Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Beta measures how a stock has historically moved relative to the overall market, not a guaranteed forecast of future movement, and a beta calculated over one period, one benchmark and one set of market conditions can shift meaningfully when any of those three inputs changes.
Before you rely on it
What to check
Confirm the historical period and benchmark used are consistent and reasonably representative before trusting a beta figure for a forward-looking decision.
The common error
Where people go wrong with investment beta calculator
Treating a single historical beta value as a fixed, permanent property of a stock. It's a backward-looking statistical relationship that can and does change as market conditions and the company itself evolve.
Sensitivity evidence
How asset-market covariance changes the estimated beta
| Asset-market covariance | Estimated beta | CAPM expected return | Market risk premium contribution |
|---|---|---|---|
| 0.014 | 0.933 | 8.7% | 4.7% |
| 0.016 | 1.1 | 9.3% | 5.3% |
| 0.018worked example | 1.2 | 10.0% | 6.0% |
| 0.02 | 1.3 | 10.7% | 6.7% |
| 0.022 | 1.5 | 11.3% | 7.3% |
Every input, tested
Which input moves the estimated beta most
| Input | Tested from | To | Estimated beta at each end | Swing |
|---|---|---|---|---|
| Market return variance | 0.013 | 0.017 | 1.4 to 1.1 | 0.326 (27%) |
| Asset-market covariance | 0.016 | 0.02 | 1.1 to 1.3 | 0.267 (22%) |
| Expected market return | 7.0% | 11.0% | 1.2 to 1.2 | none |
| Risk-free rate | 3.0% | 5.0% | 1.2 to 1.2 | none |
Two variables at once
Estimated beta by asset-market covariance and market return variance
| Asset-market covariance \ Market return variance | 0.012 | 0.015 | 0.018 |
|---|---|---|---|
| 0.014 | 1.2 | 0.933 | 0.778 |
| 0.016 | 1.3 | 1.1 | 0.889 |
| 0.018 | 1.5 | 1.2 | 1 |
| 0.02 | 1.7 | 1.3 | 1.1 |
| 0.022 | 1.8 | 1.5 | 1.2 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Asset-market covariance | 0.018 |
| Market return variance | 0.015 |
| Expected market return | 9.0% |
| Risk-free rate | 4.0% |
| Estimated beta | 1.2 |
| CAPM expected return | 10.0% |
| Market risk premium contribution | 6.0% |
Where the inputs come from
Asset-market covariance and market return variance come from a regression or a data service using the same return series and period, such as five years of monthly returns. Most people take beta directly from a fund or stock page instead of computing it. Expected market return and the risk-free rate are used for the CAPM estimate. Use a Treasury yield for the risk-free rate.
When the result stops applying
Beta is measured from past returns and changes with the period and the index chosen. It captures only market risk, not the risk specific to one company. A low beta does not mean low risk, since a stock can be volatile and unrelated to the market. CAPM's expected return is a model, not a forecast.
What to compare it with
Use the alpha calculator to see whether a manager beat the CAPM expectation, and the Sharpe ratio for risk-adjusted return. The two-asset risk and correlation calculators show how holdings combine. For a portfolio, the weighted average of the holdings' betas gives the portfolio beta.
People also ask
Frequently asked questions
What does a beta of 1.2 mean?
It means the asset has historically moved about 1.2 times as much as the market: a 10% market rise has tended to come with a 12% rise, and a 10% fall with a 12% fall.
Can beta be negative?
Yes, for assets that tend to move opposite the market, such as some gold funds or inverse funds, though negative betas are rare.
Which market index should I use?
Use the one that represents the asset's market, such as the S&P 500 for US large stocks. Different indexes give different betas.