# Regression to the mean

Consider the following statement made up by Daniel Kahneman author of Thinking Fast and Slow

Depressed children treated with an energy drink improve significantly over a three-month period.

What do you infer from this? Most likely you will think that the energy drink improved the depression among children. But it could also be that children who were depressed and did not have any energy drink could have improved significantly. Excerpt from the book

Most readers of such headlines will automatically infer that the energy drink or the cat hugging caused an improvement, but this conclusion is completely unjustified. Depressed children are an extreme group, they are more depressed than most other children – and extreme groups regress to the mean over time.

Most of us have the tendency to attribute meaning to phenomenon governed only by chance. From the book Innumeracy: Mathematical illiteracy and its consequences

A good example is provided by regression to the mean, the tendency for an extreme value of a random quantity whose values cluster around an average to be followed by a value closer to the average or mean. Very intelligent people can be expected to have intelligent offspring, but in general the offspring will not be as intelligent as the parents. A similar tendency toward the average or mean holds for the children of very short parents, who are likely to be short, but not as short as their parents. If I throw twenty darts at a target and manage to hit the bull’s-eye eighteen times, the next time I throw twenty darts, I probably won’t do as well. This phenomenon leads to nonsense when people attribute the regression to the mean to some particular scientific law, rather than to the natural behavior of any random quantity.

## Correlation and Regression are the same

Regression to the mean was discovered and named late in the nineteenth century by Sir Francis Galton, half cousin of Charles Darwin. Galton figured out that correlation and regression are not two concepts and they are different perspectives of the same concept.

The general rule is straightforward but has surprising consequences; whenever the correlation between two scores is imperfect, there will be regression to the mean.

Here is an explanation from Wikipedia

Galton showed that the height of children from very short or very tall parents would move towards the average. In fact, in any situation where two variables are less than perfectly correlated, an exceptional score on one variable may not be matched by an equally exceptional score on the other variable. The imperfect correlation between parents and children (height is not entirely heritable) means that the distribution of heights of their children will be centered somewhere between the average of the parents and the average of the population as whole. Thus, any single child can be more extreme than the parents, but the odds are against it.

## Profiting from regression

Regression to the mean is the most powerful law in finance. Periods of above average performance are inevitably followed by below average returns. Similarly periods of below average performance are inevitably followed by above average returns. In the excellent article The Intelligent Investor: Saving Investors From Themselves – Jason Zweig writes

My role, therefore, is to bet on regression to the mean even as most investors, and financial journalists, are betting against it. I try to talk readers out of chasing whatever is hot and, instead, to think about investing in what is not hot. Instead of pandering to investors’ own worst tendencies, I try to push back. My role is also to remind them constantly that knowing what not to do is much more important than what to do. Approximately 99% of the time, the single most important thing investors should do is absolutely nothing.

Until late last year experts were talking about why investors should buy gold. Given below is the 2 year gold price in USD for 1 ounce. It hit an all time high of \$1900 and currently it is selling for around \$1350 down more than 30%.

The S&P/Case-Shiller 20-City Composite Home Price Index measures the value of residential real estate in 20 metropolitan areas of the U.S. The chart given below should tell us the story of regression to mean perfectly.

If we all internalize the regression to mean concept then we can protect ourselves from the downside. As Charlie Munger tells

All I want to know is where I’m going to die so I’ll never go there.