage.
- All rates are simple annual figures; multi-period dynamics and changing betas are not modeled.
Frequently asked questions
What does a beta above or below 1 mean?
Beta measures how strongly an asset’s returns move with the market: a beta of 1.5 amplifies market swings by about half again, while 0.5 dampens them. Beta 1 is the market portfolio itself by construction, and beta 0 means returns are uncorrelated with the market, earning roughly the risk-free rate in equilibrium. In this calculator beta comes from rho x sigma_i / sigma_m, which is the covariance ratio rewritten.
Is a positive alpha a buying signal?
Alpha here is the gap between your expected-return estimate and the CAPM prediction, so it is conditional on both your estimate and the model. A positive alpha means the asset plots above the SML — cheap relative to CAPM pricing — but expected returns are estimates, and later research shows expected returns depend on more than market beta alone. Treat alpha as a structured way to express disagreement with the model, not as proof of mispricing.
What market risk premium should I use?
The premium E[R_m] - R_f is an assumption, not a computed output: it is the extra return investors demand for holding the market instead of the risk-free asset. Practitioners estimate it from long-run market history or imply it from current prices, and reasonable estimates differ. Whatever you choose shifts the whole Security Market Line one-for-one, so test your conclusions across a range of premiums.
Why compute beta from correlation and volatility instead of a regression?
The two routes are algebraically identical: Cov(R_i, R_m) / Var(R_m) equals rho_iM x sigma_i / sigma_m. Supplying the moments directly lets you stress-test beliefs about correlation and systematic risk without return data, which is useful for private assets or short histories where a clean regression is hard to run.
Can beta be negative?
Yes, whenever the correlation with the market is negative. A negative-beta asset has a CAPM expected return below the risk-free rate, because it acts as insurance against market declines and investors accept a lower expected return for that protection. The correlation slider goes down to -1 so you can price such hedge assets consistently.
How is this related to the cost of equity?
In equilibrium the CAPM expected return is the compensation investors require for bearing systematic risk, which makes the SML return a standard estimate of a firm’s cost of equity. That number then becomes the equity leg of a WACC in a discounted cash flow valuation. Beta, the risk-free rate, and the market premium are the three inputs that drive it.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.