MJG's graph (from
here, among other places) supports the thesis that mean reversion (in the
literal mathematical sense) does hold in the investing world.
The first sentence is almost right: "A reversion to the mean has to happen after a particularly outlander." Mean reversion says simply that for a sequence of random numbers, the further away from the mean the current value is the more likely the next value is to be closer to the mean. More likely, but it does not "have to happen."
This is one of those self evident statements when you think about it. Suppose we've got something with a normal probability distribution (bell curve) centered at zero (mean). The probability of the next value being above zero is 50%, and below zero is 50%.
The probability of the next value being below 1 is higher than 50% (since 50% will fall below zero, let alone 1). The probability of the next value being below 10 is even higher; the probability of the next value being below 20 is higher still. The further away from the mean, the higher the probability that the next value will be closer. Duh!
(Technically, I'm illustrating something slightly different from mean reversion, but it's close enough to convey the concept.)
In order for this "rule" to be valid, we have to be observing something random. That's what gives us the bell curve. MJG's graph purports to show that next year's returns are indeed random (zero correlation with the previous five
years' performance). So rather than showing lack of mean reversion, the graph suggests the opposite - that the yearly returns are random - a necessary condition for mean reversion.
The reason why I said "purport" is that the graph is not showing the correlation between the current year's return and the next year's. (Rather it shows the lack of correlation between the past
five years' cumulative performance and the next year's.) The original article looks at next year's performance in comparison with the current year's performance (not prior five year's total).
Looking at performance following 20%+
years, the data evinces mean reversion. The subsequent
years averaged a return that was about the same as the market long term average of
11.4% between 1928 and 2015. That suggests that next year performance of these
years was random. Further, in these
years immediately following 20% gains, the market went up roughly the same percentage of the time (69%) as the market did over all
years (72%). So it looks like the randomness requirement for mean reversion is not violated.
More important, for most of these outlier
years (20%+ returns), the next year's returns were closer to the mean. The exceptions were:
1936 (1937 returned less, but further away from the mean of 12%),
1942 (higher in 1943),
1961 (1962 returned less, but further away from the mean),
1976 (1977 less but further from mean),
1982 (1983 slightly higher),
1996 (1997 higher),
1999 (2000 less but further from mean),
That means that 25 of 32
years following 20%+ returns were closer to the mean than the
years they followed. That is, there was mean reversion. It happens most of the time, but not always. And 20% isn't even that much of an outlier - less than one standard deviation (19.7%) from the mean (11.4%).
