Beta Calculator
How much an investment moves with the market, with alpha, correlation and the R² that says whether the beta means anything.
Results
What this tool does
Beta measures one thing: how much an investment amplifies the market's movements. One means it follows along; 1.5 means it exaggerates by half; below one means it moves less. It is the slope of the line you would draw through the two sets of returns. Paste the investment's returns and the market's for the same periods, and this page gives you that slope — together with alpha, the part the market does not explain, and the R², which tells you whether drawing that line was reasonable in the first place.
Formula
β = covariance(active, market) ÷ variance(market) · α = (R̄a − Rf) − β (R̄m − Rf)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
asset | The investment's returns | — |
market | The market's returns, same periods | — |
risk_free | Risk-free rate | % |
BE | Beta | — |
ST | How it moves | — |
AL | Alpha | % |
CR | Correlation with the market | — |
R2 | Of the variation the line explains | % |
CV | Covariance | — |
MV | Market variance | — |
AS | The investment's swing | % |
MS | The market's swing | % |
AM | Average return of the investment | % |
MM | Average return of the market | % |
NN | Count | — |
Worked example
- The investment's returns5.2, -3.1, 8.4, 1.6, -6.2, 11.3, 2.8, -1.4
- The market's returns, same periods3.1, -2.0, 5.5, 1.2, -4.1, 7.2, 2.0, -0.8
- Risk-free rate0 %
- Beta1.5536
- How it movesSwings more than the market
- Alpha-0.0248 %
- Correlation with the market0.9992
- Of the variation the line explains99.84 %
- Covariance22.2582
- Market variance14.3270
- The investment's swing5.8853 %
- The market's swing3.7851 %
- Average return of the investment2.3250 %
- Average return of the market1.5125 %
- Count8
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- Standard deviation and variance are calculated for a sample (dividing by n − 1). For a full population, divide by n instead.
Frequently asked questions
What does a beta of 1.3 actually mean?
That over the period you measured, when the market moved one per cent this investment tended to move about 1.3 — up and down alike. It is a measure of how much it amplifies the market, not of how good it is. A beta above one is not riskier in every sense, only more exposed to the one risk you cannot diversify away; a beta below one moves less but may still swing wildly on news of its own. That second kind of movement shows up in the R² figure, not in beta.
Why does the R² matter as much as the beta?
Because beta is the slope of a line, and a slope means little if the points are nowhere near the line. The R² says what share of this investment's movement the market explains at all. At 80 per cent, beta is describing something real. At 15 per cent, the investment is mostly doing its own thing and the beta is a number fitted to noise — technically correct, practically empty. Look at the two together or not at all.
What does alpha add?
It is what is left over: the return this investment made beyond what its beta alone would have predicted. A positive alpha means it beat the market after adjusting for how much market risk it took. Two cautions. Over short periods alpha is mostly luck, and it takes years of data before it means anything. And it is measured against whatever you called the market — pick the wrong benchmark and the alpha is just the difference between two indices wearing a Greek letter.