Understanding stock beta
Beta (β) measures how strongly a stock's returns move in relation to the overall market. A stock that swings more than the market has a beta above 1; one that swings less has a beta below 1. This calculator estimates beta from three quantities you can read off historical data: the correlation between the stock and a market index, the stock's return volatility, and the market's return volatility.
The formula
Beta is defined as the covariance between the stock and the market divided by the variance of the market: β = Cov(stock, market) / Var(market). Because covariance equals the correlation times the two standard deviations, the same value can be written in the more intuitive form this tool uses:
- β = ρ × σstock / σmarket, where ρ is the correlation coefficient between the stock and the market (from −1 to +1), σstock is the standard deviation of the stock's returns, and σmarket is the standard deviation of the market's returns.
- The tool also reports the two pieces of the ratio: the covariance (ρ × σstock × σmarket) and the market variance (σmarket²). Dividing the first by the second returns beta.
What the numbers mean
- β = 1: the stock tends to move in line with the market.
- β > 1: more volatile than the market — a beta of 1.5 implies swings roughly 50% larger than the market's.
- 0 < β < 1: less volatile than the market, often described as defensive.
- β < 0: moves opposite the market; uncommon, and seen in some hedging assets.
Assumptions and limits
- Beta is backward-looking: it summarizes a historical sample and can drift as a company or the market changes.
- It depends on the index and the sampling period you choose (daily vs. monthly returns, one year vs. five).
- Beta captures only systematic, market-related risk — not company-specific risk, which investors reduce through diversification.
Frequently Asked Questions
What is a stock's beta?
Beta measures how much a stock moves relative to the overall market. A beta of 1 means the stock tends to move with the market, above 1 means it is more volatile, between 0 and 1 means it is less volatile, and a negative beta means it tends to move opposite the market. Formally, beta equals the covariance between the stock and the market divided by the variance of the market.
How is beta calculated in this tool?
It uses beta = correlation × stock volatility / market volatility. Enter the correlation between the stock and the market and the standard deviation of each one's returns. The tool also reports the covariance (correlation × stock volatility × market volatility) and the market variance (market volatility squared); beta equals the covariance divided by the market variance.
What does a beta of 1.5 mean?
A beta of 1.5 means the stock has historically moved about 1.5 times as much as the market. When the market rose or fell 10%, a stock with a beta of 1.5 tended to move about 15% in the same direction. It indicates higher systematic risk than the market.
Can beta be negative?
Yes. A negative beta means the stock tends to move in the opposite direction to the market. It is uncommon, but assets such as gold or certain hedging positions sometimes show a slightly negative beta over some periods.