In this mini-series, we’re examining the value of beta as a measurement of risk.  In this post, we want to examine how the betas of some popular stocks, indexes, and ETFs changed during 2008 and especially during the fall crash.  First, we should clarify exactly what we’re measuring.

What is beta?

Beta is metric that describes the systemic risk of an asset or portfolio.  Because it is not possible to alleviate all risk by simple diversification, investors and traders use beta to determine how much exposure they have to broad market risk - how closely their expected returns correlate with broad market returns.  Where a market index is assigned a beta of 1, assets with betas of 1 will tend to move with the market, assets with betas of 2 will tend to rise or fall twice as much as the market, and assets will betas of 0 will tend to move independently.

We calculate beta as the ratio of the covariance of the individual asset return (Ri) and market return (Rm) to the variance of the market return:

We use the S&P 500 (SPX) for the market returns.  Notice that beta describes a tendency, not a law: if the S&P 500 rises 2% tomorrow but some stock with a beta of 1.5 rises only 2.5% (rather than 3%), that one data point isn’t significant in itself - what matters is the relationship between returns over time.  (Note that in Excel, the function VARP should be used rather than VAR; the latter returns a benchmark beta of less than 1.)

Beta over Time

The following graph displays the beta of all of the assets mentioned in Part 1: 1) based on monthly returns over the years 1997-2007, 2) based on daily returns during 2008, and 3) based on daily returns during 9/15/08 - 12/2/08, which we’re defining as the “market crash” period.