Beta calculator
Beta measures how strongly an investment moves with the market. Paste the period returns of the stock and of a market index for the same dates, or their prices. The calculator fits a regression line of the stock's returns on the market's and gives the beta (its slope), the alpha (its intercept), the correlation, R², and the average and standard deviation of both series.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose whether you paste returns in percent or prices.
- Paste the stock series and the market series, oldest first, for the same periods.
- Read the beta, how to read it, and the regression details.
With market returns m and stock returns a over n periods:
- Beta = Σ(m − m̄)(a − ā) ÷ Σ(m − m̄)²
- Alpha = ā − beta × m̄ (per period, in %)
- r = Σ(m − m̄)(a − ā) ÷ √(Σ(m − m̄)² × Σ(a − ā)²); R² = r²
- From prices: return = (price ÷ previous price − 1) × 100
Worked example
Six monthly returns. Stock: 2, −1, 3, 4, −2, 1.5. Market: 1.5, −0.5, 2, 3, −1.5, 1.
- Averages: stock 7.5 ÷ 6 = 1.25 %, market 5.5 ÷ 6 = 0.9167 %.
- Σ(m − m̄)(a − ā) = 19.125 and Σ(m − m̄)² = 13.7083.
- Beta = 19.125 ÷ 13.7083 = 1.3951: the stock moves more than the market.
- Alpha = 1.25 − 1.3951 × 0.9167 = −0.0289 % a month.
- Correlation 0.9964, R² 0.9928.
Tips
- Six points are enough to see how it works, not for a reliable beta; use several years of data.
- Beta changes over time and with the index you choose; quote both the period and the benchmark.
- The CAPM calculator turns a beta into an expected return.
Frequently asked questions
How is beta calculated?
Beta = covariance(stock returns, market returns) ÷ variance(market returns). It is the slope of the least-squares line through the points (market return, stock return).
What does a beta of 1.4 mean?
On average the stock moved 1.4% for each 1% move of the market in the data you entered: more than the market in both directions. A beta below 1 means smaller moves, a negative beta moves against the market.
Which data should I use?
Returns of the same periods for both series, typically 36 to 60 monthly returns or a year or two of weekly returns, and an index that fits the stock (a broad national index for a large company). Different choices give different betas.
What do alpha and R² tell me?
Alpha is the average return per period not explained by the market (the intercept of the line). R² is the share of the stock's variance the market explains; with a low R², beta says little about the stock's risk.
Prices or returns?
Either. With prices the calculator first turns each series into simple period returns, (price ÷ previous price − 1) × 100, so you get one fewer return than prices.