Correlation and Beta Calculator
Free correlation and beta calculator. Paste two lists of returns to get correlation, beta, alpha per period and R squared for a stock, fund or strategy.
How closely does a stock follow the market? How much would a 1% market move change your portfolio? Would adding this asset diversify you or just add more of the same risk? Correlation and beta answer these questions. Correlation measures how consistently two series move together, from minus 1 to plus 1. Beta measures how much one moves for each 1% move in the other. Paste matching lists of returns for a benchmark and an asset, and this calculator gives correlation, beta, alpha and R squared.
Calculator#
- Calculator
- Turn on JavaScript to use it, or use the formula below
How it works#
Correlation = Covariance(asset, benchmark) / (SD(asset) × SD(benchmark))
Beta = Covariance(asset, benchmark) / Variance(benchmark)
Alpha per period = Mean asset return - Beta × Mean benchmark return
R squared = Correlation²Alpha here is a simple regression intercept without subtracting a risk free rate, so treat it as a rough figure. If the lists differ in length, only the matching pairs from the start are used. See Covariance and Correlation and Alpha and Beta.
Reading correlation#
| Correlation | Meaning |
|---|---|
| 0.8 to 1.0 | Move together strongly; little diversification |
| 0.3 to 0.8 | Moderate relationship |
| minus 0.3 to 0.3 | Weak or no linear relationship; good diversifier |
| Below minus 0.3 | Tend to move in opposite directions; natural hedge |
Reading beta#
| Beta | Meaning |
|---|---|
| Above 1 | Amplifies the benchmark's moves |
| About 1 | Moves like the benchmark |
| 0 to 1 | Dampened moves |
| About 0 | Little market sensitivity |
| Negative | Tends to move opposite |
Beta and correlation are related but different. A stock can have low correlation but high beta if it is very volatile, or high correlation but low beta if it is calm. See R-Squared.
Getting good results#
- Use returns, not prices; prices trend and produce misleading correlations. See Stationarity, Differencing and Unit Roots.
- Match the periods exactly: same dates, same order.
- Use enough data: at least 30 observations, ideally more, such as two to five years of weekly or monthly returns.
- Choose the right benchmark: a technology stock against a technology index, a small company against a small cap index.
- Check stability: correlations and betas change, and they often rise in crises. See Correlation Management.
Uses#
| Use | How |
|---|---|
| Diversification | Add assets with low correlation to your portfolio. See Diversification |
| Hedging | Use beta to size an index hedge |
| Position sizing | Size correlated positions smaller. See Correlation-Adjusted Sizing |
| Performance review | Check whether returns are just market exposure. See Information Ratio and Tracking Error |
Where to find return data#
Download daily, weekly or monthly closing prices for both series from your charting platform or a data provider, then convert them to percentage changes over the same dates before pasting them in.
Frequently asked questions#
What is the difference between correlation and beta?#
Correlation measures how consistently two series move together; beta measures how large one series' moves are relative to the other's.
How many data points do I need for beta?#
At least about 30 is a reasonable minimum, and more gives more reliable estimates, though very old data may no longer be relevant.
Can correlation change over time?#
Yes. Correlations shift with market conditions and often rise sharply during crises.
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3 quick questions on this lesson. Get them all right to finish it.
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