Regression to the Mean

The three previous cognitive biases, stemming from representativeness, buttress one of the most important and consistent sources of investment error. As intuitive statisticians, we do not comprehend the principle of regression to the mean. Although the terminology sounds formidable, the concept is simple. This statistical phenomenon was noted over 100 years ago by Sir Francis Galton, a pioneer in eugenics, and is important to avoiding this major market error.

In studying the height of men, Galton found that the tallest men usually had shorter sons, while the shortest men usually had taller sons. Since many tall men come from famiUes of average height, they are likely to have children shorter than they are, and vice versa. In both cases, the height of the children was less extreme than the height of the fathers.

The study of this phenomenon gave rise to the term regression, which has since been documented in many areas. The effects of regression are all around us. In our experience, most outstanding fathers have somewhat disappointing sons, brilliant wives have duller husbands, people who seem to be ill-adjusted often improve, and those considered extraordinarily fortunate eventually have a run of bad luck.

Regression to the mean, although alien to us intuitively, occurs frequently. Take the reaction we have to a baseball players batting average. Although a player may be hitting .300 for the season, his batting will be uneven. He will not get three hits in every ten times at bat. Sometimes he will bat .500 or more, well above his average (or mean), and other times he will be lucky to hit .125. Over 162 games, whether the batter hits .125 or .5 in any dozen or so games makes little difference to the average. But rather than realizing that the players performance over a week or a month can deviate widely from his seasons average, we tend to focus only on the immediate past record. The player is believed to be in a "hitting streak" or a "slump." Fans, sportscasters, and, unfortunately, the players themselves place too much emphasis on brief periods and forget the long-term average, to which the players will likely regress.

Regression occurs in many instances where it is not expected and yet is bound to happen. Israeli Air Force flight instructors were chagrined after they praised a student for a successful execution of a complex maneuver, because it was normally followed by a poorer one the next time. Conversely, when they criticized a bad maneuver, a better one usually followed. What they did not understand was that at the level of training of these student pilots, there was no more consistency in their maneu-

vers than in the daily batting figures of baseball players. Bad exercises would be followed by well-executed ones and vice versa. Their flying regressed to the mean. Correlating the maneuver quality to their remarks, the instructors erroneously concluded that criticism was helpful to learning and praise detrimental, a conclusion universally rejected by learning theory researchers.

How does this work in the stock market? According to the classic work on stock returns of Ibbotson and Sinquefield, then at the University of Chicago, stocks have returned 10.5% annually (price appreciation and dividends) over the last 70 years, against a return of about 5.6% for bonds. An earlier study by the Cowles Commission showed much the same return for stocks going back to the 1880s.

As Figure 10-1 shows, however, the return has been anything but consistent-not unlike the number of hits a 300 career hitter will get in individual games over a few weeks. There have been long periods when stocks have returned more than the 10.5% mean. Within each of these periods, there have been times when stocks performed sensationally, rising sometimes 50% or more in a year. At other times, they have seemed to free-fall. Stocks, then, although they have a consistent average, also have "streaks" and "slumps."

For investors, the long-term rate of retum of common stocks, like the batting average of a ballplayer, is the important thing to remember. However, as intuitive statisticians, we find it very hard to do so. Market history provides a continuous example of our adherence to the belief that deviations from the norm are, in fact, the new norm.

The investor of 1927 and 1928 or 1996 and 1997 thought that retums of 30 to 40% were in order from that time on, although they diverged far from the mean. In 1932 and 1974, he believed huge losses were inevitable, although they, too, deviated sharply from the long-term mean. The investor of mid-1982, observing the insipid performance of the Dow Jones Industrial Average (which was lower at the time than in 1965) believed stocks were no longer a viable investment instmment.

Business Week ran a cover story, just before the Great Bull Market began in July 1982, entitled "The Death of Equities."* In 1987, after die Dow had nearly quadmpled its level of 1982, I attended a dinner of money managers just prior to the crash. The almost universal opinion at the table was that stocks would go much higher. The table was right- for another ten days.

The same scenarios have been enacted at every major market peak and trough. Studies of investment advisor buying and selling indicate that most experts are closely tied, if not pilloried, to the current markets movement. The prevalent belief is always that extreme retums-

Figure 10-1

Annual Stock Retums

1926 - 1996

-20%

-40%

-60%

«1933 * 1935

«1954

«1928

> 1958

.1927 3 .,945 «1938 1950 «

«1943 5,

1942 1949

♦1975 ♦

. 1985 1989 1995

* «1961 ,976- *

♦I963*" 0 1982 .«« 1996 ♦1952 ~~ .1964 1972 ♦ ,„„«,„„„

«1926

1959 « ♦

1965

1947 «.1948 1956

1939 I960

1929

1934 «1932

♦1972 * «1971 1979 1986 1988 «1968 «1993 .1978 .1984 «,992 .,970 ♦ ♦ «1987 «1994

1940 « 1946 ♦l941

1962

► 1957

♦l966

1969

«1981

►1977

«1990

1973

► 1930

«1974

«1937

«1931

I

1930

1940

1950

1960 Year

1970

1980

I 1990 1996

whether positive or negative-will persist. The far more lilcely probability is that they are the outhers on a chart plotting retums, and that succeeding pattems will regress towards the mean.

We can maslf the relevance of these long-term retums by detailed study of a specific trend and by intense involvement in it. Even those who are aware of these long-term standards cannot always see them clearly because of preoccupation with short-term conditions. This leads to a fourth protective mle:

RULE 25

Dont be seduced by recent rates of return for individual stocks or the market when they deviate sharply from past norms (the