Calculate stock beta from return data series with regression analysis, R-squared, and systematic risk interpretation.
Beta Calculator estimates a stock's beta by regressing its periodic returns against a market benchmark's returns, using ordinary least squares. It reports the beta coefficient, R-squared, and a confidence interval, plus an interpretation of the stock's systematic risk relative to the market. The surprise most users encounter: beta is computed from returns, not from prices, and the choice of benchmark and return frequency materially changes the result. A one-month daily beta can differ from a five-year weekly beta. The tool also warns that past beta does not guarantee future behavior.
A concrete input and expected output from the current implementation.
Input
Stock returns: 1%, 2%, -1%, 3%, 0%; Market returns: 0.5%, 1%, -0.5%, 1.5%, 0.2%
Expected output
Beta: 2.06 (SE 0.13), R-squared: 0.988, Correlation: 0.994, p-value: 0.001, 95% CI: [1.64, 2.48]. Interpretation: High systematic risk, beta > 1.
Using ordinary least squares on the paired returns, the regression slope is 2.06, so a 1% market move is historically associated with a ~2.06% stock move. R-squared 0.988 means about 99% of the stock's variance is explained by the market.
If you paste price series, the tool converts them to returns first, typically using the formula return = (P_t / P_prev - 1) * 100 for each period. This is essential because beta measures the sensitivity of returns, not prices. The tool aligns the two series by date, dropping any mismatched entries.
The tool runs a simple linear regression with market returns as the independent variable and stock returns as the dependent variable. The slope is beta, and the intercept is alpha. It calculates R-squared as the square of the Pearson correlation, plus a standard error and 95% confidence interval based on the residual variance.
Both work. If you paste prices, the tool computes returns internally. But if you paste returns directly, make sure they are in percent form and aligned with the market returns by period. Mismatched dates or extra rows will be dropped, which can bias your beta if not careful.
It means only 50% of the stock's return variance is explained by the market. The other half comes from stock-specific factors. So the beta is a real signal, but with substantial noise. The tool shows a confidence interval; if that interval is wide, treat the beta as an estimate, not a precise number.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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