Friday, December 5, 2014

The Importance of Reversion To the Mean in Investing. (Part 2)

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.”

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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