Beta Estimation

What it does

Estimates beta against a benchmark across the sample or a rolling window.

Use it to measure sensitivity to the market.

Data you need

• Asset returns
• Market returns

Optional: Rolling window

Supported data: Numeric. Level: Beginner.

Formula and method

β = Cov(rᵢ, rm) / Var(rm)

The slope of excess asset returns on excess market returns gives beta, and a test compares it with one. A rolling estimate repeats Cov/Var over a moving window to show how sensitivity has changed.

How to read the result

A rolling beta shows whether sensitivity has changed.

Worked example

Illustrative run on Simulated weekly returns (teaching data, not market data). These figures are the actual output of this model on that example, and they say nothing about your own data.

• Beta = 1.2984 (s.e. 0.0708).
• The difference between beta and one is statistically significant at the 5% level.

Limitations

• Depends on benchmark, window and frequency
• Educational use, not investment advice

Numerical validation

Validated 16 of 16 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.

Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.

Questions

Why do beta estimates differ between websites?

They use different benchmarks, windows and return frequencies.