Beta (Investing)

Beta is a measure of how strongly an asset's returns move with the returns of the overall market. A beta of 1.0 means the asset has tended to rise and fall in step with the market; a beta of 1.5 means it has moved about one and a half times as much; a beta of 0.5 means about half as much. A negative beta means the asset has tended to move against the market.

Beta captures market risk, also called systematic risk: the part of an investment's ups and downs that cannot be removed by diversification. It is the central input of the capital asset pricing model (CAPM) and the starting point for calculating alpha. It is often confused with total volatility, which also includes company-specific swings that beta ignores.

Think of boats in a harbour when the tide comes in. A big ferry on a long rope rises almost exactly with the water. A small dinghy on a short rope bobs up and down more than the tide itself. A rock does not move at all.

The tide is the market. Beta tells an investor which kind of boat they are holding. A high-beta share behaves like the dinghy: it exaggerates every rise and fall of the market. A low-beta share is closer to the ferry, or even the rock. Beta says nothing about storms that hit one boat alone, such as a company losing a lawsuit; it only describes how a holding responds to the tide that lifts or lowers everything.

Beta is the covariance of the asset's returns with the market's returns, divided by the variance of the market's returns:

• $\beta_i$ is the beta of asset $i$.
• $R_i$ is the series of returns on the asset, usually monthly or weekly.
• $R_m$ is the series of returns on the market index chosen as the benchmark.
• $\text{Cov}$ measures how the two series move together, and $\text{Var}$ measures how much the market moves on its own.

An equivalent form is $\beta_i = \rho_{i,m} \times \frac{\sigma_i}{\sigma_m}$, where $\rho$ is the correlation between the two series and $\sigma$ is each one's standard deviation. Suppose a share's annual standard deviation is 30%, the market's is 20%, and the correlation is 0.8. Its beta is 0.8 × (30 ÷ 20) = 0.8 × 1.5 = 1.2. If the market falls 10%, the model expects the share to fall about 12%, before any company-specific news.

In practice beta is estimated by a regression of the asset's returns on the market's returns; the slope of the fitted line is the beta. Data providers commonly use five years of monthly returns or two years of weekly returns, which is why published betas for the same share often differ.

The CAPM, set out by William Sharpe in 1964 and independently by John Lintner and Jan Mossin, says that investors should only be rewarded for risk they cannot diversify away. The model's expected return is:

Here $R_f$ is the risk-free rate and $E(R_m) - R_f$ is the equity market risk premium. With a risk-free rate of 4%, a market premium of 5% and a beta of 1.2, the expected return is 4% + 1.2 × 5% = 10%. Companies use the same calculation to estimate their cost of equity when valuing projects, and analysts use it in valuation models that discount future cash flows.

Betas cluster in recognisable patterns, though they change over time:

• The market itself has a beta of exactly 1.0 against its own index, so a broad S&P 500 fund will show a beta very close to 1.
• Utilities and consumer staples have historically shown betas below 1, because demand for electricity or groceries changes little in a recession.
• Technology shares, small companies and businesses with high leverage have tended to show betas above 1.
• Cash and short-term Treasury bills have a beta near zero against equities.
• Some assets, such as gold or long-dated government bonds, have shown low or negative betas to shares during some periods, which is why they are used as diversifiers.

Fund fact sheets and analytics services report beta so that investors can judge how a fund will behave in a bull market or a bear market. A portfolio manager can raise or lower the overall beta of a portfolio by shifting between high- and low-beta holdings, or quickly by trading index futures. Market-neutral hedge funds aim for a beta near zero, so that their results come from security selection rather than the market's direction.

Corporate finance also adjusts beta for debt. An "unlevered" beta removes the effect of a company's borrowing so that businesses with different capital structures can be compared, and it is then "relevered" for the company being valued.

• Beta looks backwards. It is estimated from past prices and can change when a company's business, debt or industry changes. Marshall Blume showed in 1971 that betas tend to drift towards 1 over time, and some data services publish an "adjusted beta" to reflect this.
• Beta depends on the benchmark. A fund measured against the wrong index will show a misleading beta; the R-squared of the regression shows how reliable the figure is.
• Beta is not total risk. A share can have a low beta but very high company-specific risk, as many single-stock collapses have shown.
• The evidence is mixed. Studies since the 1970s have found that low-beta shares have earned more, and high-beta shares less, than the CAPM predicts.

• William F. Sharpe – Facts (Nobel Prize)