What Is Beta in Stocks? How Beta Measures Market Sensitivity, With a Worked Example

Beta measures how far an asset's returns have tended to move with a benchmark such as the S&P 500: a beta of 1 means one for one, above 1 more, below 1 less.

Many stock quote pages show a beta next to the price, usually without saying how it was measured. This page covers what beta measures, how it is calculated, a worked example done by hand, why beta is not the same thing as volatility, the choices that change a beta, and where Kresmion computes it. It is descriptive throughout.

The idea in one paragraph

Beta comes from the Capital Asset Pricing Model. William Sharpe's 1964 paper was one of several formulations of the model developed independently in the mid-1960s, and the model is one of the contributions for which he shared the 1990 Nobel Prize in Economic Sciences. In the committee's words, a share's beta value indicates its marginal contribution to the risk of the entire market portfolio: a beta above 1 adds more than an average share to that risk, a beta below 1 less. In everyday use it answers one question. When the benchmark has moved, how far has this asset tended to move with it, on average?

How beta is calculated

Beta is the slope of a straight line fitted through pairs of returns: the asset's return on the vertical axis, the benchmark's return on the horizontal one, one point per period. The formula for that slope is:

Beta = covariance of the asset's returns with the benchmark's returns / variance of the benchmark's returns

An equivalent form is often easier to read: beta equals the correlation between the two return series times the asset's volatility divided by the benchmark's volatility. Both pieces matter. An asset with high volatility but little correlation to the market can have a low beta, and an asset that tracks the market closely but swings twice as hard has a beta near 2.

Beta is computed on returns, not prices. Fitting price levels instead gives a slope between two trending series, which can look strong even when their period-to-period moves are unrelated.

A worked example

Take five months of hypothetical returns, in percent, for a benchmark and one stock.

Both columns average exactly zero, which keeps the arithmetic short.

Step 1, covariance. With zero averages, the covariance is the sum of the products divided by the number of months minus one: (6 + 12 + 3 + 20 + 28) / 4 = 69 / 4 = 17.25.

Step 2, variance of the benchmark. The sum of its squared returns divided by four: (4 + 9 + 1 + 16 + 16) / 4 = 46 / 4 = 11.5.

Step 3, beta. 17.25 / 11.5 = 1.5. Over these five months the stock moved, on average, one and a half times as far as the benchmark, in the same direction.

Check with the second form. The correlation between the two columns is 0.98, the stock's standard deviation is 5.20 points and the benchmark's 3.39 points. 0.98 x 5.20 / 3.39 = 1.50, the same answer.

The fit is not perfect: in month 3 the benchmark rose 1 point, a beta of 1.5 implies 1.5 points, and the stock rose 3. The gap between the line and each actual return is the part of the stock's movement that beta does not explain.

Beta is not volatility

Beta measures sensitivity to one benchmark, not how much an asset swings in total. Two hypothetical cases with the same benchmark volatility of 15 percent show the difference:

Both swing equally hard. Asset A tracks the market enough to carry a beta of 1.2. Asset B's swings are mostly its own, so its beta is 0.2 even though it is twice as volatile as the benchmark. A low beta can mean a calm asset, or a volatile one that moves to its own drivers. The share of an asset's variance that the benchmark explains is the correlation squared, called R squared: 0.36 for A, 0.01 for B. Risk the benchmark does not explain is the part that diversification dilutes.

What changes a beta

The same stock can show several betas, because the number depends on choices made before the calculation.

• The benchmark. Beta against the S&P 500 and beta against the Nasdaq-100 are different facts about the same stock. For a crypto asset, beta against Bitcoin and beta against an equity index are different again.
• The window. A beta measured over one calm year can differ widely from one measured over a period that includes a crash. A rolling beta, recomputed over a moving window, shows how much it drifts.
• The return frequency. Daily, weekly and monthly returns give different estimates, partly because thinly traded assets react to market moves with a delay.
• The sign. A negative beta means the asset has tended to move opposite the benchmark over the window measured.

A benchmark's beta against itself is exactly 1 by construction, which is why 1 is the reference point.

Where Kresmion computes beta

In Kresmion's signed-in charting workspace, Compare mode includes a "Beta vs benchmark" study. You pick two symbols, the asset and the benchmark, and the study reports the full-period beta, a rolling beta over an adjustable window (90 bars by default), the correlation, R squared and the number of return pairs used. Its built-in guide notes that beta against Bitcoin and beta against the S&P 500 are different facts about the same asset, and that a beta is an average over the window that hides the tails. The same signed-in account's portfolio analytics show the beta of a whole portfolio against SPY, QQQ, ACWI, BTC or a 60/40 mix of SPY and AGG, once there are at least 20 daily returns to work with.

Honest limitations

Beta is a historical average over a chosen window. It says how an asset has moved with a benchmark, not how it will move, and it can change quickly when a company's business, debt or investor base changes. It is a single straight-line slope, so it hides asymmetry: an asset can track the market closely on falling days and loosely on rising ones. A low R squared means the beta explains little of the asset's movement, and the beta itself is then a noisy estimate. The examples on this page are hypothetical returns, not data for any real security.

Key takeaways

Frequently asked questions

Is a high beta good or bad?

Neither. Beta describes sensitivity to a benchmark over a past window. A beta of 1.5 means the asset has tended to amplify the benchmark's moves in both directions, and whether that suits a portfolio is a separate question that beta does not answer.

Can beta be negative?

Yes. A negative beta means that over the window measured the asset tended to move opposite the benchmark. Such relationships are uncommon among individual stocks and can change sign from one window to the next.

What is the difference between beta and alpha?

Beta is the slope of the fitted line: how far the asset moved per unit of benchmark move. Alpha is the intercept: the average return left over after the beta-scaled benchmark return is taken out. The version usually quoted, Jensen's alpha, runs the same regression on returns minus a risk-free rate. Both numbers are historical.

Why do websites show different betas for the same stock?

Because they make different choices: the benchmark, the length of the window, and whether returns are daily, weekly or monthly. Two correctly calculated betas for one stock can differ for these reasons alone.

Does beta predict how a stock will move?

No. Beta summarises how returns have lined up with a benchmark in the past. It does not forecast the benchmark, and the relationship it measures can shift.

This page is information, not investment advice.

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Source: The Royal Swedish Academy of Sciences, press release for the 1990 Prize in Economic Sciences (Markowitz, Miller, Sharpe), https://www.nobelprize.org/prizes/economic-sciences/1990/press-release/ ; William F. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance (1964) ; beta, covariance, correlation and R squared computed by Kresmion for hypothetical return series ; Kresmion charting workspace (Beta vs benchmark study) and portfolio analytics.

Kresmion Research.