Beta measures how strongly an investment has moved with a benchmark index, usually the S&P 500 for US stocks. It is the average percentage move the investment made for each 1% move in the benchmark over a chosen stretch of past returns. A beta of 1 means it rose and fell in step with the index, 1.5 means it tended to move half again as far, 0.5 half as far, and a negative figure means it tended to go the other way. Beta counts only the part of an investment's swings that it shared with the market, which asset pricing theory calls systematic risk: the kind that owning more stocks cannot diversify away. The stocks hub covers the wider basics of owning shares and funds.
What is the formula for beta?
Beta equals the covariance between the investment's returns and the benchmark's returns, divided by the variance of the benchmark's returns over the same periods.
Covariance asks whether the two sets of returns tend to sit above or below their own averages at the same time, and by how much. Variance is the benchmark's covariance with itself: the average squared distance of its returns from their mean. Dividing one by the other scales the shared movement to the benchmark's own swings, which is why the benchmark's beta is always exactly 1. On a scatter chart of the investment's returns against the market's, beta is the slope of the best-fitting straight line, known as the security characteristic line.
Three inputs change the answer: the benchmark, the return frequency and the length of the window. Nasdaq's glossary adds that the theory is stated in excess returns, the returns above a short-term money market rate. Subtracting a bill yield that barely changes from one month to the next leaves the result almost the same, so most published betas use plain returns.
How do you calculate beta step by step?
Pair the two series' returns, subtract each series' average, multiply the paired deviations, and divide their sum by the sum of the benchmark's squared deviations.
Worked example: The Nasdaq-100's beta against the S&P 500, April to September 2026
Month-end closes from FRED, the St. Louis Fed's database, give six monthly price returns for each index. The S&P 500 averaged 2.76% a month over the six months and the Nasdaq-100 4.46%. Deviations from those averages are in percentage points.
| Month, 2026 | S&P 500 | Nasdaq-100 | S&P 500 deviation | Nasdaq-100 deviation | Product | S&P 500 deviation squared |
|---|---|---|---|---|---|---|
| April | 10.42% | 15.64% | 7.66 | 11.18 | 85.64 | 58.68 |
| May | 5.15% | 10.49% | 2.39 | 6.03 | 14.41 | 5.71 |
| June | −1.06% | −0.19% | −3.82 | −4.65 | 17.76 | 14.59 |
| July | −0.13% | −6.61% | −2.89 | −11.07 | 31.99 | 8.35 |
| August | 2.62% | 4.18% | −0.14 | −0.28 | 0.04 | 0.02 |
| September | −0.45% | 3.23% | −3.21 | −1.23 | 3.95 | 10.30 |
| Sum | 153.79 | 97.65 |
- Covariance: 153.79 ÷ 5 = 30.76, dividing by one less than the number of months, as sample statistics do
- Variance of the S&P 500: 97.65 ÷ 5 = 19.53
- Beta: 30.76 ÷ 19.53 = 1.57
Over those six months the Nasdaq-100 moved about 1.57% for each 1% move in the S&P 500, on average. The average hides single months: in July the S&P 500 slipped 0.13% while the Nasdaq-100 fell 6.61%, a gap that beta leaves unexplained. The correlation between the two series was 0.89, so R-squared, the share of the Nasdaq-100's variation that lined up with the S&P 500's, was about 0.79. Running the same steps over the 12 months from October 2025 to September 2026 gives 1.49, even though the two indexes share many of the same companies. Both FRED series are price indexes without dividends, which barely moves a beta because dividends arrive in small, steady amounts. Six returns keep the arithmetic visible; published betas use 36 or more. The guides to the S&P 500 and the Nasdaq-100 explain how each index is built.
What does a beta above or below 1 mean?
Above 1, an investment has tended to amplify the benchmark's moves; between 0 and 1, to soften them; below 0, to move against the benchmark.
| Beta | What it has meant | Average move when the benchmark fell 10% |
|---|---|---|
| 2.0 | Twice the market's moves, up and down | About −20% |
| 1.5 | Half again as large as the market's | About −15% |
| 1.0 | In step with the market | About −10% |
| 0.5 | Half the size of the market's moves | About −5% |
| 0 | No consistent link to the market | No systematic move |
| −0.5 | Against the market, at half the size | About +5% |
The last column is an average relationship, not a forecast, and it leaves out each company's own news, which can carry the actual move far from the line. FINRA notes that growth stocks generally carry higher betas than value stocks, which are priced lower relative to their earnings and react less to the market; growth vs value investing compares the two styles.
