Beta is Not Dead

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What Price Risk?
(See The Diagrams)

"Beta is dead," declared headlines on the financial pages last spring, when Eugene Fama and Kenneth French, two economists at the University of Chicago, made a widely publicized attack on a measure of share-price risk called "beta". The measure had become a standard tool for investment managers, company bosses and utility regulators. A year later, beta's rehabilitation has begun. Three new studies suggest that, even if beta is not positively thriving, reports of its death are much exaggerated.

Beta belongs to the most influential theory in financial economics, the "capital-asset pricing model" (CAPM). According to the CAPM, returns reflect risk. Beta measures a share's relative volatility - that is, it shows how much the price of a particular share jumps up and down compared with how much the stock market as a whole jumps up and down at the same time. If a share price moves exactly in line with the market, its beta is 1; if it rises by 15% when the market rises by 10%, it has a beta of 1.5; but if it rose by only 5%, it has a beta of 0.5. The more volatile a share relative to the market, the riskier it is.

Put simply, the CAPM said that the only reason an investor should, on average, earn more by investing in one share than another is that one is riskier. But when Messrs. Fama and French looked at share returns on the NYSE, AMEX and NASDAQ between 1963 and 1990, they found that differences in beta did not explain the performance of different shares. A firm's total market value and the ratio of its book value to its market value did explain it. This could mean one of two things: either that these other factors are a better guide to the riskiness of a share than its beta - and it is not obvious why they should be - or that the CAPM is wrong.

Three economists in America - Yakov Amihud, Bent Christensen and Haim Mendelson - have tackled these findings head on *. Using the same data as Messrs. Fama and French, they performed different statistical tests. These showed that beta did, in fact, explain differences in share returns during the period. But the methods they used are controversial.

Richard Roll of UCLA and Stephen Ross of Yale University take a different tack! Even if Messrs. Fama and French had found that beta explained differences in returns, they argue, such a result could not be trusted because it is impossible to measure beta accurately enough. The betas used in practice, and in academic studies, are calculated by comparing individual shares with a market index - for instance, the S&P500 or the Wilshire 5,000.

But, point out Messrs. Roll and Ross, these market indices are only proxies: they do not include all available shares. And, they say, that difference between the proxy and the "real" market index is crucial. Tiny errors in calculating a share's beta can mean that there is no relationship between it and the returns earned on the share. Worse, big errors may by chance seem to produce a clear link between the (badly wrong) beta and returns.
Messrs. Roll and Ross save beta from extinction but hardly give it a ringing endorsement. That may not be surprising: they are the authors of the CAPM's main rival. Their "arbitrage pricing theory" is based on how a share price responds to changes in macroeconomic variables such as inflation and interest rates.

A third study, by Louis Chan and Josef Lakonishok of the University of Illinois, is the most intriguing **. It looks at a much longer series of share returns than did Messrs. Fama and French: those traded on the NYSE and AMEX from 1926 to 1991. But like them, Messrs. Chan and Lakonishok found little evidence of a link between beta and returns over this period. However, when they excluded share-price data from the period after 1982, the results suggested that beta worked: if beta dies, it did so in the 1980s.

This seems odd. After all, it was during that decade that the CAPM really caught on with investors; yet it appears that the model worked better when nobody was using it. But, say the study's authors, the very popularity of the CAPM may lie behind beta's demise.

During the 1980s there was a rapid rise in indexing - assembling a portfolio of shares to mimic a particular market index - by risk-averse institutional investors. This was largely driven by the CAPM's message that it is only possible to earn higher returns than the market as a whole - previously the aim of most investors - by taking on higher (beta) risk. The most widely used market index was the S&P500, so in the 1980s there was a big rise in demand for the shares in that index. At the same time, there was a relative fall in demand for the (smaller) shares outside the S&P500. Thus shares in the S&P500 on average earned higher returns than smaller stocks during the 1980s, regardless of their betas.

If indexing continues to grow, the S&P500 shares may continue to outperform smaller shares too, say Messrs. Chan and Lakonishok. But if, as seems likely, indexing has now more or less peaked, the more normal relationship between risk and return may soon be resumed. The authors raise a further, novel, reason why beta might live on. They reckon that many investors are especially concerned with managing big "downside" risks. Beta might be a particularly useful guide to riskiness in extreme market conditions.

To find out, they looked at the ten worst months ever for America's shareholders (see chart), when total returns fell by an average 21% during each month. The riskiest firms (the 10% with the highest betas) did indeed perform far worse than the market as a whole (down by an average 26%), and the least risky (the 10% with the lowest betas) did least badly (down by 15%). Beta worked in bull markets, too: in the ten best-ever months. American shares rose, on average, by 38%; the low-risk shares rose by 26%; and the riskier, high-beta shares jumped a hefty 50%. Beta is dead; long live beta.

* "Further Evidence on the Risk-Return Relationship", by Yakov Amihud et al., New York University, November 1992. "On the Cross-Sectional Relation Between Expected Returns and Betas", by Richard Roll and Stephen Ross, Yale University, January 1993.

** "Are the Reports of Beta's Death Premature?", by Louis Chan and Josef Lakonishok, Illinois University, December 1992.