Overview

In finance, the beta (β or market beta or beta coefficient) is a statistic that measures the expected increase or decrease of an individual stock price in proportion to movements of the stock market as a whole. Beta can be used to indicate the contribution of an individual asset to the market risk of a portfolio when it is added in small quantity. It refers to an asset's non-diversifiable risk, systematic risk, or market risk. Beta is not a measure of idiosyncratic risk.

Beta is the hedge ratio of an investment with respect to the stock market. For example, to hedge out the market-risk of a stock with a market beta of 2.0, an investor would short $2,000 in the stock market for every $1,000 invested in the stock. Thus insured, movements of the overall stock market no longer influence the combined position on average. Beta measures the contribution of an individual investment to the risk of the market portfolio that was not reduced by diversification. It does not measure the risk when an investment is held on a stand-alone basis.

The beta of an asset is compared to the market as a whole, usually the S&P 500. By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above 1, it indicates that its return moves more than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3.

Relationship between own risk and beta risk

Attempts have been made to estimate the three ingredient components separately, but this has not led to better estimates of market-betas.

Beta as a linear operator

Market-beta can be weighted, averaged, added, etc. That is, if a portfolio consists of 80% asset A and 20% asset B, then the beta of the portfolio is 80% times the beta of asset A and 20% times the beta of asset B.

Financial analysis

In practice, the choice of index makes relatively little difference in the market betas of individual assets, because broad value-weighted market indexes tend to move closely together. Academics tend to prefer to work with a value-weighted market portfolio due to its attractive aggregation properties and its close link with the capital asset pricing model (CAPM). Practitioners tend to prefer to work with the S&P 500 due to its easy in-time availability and availability to hedge with stock index futures.

In the idealized CAPM, beta risk is the only kind of risk for which investors should receive an expected return higher than the risk-free rate of interest. When used within the context of the CAPM, beta becomes a measure of the appropriate expected rate of return. Due to the fact that the overall rate of return on the firm is weighted rate of return on its debt and its equity, the market-beta of the overall unlevered firm is the weighted average of the firm's debt beta (often close to 0) and its levered equity beta.

In fund management, adjusting for exposure to the market separates out the component that fund managers should have received given that they had their specific exposure to the market. For example, if the stock market went up by 20% in a given year, and a manager had a portfolio with a market-beta of 2.0, this portfolio should have returned 40% in the absence of specific stock picking skills. This is measured by the alpha in the market-model, holding beta constant.

Special cases

Utility stocks commonly show up as examples of low beta. These have some similarity to bonds, in that they tend to pay consistent dividends, and their prospects are not strongly dependent on economic cycles. They are still stocks, so the market price will be affected by overall stock market trends, even if this does not make sense.

Foreign stocks may provide some diversification. World benchmarks such as S&P Global 100 have slightly lower betas than comparable US-only benchmarks such as S&P 100. However, this effect is not as good as it used to be; the various markets are now fairly correlated, especially the US and Western Europe.

Derivatives are examples of non-linear assets. Whereas Beta relies on a linear model, an out of the money option will have a distinctly non-linear payoff. In these cases, then, the change in price of an option relative to the change in the price of its underlying asset is not constant. (True also - but here, far less pronounced - for volatility, time to expiration, and other factors.) Thus "beta" here, calculated traditionally, would vary constantly as the price of the underlying changed.