Beta Calculator
A stock's beta from its returns and the market's (covariance ÷ market variance), with the correlation and R², or a portfolio's beta as the weighted average of its holdings' betas.
Result…
How it's calculated
β = cov(stock, market) ÷ var(market) r = cov ÷ (σ stock × σ market), R² = r² Alpha = mean stock − β × mean market Portfolio β = Σ wᵢ βᵢ ÷ Σ wᵢ
Beta measures how much a stock has moved with the market. It is the covariance of the stock's returns with the market's returns divided by the variance of the market's returns, which is the same as the slope of a straight line fitted through the pairs of returns. A beta of 1 moves with the market, above 1 swings more, below 1 swings less, and a negative beta tends to move the other way. The correlation r and R² show how closely the points follow that line. A portfolio's beta is the weighted average of its holdings' betas. Published betas differ between data providers because they use different periods, intervals and indexes. This is an educational tool, not financial advice.
Your numbers, step by step
About the Beta calculator
This beta calculator measures how strongly a stock or fund has moved with the market. Paste its periodic returns and a market index's returns for the same periods, and it works out beta as the covariance of the two divided by the market's variance, with the correlation r, R², the covariance, the market variance and the alpha (intercept) per period. A second mode finds a portfolio's beta as the weighted average of its holdings' betas, from lines like “Fund A, 40, 1.2”, where the weights can be percentages or amounts invested. It suits students learning the capital asset pricing model, investors comparing how jumpy their holdings have been, and anyone checking a published beta against their own data. Every step is shown with your numbers. It describes past behaviour only and is not financial advice.
How to use it
- Choose what to “Find”: “Beta from returns” or “Portfolio beta”.
- For a stock, paste the “Stock returns (%)” and the “Market returns (%)” for the same periods, oldest first, one pair per period.
- For a portfolio, list the “Holdings, one per line: name, weight, beta”.
- Read the beta, then check R²: the closer it is to 1, the more the beta tells you.
Worked example
Twelve monthly returns for a stock (2.1, −1.4, 3.5 … 0.4%) against an index (1.5, −0.8, 2.2 … 0.3%) give a covariance of 3.324 and a market variance of 2.229, so β = 3.324 ÷ 2.229 = 1.491. The correlation is 0.9968 and R² is 0.9935, so the market explains almost all of the stock's moves in this sample. For a portfolio of 40% at beta 1.2, 35% at 0.9 and 25% at 0.2, the beta is 0.4 × 1.2 + 0.35 × 0.9 + 0.25 × 0.2 = 0.845.
Updated
Questions people ask
How do I calculate the beta of a stock from its returns?
Work out the covariance between the stock's returns and the market's returns, then divide by the variance of the market's returns. That equals the slope of a straight line fitted through the pairs of returns.
What does a beta of 1.5 mean?
The stock has tended to move about 1.5% for every 1% move in the market, up or down. A beta below 1 means smaller swings than the market, and a negative beta means it has tended to move the other way.
Why is my beta different from the one on a finance website?
Beta depends on the period, the return interval (daily, weekly or monthly) and the index chosen, and providers make different choices. Using the same returns as the provider should give the same answer.
How is a portfolio beta calculated?
Multiply each holding's beta by its share of the portfolio and add them up. This calculator scales the weights so they add up to 100%, so you can enter amounts invested instead of percentages.
Is a high R² needed for beta to be useful?
A low R² means the market explains little of the stock's moves, so the beta is a weak summary of its risk. Look at the correlation coefficient calculator or the Sharpe ratio calculator for other views of the same returns.
Can beta tell me what a stock will do next?
No. It describes how the stock behaved over the period you entered, and that can change. For decisions about your own money, speak to a qualified financial adviser.