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Bloopers & Blunders: beta coefficient

Quotation
"A means of measuring the volatility of a security or portfolio of securities in comparison with the market as a whole. A beta of 1 indicates that the security's price will move with the market. A beta greater than 1 indicates that the security's price will be more volatile than the market. A beta less than 1 means that it will be less volatile than the market." (CNNfn Business Glossary)

Intermediate Level Analysis

The last sentence is not necessarily true. To see this, remember

volatility = total risk = systematic risk + idiosyncratic risk (*)

 But beta only measures systematic risk. Thus, a company or a portfolio with a beta less than one would have the systematic component of risk less volatile than the market. But what about the idiosyncratic risk component? If the latter component is large, it can offset the first, thus making a low beta stock or portfolio more volatile than the market.

 The beta-volatility retaliation is more likely to hold for a portfolio as idiosyncratic risk is potentially diversified away. Moreover, for an average stock, the systematic component is less than 25 percent of total risk as measured by the variance of asset returns.

Let's make the argument more precise. Equation (*) can be rewritten as:

volatility = variance = (beta)² x (variance of market) + idiosyncratic risk

Now consider a stock with beta less than zero, say, beta=-2. Substituting this in the above equation has to yield a variance greater than the market, i.e.,

(-2)² x (variance of market) > (variance of market)

 Remember, in practice when the betas are estimated, the S&P 500 is used as a proxy for the "market."

By Alex Tajirian