How to use the beta calculator
The calculator has two tools.
From returns estimates a stock’s beta from data:
- Paste the stock’s returns in percent, oldest first, one per line or separated by commas. You can also paste a fund’s or your own portfolio’s returns.
- Paste the market’s returns for exactly the same periods. For US stocks the usual benchmark is the S&P 500. The two lists must have the same length.
- Choose the frequency of the returns. It sets how volatility and alpha are annualized; beta itself does not depend on it.
Monthly returns over three to five years are the most common choice: 36 to 60 pairs. The example uses 24 months so it fits on screen.
Portfolio beta combines holdings you already know the beta of:
- List each holding with its market value and its beta. Stock pages and fund factsheets show beta; cash has a beta of 0.
- Enter a market move to test, such as −10 for a 10% fall.
The beta formula
Correlation ρ = Cov(Rs, Rm) ÷ (σs × σm)
R² = ρ²
α = mean(Rs) − β × mean(Rm)Rs and Rm are the stock's and the market's returns for the same periods, σ their standard deviations. β is the slope and α the intercept of the regression line Rs = α + β × Rm.
Beta can also be written as β = ρ × σs ÷ σm. That form shows where beta comes from: a stock has a high beta either because it is volatile or because it tracks the market closely, or both.
For a portfolio, beta is simply the weighted average:
A worked example
A single stock. Over 24 months, a large-cap growth stock had annualized volatility of 25.38%, against 14.25% for the market. The two moved together closely, with a correlation of 0.87. The beta is 1.54: in a month when the market rose or fell 10%, the stock typically moved about 15.4%.
The market explains 75% of the stock’s ups and downs (R²). The remaining stock-specific volatility, 12.72% a year, comes from company news rather than the market.
A portfolio. Five holdings worth $100,000.00 mix a tech stock (beta 1.3), a bank (1.1), a utility (0.45), an index fund (1.0) and a bond fund (0.1). The portfolio beta is 0.92. If the market fell 10%, the portfolio would be expected to fall about 9.23%, or $9,225.
How to read beta
| Beta | What it means | Typical examples |
|---|---|---|
| Below 0 | Tends to move against the market | Some gold miners at times, inverse funds |
| 0 to 0.5 | Little connection to the market | Cash, short-term bonds, some utilities |
| 0.5 to 0.9 | Defensive: smaller swings than the market | Consumer staples, healthcare, utilities |
| About 1 | Moves with the market | Broad index funds, many large companies |
| 1.1 to 1.5 | Aggressive: amplifies market moves | Technology, banks, consumer discretionary |
| Above 1.5 | Highly sensitive | Small growth stocks, leveraged funds |
The examples are general tendencies, not fixed rules: a company’s beta changes as its business and balance sheet change, and sector betas shift between market cycles.
Check R² before trusting beta. Beta is the slope of a line through the return pairs, and R² says how tightly the points sit around that line. With an R² of 75%, as in the example, the market drives most of the stock’s moves and beta is a useful summary. With an R² of 10% or 20%, the stock mostly moves on its own news; its beta can be low even when the stock is very volatile, and beta says little about its total risk.
Beta is an estimate. The calculator shows a 95% confidence range for beta, here 1.17 to 1.91. Even with a strong relationship, two years of data leave a wide range. Longer histories narrow it, but also mix in older periods when the company may have been a different business.
Using portfolio beta
Portfolio beta turns a market scenario into money. With the example portfolio:
| Market move | Expected portfolio move | In dollars |
|---|---|---|
| +10% | +9.23% | $9,225 |
| −10% | -9.23% | -$9,225 |
| −30% | -27.68% | -$27,675 |
The portfolio has market-equivalent exposure of $92,250: it behaves roughly like that amount in an index fund plus cash. To lower the beta you can add low-beta holdings or cash, or hedge with index futures or put options; to raise it, add higher-beta stocks. Our hedge ratio and market-neutral portfolio calculators size those trades.
The contribution column in the table shows which holdings drive the portfolio’s market risk. A position can be modest in size but dominate the beta if its own beta is high.
Beta, alpha and the intercept
The alpha in the results is the intercept of the regression on raw returns: the average return per period that the market’s movement does not explain. In the example it is +0.30% a month. That figure is a first look, not Jensen’s alpha, which subtracts the risk-free rate from both return series first. Our alpha calculator does that properly and tests whether the alpha is statistically meaningful.
What this calculator does not include
- Future behavior. Beta is measured from the past. Companies change, and betas drift over time.
- Non-market risk. A low beta does not mean low risk. A biotech stock can have a beta near 0.5 and still halve in a day on trial results.
- Asymmetry. Beta treats up and down markets the same. Some stocks fall more in sell-offs than they rise in rallies.
- Adjusted beta. Some providers shrink raw beta toward 1 (for example 0.67 × raw beta + 0.33). This calculator shows the raw figure.
- Holding betas in the portfolio tab are taken as given; if they were measured against different benchmarks or periods, the weighted result mixes them.