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Reversion
to the mean is the phenomenon (discovered by Charles Darwin's cousin,
Sir Francis Galton (1822-1911)) whereby a stock's average performance
(or a mutual fund's, or many other non-investing statistics) tend
to become more average (i.e., less extreme) over time. If true,
this implies that recent good performers are perhaps somewhat more
likely than average to be below average performers in the future
(and vice versa). This idea is supported by much of the research. |
A
mathematical description of this generic concept: "Reversion
to the Mean" is the statistical phenomenon stating that the
greater the deviation of a random variate from its mean, the greater
the probability that the next measured variate will deviate less
far. In other words, an extreme event is likely to be followed by
a less extreme event. Although this phenomenon appears to violate
the definition of independent events, it simply reflects the fact
that the probability function P(x) of any random variable x, by
definition, is nonnegative over every interval and integrates to
one over the interval . Thus, as you move away from the mean, the
proportion of the distribution that lies closer to the mean than
you do increases continuously |
[Shiller]
"Thus there is a sort of regression to the mean (or to longer-run
past values) for stock prices: what goes up a lot tends to come
back down, and what goes down a lot tends to come back up".
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 "I
asked Daniel Kahneman, which of his 131 papers was his all-time
favorite? "On
The Psychology of Prediction" (1973, with Amos Tversky,
Psychological Review, 80, 1973, pp. 237-251), he responded. This
paper began when Kahneman and Tversky were at the Hebrew University
in 1968. In tutoring Israeli Air Force flight instructors, they
discovered the following: In conflict with psychologists' stock-in-trade
(reward is far more effective than punishment in changing behavior),
the instructors believed the opposite. The reason: Nearly every
time they rewarded their student pilots, their performance declined.
And nearly every time they punished their student pilots, their
performance subsequently improved. How should a psychologist respond?
Regression to the mean, explained Kahneman and Tversky. In flight
maneuvers, progress between successive maneuvers is slow. It is
likely that pilots who did well in one trial deteriorate in the
next. Instructors wrongly attributed this 'regression' to the detrimental
impact of their positive reinforcement -- an example of attribution
error, attributing to human action what is in fact random. This
erroneous and destructive feedback loop is ubiquitous. Armies of
school psychologists labor intensively to repair the damage it causes.
As Kahneman and Tversky conclude: "We normally reinforce others
when their behavior is good and punish them when their behavior
is bad. By regression alone, therefore, they are most likely to
improve after being punished and most likely to deteriorate after
being rewarded. Consequently, we are exposed to a lifetime schedule
in which we are most often rewarded for punishing others, and punished
for rewarding". (p. 251). This powerful insight, were it understood
and applied in our schools, universities, businesses, families,
shops, and public policies, could alone alter human society for
the better. And there are 130 more where that came from". |
Reversion
in Action, Schultheis, 1999
If you want to live a long and healthy life conventional wisdom
says that you should eat in moderation and exercise regularly. If
you want to be a successful investor of common stocks conventional
wisdom says you should spend lots of time analyzing companies or
mutual fund managers and then try to pick the best ones. That is
mistake #1. If you want to be a successful investor of common stocks
forget about conventional wisdom and focus instead on reversion
to the mean. |
Bogle
on Investment Performance and the Law of Gravity: Reversion to the
Mean-Sir Isaac Newton Comes to Wall Street, Bogle, 1998
"... RTM is a rule of life in the world of investing—in
the relative returns of equity mutual funds, in the relative returns
of a whole range of stock market sectors, and, over the long-term,
in the absolute returns earned by common stocks as a group".
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Reversion-to-the-mean
is not a glide path phenomenon, Bronson, 2000
This commentator notes that mean reversion doesn't mean that an
investment's future performance is likely to gradually approach
some asymptote. Rather, it is likely to cycle to the other extreme
(i.e., good performance is likely to be followed by bad performance,
and vice versa), which over time will cause the average performance
to approach some asymptote. "Keep in mind that means of investment
returns, like the underlying returns themselves, do not have a goal
or a deterministic path so that mean reversion is probably best
understood as simply reversion-to-the-extreme, much more like aperiodic
pendulums than glide-path landings". |
Temporary
Movements in Stock Prices, Lewellen
"Mean reversion in stock prices is stronger than commonly believed.
... The reversals are also economically significant. The full-sample
evidence suggests that 25% to 40% of annual returns are temporary,
reversing within 18 months. The percentage drops to between 20%
and 30% after 1945. Mean reversion appears strongest in larger stocks
and can take several months to show up in prices". |
A
Mean-Reversion Theory of Stock-Market Crashes, Hillebrand, 2003
"Errors in the perception of mean-reversion expectations can
cause stockmarket crashes. Using daily data of the Dow Jones Industrial
Average and the S&P500 index I show that mean-reversion in returns
is a transient but recurring phenomenon. In the case of the crash
of 1987 I show that during the period 1982–1986 mean-reversion was
higher than during the nine months prior to the crash. This indicates
that meanreversion expectations were underestimated in 1987. This
error was disclosed when in the week prior to the crash it became
known that a surprisingly high volume of equities was under portfolio
insurance and thus hedged against a faster reversion". |
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