What is beta?

Beta measures how sensitive an investment is to movements of the overall market. A beta of 1 means the investment has tended to move in line with the market; above 1, it has amplified the market's moves; below 1, it has dampened them. Beta describes market risk: the part of an investment's risk that diversification cannot remove.

The formula

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

\beta = \frac{\operatorname{Cov}(r_i, r_m)}{\operatorname{Var}(r_m)} = \rho_{i,m} \, \frac{\sigma_i}{\sigma_m}

where $r_i$ and $r_m$ are the returns of the investment and of the market index, $\rho_{i,m}$ their correlation, and $\sigma_i$ and $\sigma_m$ their volatilities. Graphically, beta is the slope of the line through a scatter plot of the investment's returns against the market's.

How to read it

Beta	Behaviour
above 1	amplifies market moves (many technology stocks, small caps)
about 1	moves with the market (a broad index fund)
between 0 and 1	dampens market moves (utilities, consumer staples)
about 0	unrelated to the market (cash, money market funds)
below 0	tends to move against the market (rare)

A simple illustration

A stock has a volatility of 30%, the market 15%, and their correlation is 0.6:

\beta = 0.6 \times \frac{30\%}{15\%} = 1.2

If the market falls 10%, the stock can be expected to fall about 12% on average — plus or minus moves of its own that have nothing to do with the market.

High volatility alone does not mean high beta. A stock with 40% volatility but almost no correlation with the market can have a beta close to zero: it is risky, but its risk is its own, and it largely diversifies away in a big portfolio.

The beta of a portfolio

A portfolio's beta is the weighted average of its holdings' betas:

\beta_p = \sum_i w_i \, \beta_i

A portfolio with 70% in a world equity ETF (beta about 1) and 30% in cash (beta 0) has a beta of about 0.7.

Limits

It depends on the index. A European stock has one beta against the MSCI World and another against the DAX. Beta always needs the question: against what?
It changes over time. Betas estimated over different periods can differ considerably, and they tend to rise in crises, when correlations go up.
It captures only one kind of risk. Company-specific events, currency moves and sector shocks are invisible in beta.

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