Stock Beta Calculator (from stock and market returns: beta, correlation, R²)

Understanding the stock beta calculator — concept and principle

This calculator estimates a stock's beta from matching lists of stock and market returns, together with correlation, R², alpha, both volatilities and a plain-language reading. Use it for portfolio risk analysis, the capital asset pricing model (CAPM), finance courses and comparing how sensitive stocks are to market moves.

How it is calculated

• Beta β = covariance(stock, market) ÷ variance(market), the slope of the regression of stock returns on market returns.
• Correlation ρ measures how closely the points follow a line; R² = ρ².
• Alpha = mean stock return − β × mean market return (the intercept).
• Volatility = standard deviation of returns per period.

Both lists must cover the same periods, for example 36 to 60 monthly returns.

The principle

Beta asks: when the market moves 1%, how much does this stock tend to move? Covariance captures how the two move together, and dividing by the market's variance scales it into a slope. Beta 1 means the stock moves in line with the market; above 1, more; below 1, less; negative, opposite. In CAPM, beta is the measure of risk that cannot be removed by diversification, so it drives the expected return. R² tells you how much of the stock's movement is explained by the market; the rest is company-specific.

Worked example

Default inputs: 12 monthly returns for the stock and the index (made-up example data).

1. Stock volatility ≈ 2.46% per period; market volatility ≈ 1.71%.
2. Correlation ≈ 0.994, so R² ≈ 98.8%.
3. β = ρ × (σ_stock ÷ σ_market) = 0.994 × (2.46 ÷ 1.71) ≈ 1.43.
4. Alpha ≈ −0.09% per period.
5. Reading: moves more than the market.

How to read the result

A beta of 1.43 means the stock has tended to rise about 1.43% when the index rose 1% and fall about 1.43% when it fell 1%. A high R² makes beta a reliable summary; a low R² means beta explains little and other factors dominate. Alpha is the average return not explained by the market over the sample; it is noisy and not a forecast.

Common mistakes

• Using price levels instead of returns.
• Mixing periods, such as daily stock returns with monthly market returns.
• Relying on very few data points, which makes beta unstable.
• Treating beta as fixed; it changes with the period and the index chosen.

Frequently asked questions

What does a beta of 1 mean?

The stock has tended to move one for one with the benchmark index.

Can beta be negative?

Yes, if the stock tends to move opposite to the market, as some hedging assets do.

How much data should I use?

Common practice is 36 to 60 monthly returns, or one to two years of weekly returns.

Sources: OpenStax, Principles of Finance 2e, §14.4 Regression Applications in Finance