# What is the stock's beta?

Computes the beta of a stock from its returns and the market’s returns over the same periods: the slope of the regression line, with the correlation, R² and the intercept.

- Page: https://www.acalculator.org/finance/beta-calculator
- JSON spec: https://www.acalculator.org/finance/beta-calculator.json
- Version: 652b27fe7f6c

## Default answer

Example with the default inputs (Stock returns (%) [1.5, 3, −2, 4, 0.5], Market returns (%) [1, 2, −1, 3, 0]): Over these 5 periods, the stock’s beta against the market is 1.45.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| asset | Stock returns (%) | The stock’s return in each period, in percent, oldest first, separated by spaces or new lines. |
| market | Market returns (%) | The market index’s return in the same periods and the same order, in percent. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| beta | Beta (β) | The slope of the stock’s returns against the market’s: covariance ÷ market variance. |
| correlation | Correlation (r) | How closely the returns follow a straight line, from −1 to 1. |
| rSquared | R² | The share of the stock’s variance that the market explains: r². |
| intercept | Intercept (return when the market is flat) | Mean stock return − β × mean market return, in percent per period. |
| covariance | Covariance of the returns (sample) | Σ(x − x̄)(y − ȳ) ÷ (n − 1), in percent squared. |
| variance | Variance of the market returns (sample) | Σ(x − x̄)² ÷ (n − 1), in percent squared. |
| periods | Periods | How many pairs of returns. |

## Method

β = Σ(xₜ − x̄)(yₜ − ȳ) ÷ Σ(xₜ − x̄)², where xₜ are the market’s returns and yₜ the stock’s; intercept = ȳ − β × x̄; r = Σ(xₜ − x̄)(yₜ − ȳ) ÷ √(Σ(xₜ − x̄)² × Σ(yₜ − ȳ)²).

## Assumptions

- Both lists cover the same periods, in the same order, at the same frequency (for example monthly).
- Returns are typed as percents; no price or index level is looked up.
- Arithmetic is exact on the typed decimals; only the correlation uses a floating-point square root.

## Worked examples

1. asset = 1.5 or 3, market = 1 or 2 gives beta = 1.45, intercept = -0.05%, correlation = 0.984324, rSquared = 0.968894, covariance = 3.625, variance = 2.5, periods = 5. Source: OpenStax, Introductory Statistics 2e, 12.3 The Regression Equation (b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², a = ȳ − b × x̄). https://openstax.org/books/introductory-statistics-2e/pages/12-3-the-regression-equation; OpenStax, Principles of Finance, 15.3 The Capital Asset Pricing Model (CAPM) (beta measures how much a stock moves with the market: the slope of the line through its monthly returns against the market’s; Delta Air Lines 1.39). https://openstax.org/books/principles-finance/pages/15-3-the-capital-asset-pricing-model-capm.
2. asset = -2 or 4, market = -1 or 2 gives beta = 2, intercept = 0%, correlation = 1, rSquared = 1. Source: OpenStax, Principles of Finance, 15.3 The Capital Asset Pricing Model (CAPM) (beta measures how much a stock moves with the market: the slope of the line through its monthly returns against the market’s; Delta Air Lines 1.39). https://openstax.org/books/principles-finance/pages/15-3-the-capital-asset-pricing-model-capm (a beta of 2: a 10% market rise means a 20% rise in the stock); OpenStax, Introductory Statistics 2e, 12.3 The Regression Equation (b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², a = ȳ − b × x̄). https://openstax.org/books/introductory-statistics-2e/pages/12-3-the-regression-equation.
3. asset = 2 or -1, market = -2 or 2 gives beta = -0.75, intercept = 0.5%, correlation = -0.948683. Source: OpenStax, Introductory Statistics 2e, 12.3 The Regression Equation (b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², a = ȳ − b × x̄). https://openstax.org/books/introductory-statistics-2e/pages/12-3-the-regression-equation.

## FAQ

### What is beta?

Beta measures how much a stock moves with the market. A beta of 1 means it tends to move as much as the market; 2 means twice as much, so a 10% market rise goes with about a 20% rise in the stock; 0.5 means half as much.

### How do I calculate beta?

Put the market’s returns on the x axis and the stock’s on the y axis, and fit the least-squares line. Beta is its slope: β = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², which is the covariance of the two return series divided by the variance of the market’s returns.

### Which returns should I use?

Returns for the same periods and in the same order, such as several years of monthly returns against a broad index (OpenStax uses three years of monthly returns against the S&P 500). A monthly return is (this month’s price − last month’s price) ÷ last month’s price, with dividends added if you have them.

### Why do websites show different betas for the same stock?

They use different periods, return frequencies and market indexes. OpenStax found 1.39 for Delta Air Lines from 2018 to 2020 monthly returns, while two finance sites showed 1.46 and 1.29 at about the same time.

### What do the correlation and R² tell me?

How well the line fits. A correlation near 1 or −1 means the points lie close to the line; R², the correlation squared, is the share of the stock’s ups and downs that the market’s moves explain. A beta from a fit with a low R² is less reliable.

### Can beta be negative?

Yes. A negative beta means the investment tended to move against the market: up when the market fell and down when it rose.

### Is the intercept the same as alpha?

Not quite. The intercept here is the stock’s average return in a period when the market return is 0. Jensen’s alpha compares the stock’s return with what CAPM predicts from the risk-free rate, so it needs the risk-free rate as well.

## Sources

- OpenStax, Principles of Finance, 15.3 The Capital Asset Pricing Model (CAPM): beta measures how much a stock moves with the market; the slope of the line through Delta Air Lines’ monthly returns against the S&P 500 (2018–2020) is 1.39, against 1.46 and 1.29 on two finance sites; with a beta of 2, a 10% market rise means a 20% rise in the stock. https://openstax.org/books/principles-finance/pages/15-3-the-capital-asset-pricing-model-capm (retrieved 2026-10-18)
- OpenStax, Principles of Finance, 15.5 Using Excel to Make Investment Decisions: monthly return = (this month’s price − last month’s price) ÷ last month’s price; beta as the slope of the best-fit line (Amazon 1.1477). https://openstax.org/books/principles-finance/pages/15-5-using-excel-to-make-investment-decisions (retrieved 2026-10-18)
- OpenStax, Introductory Statistics 2e, 12.3 The Regression Equation: slope b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², intercept a = ȳ − b × x̄, and the correlation coefficient r. https://openstax.org/books/introductory-statistics-2e/pages/12-3-the-regression-equation (retrieved 2026-10-18)