Beta is the number that tells you how much a stock tends to move when the whole market moves. A stock with a beta of 1.0 rises and falls about in line with the S&P 500. A beta of 1.5 swings 50% harder, and a beta below 1.0 is calmer than the market. This calculator estimates that sensitivity coefficient from three inputs — the correlation between the stock and the market, and each one's volatility — so you can size risk before you buy.
Note what beta is and what it is not. Beta is a sensitivity coefficient, the slope of the line that describes a stock's movement relative to the benchmark. It is not a projected or expected return on its own. Expected return comes from the full CAPM equation that adds the risk-free rate and the market risk premium; beta is only the dial that scales how much of the market's risk you are actually taking.
How to Use
- Enter the Stock–Market Correlation — how closely the stock and the benchmark move together. It ranges from -1 (moves exactly opposite) through 0 (no relationship) to +1 (moves in lockstep). A broad-market US stock typically sits between 0.5 and 0.8.
- Type the Stock Volatility — the annualized standard deviation of the stock's returns, in percent. Utility and consumer-staple stocks run near 15%; high-growth or energy names can be 30% or more.
- Enter the Market Volatility — the annualized standard deviation of your benchmark, usually the S&P 500, also in percent. Over long periods this is roughly 15–18%.
- Optionally add your Portfolio Value to see the expected dollar swing of the position for a 1% move in the market.
- Read the result card: the Beta Coefficient is highlighted, and underneath it the covariance and market variance show the two ingredients behind the number.
The engine computes beta the textbook way: Beta = Cov(stock, market) / Var(market). Because covariance equals correlation times the two standard deviations, that reduces to the equivalent and easier formula Beta = correlation × (stock volatility ÷ market volatility). The percentage units cancel, which is why beta is a plain, unitless number.
How to Read Your Beta
- Beta near 1.0 — the stock behaves like the market. If the S&P 500 moves 2%, expect roughly a 2% move.
- Beta above 1.0 (aggressive) — the stock amplifies the market. At 1.5, a 2% market move becomes roughly a 3% move, on the way up and down.
- Beta between 0 and 1.0 (defensive) — the stock rises and falls less than the market. Utilities, utilities, and consumer staples often sit here.
- Beta of 0 — no measured relationship to the market; the stock's moves look independent of the benchmark.
- Beta below 0 (negative) — the stock tends to move opposite the market, a rare but useful hedging characteristic.
Higher beta means more systematic risk — the risk you cannot diversify away by adding more stocks. That is the risk the market actually pays you to take.
Examples
Example 1 — A typical large-cap growth stock. Correlation 0.75, stock volatility 18% per year, market volatility 12% per year. Beta = 0.75 × (18 ÷ 12) = 1.125. This stock moves about 12.5% more than the index. With a $100,000 position, a 1% market move implies roughly a $112.50 swing.
Example 2 — A market-tracking fund. Correlation 1.0, stock volatility 12%, market volatility 12%. Beta = 1.0 × (12 ÷ 12) = 1.00. With a $250,000 holding, a 1% market move moves the position about $2,500, exactly one percent of the investment.
Example 3 — A low- or zero-correlation holding. Correlation 0.0, stock volatility 18%, market volatility 12%. Beta = 0.00. Despite being individually volatile, the stock has no measured tendency to follow the market, so it adds diversification rather than market exposure.
Example 4 — A high-risk position worth $1,000,000. Correlation 0.8, stock volatility 20%, market volatility 10%. Beta = 0.8 × (20 ÷ 10) = 1.60. A 1% move in the market implies about a $16,000 swing on the seven-figure position — a reminder that volatility and position size together drive real money risk.
The Math Behind the Number
Beta comes from regressing the stock's returns on the market's returns. The slope of that regression line is exactly the ratio of the two variances:
Beta = Cov(stock, market) / Var(market)
Expanding covariance:
Beta = ρ × σ_stock × σ_market / σ_market² = ρ × σ_stock / σ_market
This is why the three inputs on this page are sufficient. The result was cross-checked against a paired return series computed with NumPy (np.cov divided by np.var), which returns the identical value to four decimals.
FAQ
What is a good beta for a stock?
There is no single good beta — it depends on your goals. A beta near 1.0 matches the market; a beta above 1.0 offers more upside (and downside) potential; a beta below 1.0 smooths portfolio swings. Growth investors often seek betas above 1.2, while retirees may prefer defensive betas between 0.5 and 0.9.
How do I find the correlation and volatility inputs?
Most brokerage and charting platforms show a stock's beta and standard deviation directly. To estimate them yourself, pull three to five years of monthly returns for the stock and your benchmark, then compute their correlation and each one's standard deviation. Plug those three numbers into this calculator.
Is a beta of 1.5 risky?
A beta of 1.5 means the stock historically amplifies market moves by about 50%. When the market rises 5%, the stock might rise 7.5%; when it falls 5%, it might fall 7.5%. That amplifies both gains and losses, so it is considered aggressive, not necessarily dangerous on its own.
Can beta be negative?
Yes. A negative beta means the stock tends to move opposite to the market — for example, certain gold-mining shares or long-volatility instruments. A negative beta acts like a partial hedge against market declines, but it is uncommon for ordinary equities.
Why does a volatile stock sometimes have a low beta?
Because beta measures sensitivity to the market, not total risk. A stock can be very volatile on its own yet move independently of the benchmark, giving it a low correlation and therefore a low beta. Diversifiable, stock-specific risk does not show up in beta.
What is the difference between beta and expected return?
Beta measures sensitivity — how much the stock moves with the market. Expected return is a forecast percentage that uses beta as one input inside the CAPM: expected return equals the risk-free rate plus beta times the market risk premium. This calculator computes the sensitivity coefficient, not the projected return.
Disclaimer
This beta calculator is provided for informational purposes only and does not constitute investment, financial, or tax advice. Beta is a backward-looking estimate based on the correlation and volatility figures you enter; future sensitivity can differ sharply, especially after changes in a company's business, leverage, or market conditions. Always verify estimates against your brokerage data and consult a qualified financial professional before making investment decisions.