Stock Beta Calculator
Calculate a stock's beta coefficient from its correlation with the market, stock standard deviation, and market standard deviation to measure systematic risk.
How to use this tool
- Enter correlation with market (r), stock standard deviation (%) and market standard deviation (%) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your beta (β) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
β = r × (σstock / σmarket)
Equivalently: β = Cov(Rstock, Rmarket) / Var(Rmarket)
where r is the Pearson correlation, σstock is the stock return standard deviation, and σmarket is the market return standard deviation.
How it works
Beta measures a stock's sensitivity to movements in a benchmark market index (typically the S&P 500). A beta of 1.0 means the stock historically moves in line with the market; above 1.0 indicates greater volatility; below 1.0 indicates less volatility; and a negative beta means the stock tends to move opposite to the market.
The formula used here, β = r × (σstock / σmarket), is algebraically equivalent to the covariance-over-variance formula and requires only the correlation coefficient and both standard deviations as inputs. All standard deviations should be measured over the same historical period (commonly 36 to 60 months of monthly returns).
Worked example
Calculate Beta from Correlation and Standard Deviations
- Stock correlation with market: r = 0.8.
- Stock standard deviation: σstock = 20%.
- Market standard deviation: σmarket = 15%.
- Beta = 0.8 × (20 / 15) = 0.8 × 1.3333 = 1.0667.
Beta = 1.0667, indicating the stock is about 6.67% more volatile than the market.
Common mistakes to avoid
- Using a benchmark index that does not match the stock market (e.g., using a bond index for a tech stock), producing a meaningless beta.
- Calculating beta from too short a return history (e.g., 30 days), which is dominated by noise and produces an unstable estimate.
- Interpreting beta as a standalone risk measure — beta only captures systematic (market) risk; idiosyncratic company risk is not reflected.
Key terms
- Beta (β)
- A measure of a stock's systematic risk relative to the market; beta > 1 means more volatile than the market, beta < 1 means less volatile.
- Correlation (r)
- A statistical measure of the linear relationship between two variables, ranging from -1 (perfect inverse) to +1 (perfect positive).
- Standard Deviation (σ)
- A measure of the dispersion of returns around the mean; higher values indicate greater historical volatility.
- Systematic Risk
- Market-wide risk that cannot be eliminated through diversification, captured by the beta coefficient.
- CAPM
- Capital Asset Pricing Model — a framework that uses beta to relate expected return to systematic risk: E(R) = Rf + β(Rm − Rf).
Frequently asked questions
- What does a beta of 1.5 mean?
- The stock is expected to move 1.5% for every 1% move in the market index. It amplifies both gains and losses relative to the benchmark.
- What does a negative beta mean?
- The stock tends to move in the opposite direction to the market. Gold miners and some utility stocks sometimes exhibit negative betas during market sell-offs.
- How long a return history should I use to calculate beta?
- A common practice is 5 years of monthly returns, or 2 years of weekly returns. Shorter windows capture recent sensitivity but are noisier; longer windows may mix different business conditions.