The Three Illusions of Reversion to the Mean. (Part 2)
Reversion to the mean creates three illusions - cause and
effect, feedback and declining variance, (Mauboussin, The Success Equation).
1. Illusion of
Cause and Effect – The human mind has an innate programming to want to explain
occurrences by finding the cause of them, even if there isn’t one. Yet, reversion to the mean is a
“statistical artifact,” that our minds try to interpret with a cause that often
is not there, (Mauboussin).
Reversion to the Mean “happens without the need of a
cause.” This is problematic to our
minds with that need to assign one, even if it causes an error.
“The DOW fell 2% on the back of weak employment data.” No – it probably just regressed back
towards its 50 day Moving Average, more likely.
2. Illusion of
Feedback – The idea here is that after an event, you take an action and believe
that this causes the next event to occur as a result of that, even though reversion
to the mean might be all that is occurring.
Mauboussin’s example of doctors is: You have higher blood
pressure than your last consultation, which the doctor treats with a drug. Blood pressure subsequently lowers
towards the average at the next consultation, which the doctor believes is due
to his treatment (which it may, or may not be). But in the whole population, everyone’s blood pressure would
revert towards the mean with or without treatment.
The illusion of feedback will persuasively suggest that the
treatment was the cause and lower blood pressure the effect,” (Mauboussin). Clearly the illusion of feedback plays
right into the hands of the illusion of cause and effect, and the narrative
produced can be a strong and highly erroneous belief.
3. The illusion
of Declining Variance – (the hardest to conceptualize) is the illusion that as
something moves to its average, the variation in the numbers shrinks. This is not necessarily the case, and
sets a trap in our analysis. In
other words as stock price reverts to its mean, it does not imply that the individual
prices observed will cluster closer together around the mean, as would be
evident by a closer standard deviation.
The chart below shows how price reverts to its mean at P
from Po, variance increases initially as price begins to move, but then
stabilizes, yet does not contract, as the illusion would dictate.
Also, reversion to the mean occurs even when the statistical
properties of the distribution remain unchanged (Mauboussin). According to Bob Jensen at Trinity
University it looks like this:
The red line can be flipped to show a declining price
reversion to the mean with similar variance results.
Mauboussin’s final point on the Illusion of Declining
Variance offers the warning that; “None of this is to say that results cannot
exhibit a decline in variance over time… But just because you observe reversion
to the mean, that’s doesn’t suggest that individual outcomes are converging
toward the average.”
Summary:
Reversion to the Mean does not need a cause.
We fail to predict to an adequate amount its effect when
making predictions about the future.
Reversion to the Mean is most pronounced at extremes. Things that are great won’t stay that
great, things that are terrible rarely stay that terrible.
When a lot of luck is involved Reversion to the Mean is
stronger, and inevitable.
The paradox of skill, (increases in the skills of investors
and access to information, has narrowed the skill variation in the population,
making luck more important in success), has lead to an increase in the power of
Reversion to the Mean, (Mauboussin).
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