The two flavors of mean reversion

 

Most investors are familiar with mean reversion, the idea that extremes tend not to persist, and that outstandingly good (or bad) performance tends back toward the average in time.

Far fewer are familiar with the fact that there are two distinct types of mean reversion, and these two types need to be handled differently.

The first type of reversion is the most common and can be thought of as a dilution of the extreme finding. For example, extremely tall parents tend to have children who are not quite as tall as they are; sports teams that do well enough to make the cover of Sports Illustrated magazine tend to see a subsequent drop-off in performance; and if you return to the restaurant where you had the best meal of your life, you are unlikely to have quite as good an experience second time around.

The second type of mean reversion is not mere dilution of an extreme outcome, but a reaction to it. Examples of this are less common, but would include the incidence of aces in a game of blackjack (until the deck is shuffled) and stock market bubbles in which prices run up well above reasonable valuations, creating the likelihood of a fall. This reaction-type reversion is quite different from the dilution variety.

The two flavors of mean reversion
Exceptional performance… is unlikely to persist

A technical description of the difference between these two types of reversion—complete with formulae and definitions of conditional expectations—is provided in a 1991 Myra Samuels paper.

For investors, the distinction is important.

Reaction-type reversion would mean that likely outcomes change following a period of unusually high or low returns. So if there’s been a run-up in equity values, or in the value of a particular stock, or in a particular mutual fund’s performance, then—in the presence of this type of reversion—we ought to sell. But that is the exception rather than the rule: most mean reversion is not reaction, but dilution. As Samuels puts it, dilution-type reversion is almost universal; statistically speaking, it is difficult for extreme outcomes not to get diluted. But reactions or snapbacks (which she terms “regression”) are more rare.

Unlike reaction-type reversion, dilution carries no obvious implication for action. Dilution tells us that the #1 performing stock or fund is unlikely to repeat that feat, but it does not tell us whether it should now be expected to underperform the average. Dilution tells us that the stock market cannot go up 20% a year for ever, but it does not tell us whether a 30% year means we are due for a correction or not. So, next time you are wondering about an expected reversion to the mean (whether of a market, a stock, or anything else for that matter), make sure you know which type of reversion you really expect.


USI-20408-12-17

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