Beta

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Beta is a risk metric employed primarily in the equity markets. It measures the systematic risk of a single instrument or an entire portfolio. William Sharpe (1964) first used the notion in his landmark paper introducing the capital asset pricing model (CAPM). The name “beta” was applied later.

Beta describes the sensitivity of an instrument or portfolio to broad market movements. The stock market (represented by an index such as the S&P 500 or FT-100) is assigned a beta of 1.0. By comparison, a portfolio (or instrument) which has a beta of 0.5 will tend to participate in broad market moves, but only half as much as the market overall. A portfolio (or instrument) with a beta of 2.0 will tend to benefit or suffer from broad market moves twice as much as the market overall.

The formula for beta is

[1]

where

  • cov(Zp,Zm) is the covariance between the portfolio (or instrument) return and the market return, and
  • is the variance of the market’s return (volatility squared).

Both quantities are calculated using simple returns. Beta is generally estimated from historical return data. For example, 60 trading days of simple returns might be used with sample estimators for covariance and variance.

It is possible to construct negative beta portfolios. Approaches include

  • holding stocks (such as gold mining stocks) that tend to move against the market,
  • shorting stocks, or
  • putting on suitable options spreads.

Beta is sometimes used as a metric of a portfolio’s market risk. This can be misleading because beta does not capture specific risk. Because of specific risk, a portfolio can have a low beta but still be highly volatile. Its price fluctuations will simply have a low correlation with those of the overall market.

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