Beta Calculator

A beta calculator measures the sensitivity of a stock or portfolio's returns relative to a benchmark index, such as the FTSE 100 or S&P 500. It is used by investors and analysts to assess how much market risk a particular asset adds to a portfolio and to compare the risk profiles of different investments.

How to Use the Beta Calculator

1. Enter the historical returns for the stock or portfolio (weekly or monthly returns work best).
2. Enter the corresponding historical returns for the benchmark index over the same period.
3. Click calculate to see the beta coefficient.

The Formula

Beta = Covariance(Stock Returns, Market Returns) / Variance(Market Returns)

Where:

Covariance(Stock, Market) = average of (Stock return - Mean stock return) x (Market return - Mean market return) across all periods

Variance(Market) = average of (Market return - Mean market return)^2 across all periods

Beta can also be expressed as:

Beta = Correlation(Stock, Market) x (Standard Deviation of Stock / Standard Deviation of Market)

A beta of 1 means the stock moves in line with the market. A beta above 1 means it amplifies market moves (more volatile). A beta below 1 means it is less sensitive to market movements. A negative beta means the stock tends to move in the opposite direction to the market.

Real-World Example

Using 12 months of monthly returns for a technology stock and the FTSE 100:

Average monthly stock return: 1.8%. Average market return: 1.0%.

Covariance of stock and market returns: 0.0045. Variance of market returns: 0.0032.

Beta = 0.0045 / 0.0032 = 1.41

A beta of 1.41 means that for every 1% move in the FTSE 100, this stock tends to move approximately 1.41% in the same direction. In a bull market, this amplifies gains. In a bear market, it amplifies losses.

How Beta Is Used in Portfolio Construction

Beta is a component of the Capital Asset Pricing Model (CAPM), which relates expected return to market risk:

Expected Return = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)

This formula (the Security Market Line) states that investors should be compensated for taking on more market risk. A stock with beta of 1.5 should theoretically offer a higher expected return than one with beta of 0.8 to compensate for its higher volatility. In practice, portfolio managers use beta to balance risk exposure: adding a low-beta defensive stock reduces overall portfolio sensitivity to market downturns, while high-beta growth stocks increase it. Beta is backward-looking (calculated from historical data) and may not predict future sensitivity accurately, particularly if a company's business model, gearing, or industry has changed significantly.

Frequently Asked Questions

What is considered a high or low beta? Utilities, consumer staples, and large healthcare companies typically have betas below 1 because their revenues are relatively stable regardless of economic conditions. Technology, small-cap, and cyclical companies often have betas above 1.5. Market index funds have a beta of exactly 1 by definition. Commodities, long-dated bonds, and some defensive sectors occasionally have negative or near-zero betas.

Is a high beta always bad? No. A high beta means higher volatility in both directions. In rising markets, high-beta stocks outperform. In falling markets, they underperform. Risk tolerance and investment horizon determine whether a high-beta stock is appropriate. Long-term investors with a high capacity for short-term volatility may choose high-beta stocks in pursuit of higher long-run returns. Short-term investors or those approaching retirement typically prefer lower-beta holdings to reduce drawdown risk.

What time period should I use to calculate beta? A common approach uses 3 to 5 years of monthly returns, balancing a long enough history to be statistically meaningful with recent enough data to reflect current business conditions. Very long histories (10 or more years) may include periods when the company operated very differently. Weekly returns increase the number of data points but can amplify short-term noise. Monthly returns are the standard for most published beta figures.

Why does my beta calculation differ from a published figure? Published betas from data providers use specific calculation methodologies: the choice of benchmark index, time period, return frequency, and whether beta is adjusted (Blume adjustment pushes raw beta towards 1 to improve predictive accuracy) all affect the result. Data providers also apply consistent methodologies across all stocks; small differences in your inputs or period can shift the result notably.