Fund documents show the range in practice. Vanguard prints beta and R-squared on its quarterly fund profiles, calculated from 36 months of fund returns against both the fund's own index and a broad US market index.
| Vanguard ETF, September 30, 2026 | Beta vs a broad US index | R-squared | Three-year standard deviation |
|---|---|---|---|
| Information Technology ETF (VGT) | 1.43 | 0.73 | 21.61% |
| S&P 500 ETF (VOO) | 0.96 | 0.99 | 12.43% |
| Utilities ETF (VPU) | 0.36 | 0.10 | 14.77% |
The broad index is the MSCI US Investable Market 2500 for the two sector funds and a Dow Jones total US stock market index for the S&P 500 fund. The utilities row is the instructive one. Its beta of 0.36 says the fund moved about a third as much as the market on average, yet its R-squared says the market explained only about a tenth of its variation, and its standard deviation was higher than the S&P 500 fund's. In the third quarter of 2026 its index fell 12.05% while the broad market rose 1.35%, a sector-specific slide that a low beta does nothing to rule out.
Where do you see beta?
Beta appears on stock quote screens, fund fact sheets and risk pages, in cost-of-equity calculations and in studies that compare stocks with an index.
- Quote screens. Brokerage and market-data pages show a beta beside the P/E ratio and dividend yield, each from its own window and benchmark. Free quote sites commonly use 60 months of price returns against the S&P 500, while professional terminals often default to about two years of weekly returns and adjust the raw figure toward 1. How to read a stock quote explains the other fields.
- Fund documents. Fact sheets list beta with R-squared, as in the table above. A beta of 1.00 against its own index is what an index fund is built to show, as index funds explained describes.
- Required returns. The capital asset pricing model multiplies beta by the equity risk premium and adds the risk-free rate to get the return investors demand from a stock. What is the risk-free rate works that through, and alpha measures what a fund earned beyond it.
- Research. The study of the biggest stocks' volatility reports a three-year beta against SPY for five of the largest US companies, and the SPY page tracks the benchmark fund itself.
- Portfolio statistics. A portfolio's beta is the weighted average of its holdings' betas, as long as each was measured against the same benchmark.
Worked example: Beta of a two-fund mix
Take the two sector funds from the table, both measured against the same broad index over the same 36 months.
- 60% in the technology fund: 0.60 × 1.43 = 0.858
- 40% in the utilities fund: 0.40 × 0.36 = 0.144
- Portfolio beta: 0.858 + 0.144 = 1.00
The mix carries the market's beta while holding only two sectors, so its returns could still stray far from the market's. A beta of 1 describes sensitivity, not diversification.
How is beta different from volatility, correlation and alpha?
Beta measures sensitivity to a benchmark; standard deviation measures total swings; correlation measures how consistently two investments move together; alpha measures the return beta does not account for.
| Measure | Question it answers | Range | Needs a benchmark? |
|---|---|---|---|
| Beta | How far has it moved for each 1% move in the market? | Any value; the benchmark is 1 | Yes |
| Standard deviation | How widely have its returns swung around their average? | Zero or more | No |
| Correlation | How consistently has it moved in the same direction as the market? | −1 to 1 | Yes |
| R-squared | What share of its variation lined up with the market's? | 0 to 1 | Yes |
| Alpha | How much did it earn above or below what its beta implied? | Any value; 0 means as expected | Yes |
The measures connect. Beta equals the correlation multiplied by the investment's standard deviation and divided by the benchmark's, so a weak correlation can produce a low beta even for an investment that swings hard, which is the utilities fund's story. The standard deviation entry covers that statistic on its own. Risk-adjusted scores build on both: the Sharpe ratio divides return above Treasury bills by standard deviation, while the Treynor ratio divides the same excess return by beta.
What are the limits of beta?
Beta is a backward-looking average that shifts with the window, the data frequency and the benchmark, and it says nothing about risks the market does not share.
- Reading it as total risk. Nasdaq's glossary calls beta a measure of co-movement rather than volatility and notes that a security can have a beta of zero yet swing more than the market. The utilities fund above, with a beta of 0.36 and wider swings than the S&P 500 fund, comes close.
- Ignoring R-squared. A beta backed by an R-squared of 0.10 describes a loose relationship. The higher the R-squared, the more of the investment's movement the beta actually explains.
- Comparing betas built differently. Vanguard's S&P 500 fund shows 1.00 against the S&P 500 but 0.96 against a total-market index, and the Nasdaq-100 example gave 1.57 or 1.49 depending on the window. Check the benchmark, frequency and period before comparing two figures.
- Treating it as fixed. Betas drift as businesses, debts and markets change, and Nasdaq's glossary warns they can be larger in falling markets than in rising ones and biased for securities that trade infrequently. A 2024 study of 53 stock markets in the Critical Finance Review found that the five-year monthly betas common on free quote sites did a poor job of predicting the betas stocks went on to show.
- Expecting a leveraged fund to deliver its multiple. A fund built to return twice an index each day shows a beta near 2 on daily data, but the SEC warns that its return over weeks, months or years can differ significantly from twice the index's. If an index rises 10% and then falls 10%, it ends down 1%; the daily 2x fund ends at 1.20 × 0.80 = 0.96, down 4% rather than 2%.
How much market sensitivity a portfolio carries is an allocation choice rather than a property of any one holding; asset allocation by age and types of investment risk set out those trade-offs.