Mean Reversion and Regression Toward the Mean

In the past I have incorrectly assumed mean reversion and regression toward the mean to be essentially the same thing. According to Wikipedia:

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first. To avoid making incorrect inferences, regression toward the mean must be considered when designing scientific experiments and interpreting data.

In finance, the term mean reversion has a different meaning. Jeremy Siegel uses it to describe a financial time series in which “returns can be very unstable in the short run but very stable in the long run.” More quantitatively, it is one in which the standard deviation of average annual returns declines faster than the inverse of the holding period, implying that the process is not a random walk, but that periods of lower returns are systematically followed by compensating periods of higher returns, in seasonal businesses for example.

I’ll be honest and just say the above doesn’t really explain to me how they are different outside of one term being used in statistics and the other in the world of finance. But for our purposes and looking at the big picture or the big idea, we care about the concept of extreme observations and how they are more likely to be followed by less extreme ones. For the purposes of this article, I will use reversion and regression interchangeably unless otherwise noted.

There are several examples that are often used to demonstrate mean reversion such as the basketball player who ‘catches fire’ and can’t seem to miss. More likely than not after some time has passed, the player will regress to his/her usual shooting percentages. The opposite would also hold true. Another example, highly intelligent parents in general are not expected to have offspring as intelligent as themselves (ignoring the structural advantages that may be present).

Outliers from the expected average can more often than not be attributed to randomness and small sample sizes.

Let’s move towards its significance to the world of finance. Consider the following from Jason Zwieg:

From financial history and from my own experience, I long ago concluded that regression to the mean is the most powerful law in financial physics: Periods of above-average performance are inevitably followed by below-average returns, and bad times inevitably set the stage for surprisingly good performance.

In other words, investments can be priced far above or far below their long-term average returns for periods of time, but in the end they eventually tend to move back towards their average. Outperformance is followed by underperformance and vice versa. To the contrarian investor this translates to buy low and sell high.

We can also note the tendency for people to create narratives and attribute causes to effects while completely ignoring the mental model of reversion/regression to the mean. A prime example of this is, “this time it’s different because…”.

We cannot say with certainty that when one observes fairly favourable/unfavourable results that the opposite will immediately occur. But we can surmise that the probability increases as extremes are reached.

Finally, regression/reversion to the mean is one mental model to consider when filtering information that comes your way and should not be used exclusively as real changes do occur which can explain a long-term and sustainable drift away from averages.

 

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