Also try these free tools:

• Portfolio Volatility Calculator
• Sharpe Ratio Calculator
• Standard Deviation Calculator

A worked example from six months of returns

The example above quotes a covariance of 0.0045 and a variance of 0.0032. Building the same figures from raw returns shows where they come from. Take six monthly returns for a stock and for its benchmark, in percent.

The mean stock return is 12 / 6 = 2.0 percent and the mean market return is 6 / 6 = 1.0 percent. Subtract each mean from its own series, multiply the pairs together, and square the market deviations.

Covariance is the average product, 21 / 6 = 3.5. Variance is the average squared deviation of the market, 10 / 6 = 1.6667. Divide one by the other and the beta is 3.5 / 1.67 = 2.1.

Two details from that arithmetic are worth carrying.

• The divisor cancels. Using the sample convention, which divides by 5 rather than 6, gives a covariance of 4.2 and a variance of 2.0, and 4.2 / 2.0 is still 2.1.
• The correlation route gives the same answer. The standard deviation of the stock returns is 2.7689 and that of the market returns is 1.2910, so their ratio is 2.1448. The correlation is 0.9791, and 0.9791 x 2.1448 = 2.10.

Reading a beta of 2.1

Beta describes the expected move for a given market move, holding the linear relationship fixed.

The same figure feeds the Capital Asset Pricing Model, with a risk-free rate of 4.2 percent and an expected market return of 9.0 percent, giving a market premium of 4.8 percent.

• Expected return at beta 2.1: 4.2 + 2.1 x 4.8 = 4.2 + 10.08 = 14.28 percent
• Expected return at beta 1.41: 4.2 + 1.41 x 4.8 = 4.2 + 6.77 = 10.97 percent
• Expected return at beta 0.8: 4.2 + 0.8 x 4.8 = 4.2 + 3.84 = 8.04 percent

A beta of 2.1 asks an investor to accept a 14.28 percent expected return as compensation for holding a position that loses 6.3 percent when the market falls 3 percent. Whether that trade suits a portfolio depends on the horizon and on what else the portfolio holds.

Adjusted beta and why it moves the answer

Marshall Blume showed in 1971 that betas measured over one period tend to drift toward 1 in the next, so a high reading usually overstates the future and a low reading understates it. The correction used in practice shrinks the raw figure toward the market:

Adjusted beta = 0.67 x raw beta + 0.33 x 1.0

Worked line for 2.1: 0.67 x 2.1 = 1.407, plus 0.33 x 1.0 = 0.33, giving 1.737. The correction pulls the extreme readings inward and leaves a beta near 1 almost untouched, which is the point of it. Published betas from data providers often carry an adjustment of this kind, and the methodology notes say which form they use.

What changes the number

• Return frequency. Daily returns give more data points and more noise. Monthly returns are the convention for published figures.
• Window length. Three to five years of monthly returns is a common compromise between enough observations and a period that reflects the current business.
• Benchmark choice. Beta against the FTSE 100 and beta against a world index are different numbers, because the benchmarks move differently.
• Index construction. A price index excludes dividends while a total return index includes them, and the difference shows up in the beta.
• Currency. Returns measured in the investor's currency include the exchange rate move, which shows up in the covariance.

Method and assumptions

• Beta measures sensitivity to one benchmark. It is silent about what the stock does for reasons of its own, and it does not capture company-specific risk.
• The model is linear. It assumes a straight-line relationship between the two return series over the window, and it will misstate the sensitivity of an asset whose response changes with market direction.
• The measure is backward looking. A beta built from five years of history describes a company that may no longer exist in the same form.
• One number cannot separate a genuinely volatile business from a thin trading history that produced a few large moves.

A note on the two papers behind the measure

Beta as a measure of systematic risk comes from the capital asset pricing work of William Sharpe, whose 1964 paper "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk" set out the relationship between expected return and market risk that appears above as the security market line. The shrinkage correction comes from Marshall Blume's 1971 paper "On the Assessment of Risk" in the Journal of Finance, which found that betas estimated over one period regress toward 1 in the next. The 0.67 and 0.33 weights are the form of that correction that data providers have settled on in practice.