Academic Attack 3: Estimated Betas Are Unstable

Academic Attack 3: Estimated Betas Are Unstable

Another problem the theory encounters is the instability of measured betas. One might well be skeptical about the wisdom of relying on beta estimates based on historical data. Beta really looks suspiciously like a tool of technical analysis in academic dress – a bastard cousin of the technicians' charts. And as far as individual securities go, historical betas – used as a basis for predicting future betas and, hence, expected security returns – do not seem to be much more reliable as predictors of security performance than any of the devices cooked up by technical analysis.

In order to see how beta familiarity breeds contempt, we should know how beta is bred in the first place. The typical procedure in estimating betas for an individual stock is ti measure the relationship between the security's past return and the return from the market as a whole. For example, suppose that in the last quarter AT&T's total return (including both dividends and capital gains) was 5 percent and the market return (similarly measured) was 10 percent. We plot this pair of returns on a graph, as is done next.

We can continue the process by measuring the rate of return for AT&T and for the S&P 500 (our proxy for the market) in many other past three-month periods, and we can plot these observations on the same graph. After many pairs of returns for AT&T and for the market have been plotted, a line of best fit (a regression line) is drawn to represent the average relationship between the returns from AT&T and those from the S&P 500 (The regression line is also called a least-squares line, since it is estimated by finding the line that minimizes the sum of the squared vertical distances from each of the black dots to the line). The slope of the regression line (i.e., the ration between the vertical and horizontal sides of a right triangle having the regression line as its hypotenuse) is our measure of the security's historical beta. In this example, we get a beta estimate for AT&T of ½, or 0.5, as shown in the chart. This means that AT&T has been about half as volatile as the overall market, and the assumption is that it will continue to be so in the future. It is clear why this last assertion may be wrong. After the divestiture of 1983 and with deregulation of the telecommunications industry, AT&T is not the same company as it previously was. Even without such major changes affecting the characteristics of the company's stock, some unforeseen event(s), not reflected in past returns, may decisively affect the security's future returns.

Elk. Photo by Elena

To illustrate this hazard in measuring an individual stock's beta, consider the following example : During some periods in the 1960d, Mead Johnson and Company (now part of Bristol-Myers Company) had a measured beta that was negattive; it tended to move against the marker, and thus appeared to be preceisely the kind of stock investors would seek to reduce the risks of their portfolio. But looking behind the reasons for this measured beta's being less than zero did not give one very much comfort that the beta for the future – which is after all what is really relevant – would turn out to be anything like the beta from the past.

What happened in the Mead Johnson case was that in 1962 the company came out with a marvelous new product that became an instant best-seller. The product, called “Metrecal,” was a liquid dietary supplement. Consumers were urged to have a can of Metrecal rather than their normal lunch. Metrecal would provide all the vitamins and nutrients needed for health with few of the calories that usually went along with lunch. An so, in 1962, as Americans became more diet-conscious, drinking Metrecal became quite a fad, and the earnings and stock price of Mead Johnson climbed sharply at precisely the time the stock market was taking one of its worst baths since the Great Depression.

Like most fads, the Metrecal boom did not last very long; by 1963 and 1964, just when the general stock market was recovering, Americans got pretty sick and tired of drinking Metrecal for lunch, and the big boost in earnings and stock prices that Mead Johnson had earlier enjoyed began to fade away.

Later in the 1960s, just about the time the market took another slump, Mead Johnson came out with another new product. This one was called “Nutrament.” Nutrament was a dietary supplement that was supposed to put on weight, and skinny teenagers bought it by the case to improve their appearance. Yes, you guessed it! Nutrament was the same product as Metrecal except that if you drank Nutrament in addition to lunch you could put on weight, rather than lose it. Again, Mead Johnson prospered while the market slumped, and it is this unusual combination of circumstances that produced the negative betas of the period.

The problem is, of course, whether such a fortuitous string of events could reasonably be anticipated to occur in the future. On a priori grounds we would expect not. Indeed, what was in fact measured was anything but a systematic relationship with the market. Of course, this is precisely the problem in predicting betas on the basis of past experience. Any changes in the economy, in the characteristics of an individual company, or in the competitive situation facing the company can be expected to change the sensitivity of the company's stock to market fluctuations. It would be surprising to discover that betas of individual stocks did not vary widely over time. In fact, they do vary. The Mead Johnson example is not just an isolated case, the exception that tastes the rule.

Marshall Blume, a professor at the Wharton school of Finance, conducted several tests of the stability of historical beta estimates. He found that the smaller the number of securities in the portfolio, the weaker the relationship between portfolio betas for consecutive periods. For a portfolio of one security, the earlier beta is a very poor predictor of the beta in the second period. Past betas are not useful predictors of future betas for individual stocks. Better productive power is obtained from betas calculated for portfolios containing larger number of stocks. Thanks to the law of large numbers, the number of inaccurate beta estimates on individual  stocks can be combined to form a much more accurate estimate of the risk of the portfolio as a whole. While the beta estimates for some securities will be much too high, the estimates for many others will be too law.

Mutual-fund betas are not quite as easy to predict from period to period as are betas for unmanaged portfolios, because fund managers will often deliberately change the risk composition of the portfolio. Still, the general investment objective of the fund (e.g. growth, stability, etc.) does put a limit on the degree of change possible, and mutual fund betas also tend to be far more stable from period to period than are the betas for individual stocks. Still, the general conclusion that should be drawn from this discussion is that historical betas may be quite imperfect indicators of future betas. The people who oversold beta as a useful tool in predicting the behavior of individual stocks did the new investment technology a great disservice. In judging risk, beta cannot substitute for brains. Many beta boomers, however gone to great lengths to legitimize their technical bastard.