Latticework of Mental Models: Mean Reversion

This article is the fourth of this new weekly series called Latticework of Mental Models, which will be authored by my friend and partner in writing the Value Investing Almanack, Anshul Khare. Anshul will write on various mental models – big ideas from various disciplines – which can help you think more rationally while analyzing businesses and making your stock investment decisions.

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There are certain days in everybody’s life which in spite of being ordinary remain etched in the memory for a long time. It was 15th of December. I distinctly remember it because I bought my car that day.

The ownership of new car brought with it an excitement to take care of it which included an urge to diligently track the car mileage. You know, boys with toys. At an average of 13 km/litre it was a satisfactory performance. However, after few weeks I started noticing that the mileage numbers would go down occasionally and then come back again to the normal.

There wasn’t any change in my driving style or driving routes. Except the source of fuel there was no other variable that could cause the variation in performance. So my hypothesis was that the quality of fuel was affecting my vehicle’s performance. To empirically validate my theory I decided to keep track of different fuel stations where I got the petrol from.

The next time when I saw a dip in the mileage numbers I went to a different fuel station and the improvement in the numbers followed. This made me conclude that my earlier fuel station was the culprit. Having discovered this, yours truly (i.e. me) proudly announced his statistical prowess to everybody and asked them to avoid that particular fuel station.

Now before I tell you the rest of the story, I’ll give you a chance to answer this question – “Was my conclusion correct?”

The second part of the story is where my stupidity is revealed. Not long after discovering and avoiding the “dishonest fuel pump,” I started seeing those mileage fluctuations again. Obviously my earlier deduction was flawed. So what happened then?

Daniel Kahneman recounts a similar experience in his book Thinking Fast and Slow. While teaching flight instructors he was told how the act of praising the pilots on a recent good performance usually resulted in a poorer performance subsequently and vice versa. This logic goes against the conventional motivation theory that encouragement leads to improved performance.

According to Kahneman, the flaw in their reasoning was that they had attached a causal interpretation to the inevitable fluctuations of a random process.

Let’s try to understand the concept in light of my mileage counting experiment.

The reality was that my mileage numbers were experiencing fluctuations due to randomness and there didn’t exist any specific pattern. Even if I hadn’t changed my fuel station, I would have seen the mileage numbers improving anyway because the numbers were simply fluctuating around a mean. This phenomenon is called Mean Reversion. It’s a mental model from the field of statistics.

Reversion to the mean says that an event that is not average will be followed by an event that is closer to the average. I was suffering from the tendency to attribute meaning to a phenomenon governed only by chance.

Here is an interesting insight from the book Innumeracy: Mathematical Illiteracy and Its Consequences –

…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.

Nassim Taleb in his book Fooled by Randomness observes –

“The ‘hot hand in basketball’ is another example of misperception of random sequences: It is very likely in a large sample of players for one of them to have an inordinately lengthy lucky streak. As a matter of fact it is very unlikely that an unspecified player somewhere doesn’t have an inordinately lengthy lucky streak. This is a manifestation of the mechanism called regression to the mean….in real life, the larger the deviation from the norm, the larger the probability of it coming from luck rather than skills…This can be easily verified in stories of very prominent people in trading rapidly reverting to obscurity, like the heroes I used to watch in trading rooms.

Let’s see some of the areas where mean reversion wreaks havoc. Okay not havoc per say but it does raise some serious concerns about our decisions.

Your Doctor’s Secret Weapon
Let me introduce you to my friend Mr. Irrational, a figment of my imagination, inspired by Ben Graham’s Mr. Market. You will be hearing a lot of stories about him in coming weeks.

So Mr. Irrational isn’t keeping well and his body has been home to the common cold virus for past few days. But the good news is that his immune system is strong enough to fight the virus and heal itself, although this healing process usually takes few days.

After two days of discomfort, right when his body is on the verge of bouncing back to normal healthy state, Mr. Irrational decides to visit his doctor, Dr. Placebo. Now Dr. Placebo is afflicted by another kind of behavioural anomaly called “Do something Bias” but let’s save that story for another day.

Dr. Placebo prescribes a mild antibiotic drug, which is quite unnecessary in this case. The very next day Mr. Irrational is back to normal, healthy as a horse. He concludes, irrationally of course, that Dr. Placebo has the ability to cure any disease in a single day.

The inherent randomness present in the natural process of falling sick and healing back makes it an obvious candidate for mean reversion. Alas! Mr. Irrational hasn’t heard about mean reversion.

Scope of Mean Reversion
It’s very important to understand that reversion to the mean is meaningful only in those activities or situations where there is some element of randomness involved. The intensity with which mean reversion affects an activity is directly proportional to the element of luck controlling the outcome in that activity.

So if you are looking at something like professional swimming and recording the lap time for Michael Phelps, it won’t be a revelation that the outcome (lap timings) stays pretty much consistent with very little scope for reversion to the mean.

Sports like swimming or chess are activities where luck plays relatively small role. They are dominated by skill resulting in a very consistent and predictable outcomes. I am not saying that all sports enjoy the same level of predictability. Games like Cricket, Basketball and especially many other team sports have quite a bit of luck dictating the end result.

When it come to my car mileage there were myriad of factors like traffic conditions, road condition, the minor fluctuations in my driving style, the weather, wind speed etc which affected the mileage. The randomness introduced by these environmental factors makes this activity prone to mean reversion.

Mean Reversion in Investing
You would agree with me that stock market investing is also one such activity where luck plays a significant role in investor’s performance.

Consider this typical process that many investors follow. They look at the last few years’ performance of a fund manager and put their money in his fund. Soon they observe that the fund underperforms the benchmark for next few years. Frustrated and flabbergasted, they pull out the money and find another fund manager based on the same criteria i.e., last few years’ performance.

The naive investor is clueless why the fund performance deteriorates immediately after he puts his money into it. Mean reversion buddy!

In stock market periods of above average performance are usually followed by below average returns and periods of below average performance are typically followed by above average returns.

Every value investor loves to quote Buffett’s following statement –

Be greedy when others are fearful and be fearful when others are greedy.

I smell mean reversion here. Do you?

And that’s why it’s essential that you shouldn’t go just by the outcome (fund performance) of such activity. The trick is to look at the process that leads to the outcome. Choose the process which is sound and rational.

The second trick for dampening the effect of mean reversion is to take a bigger sample size. Which means you shouldn’t rely on short term performance records. If you are looking at ten year performance figures of a fund then odds are high that the fluctuations introduced by randomness and luck have evened out over long term and what you see is a reasonable proxy for fund manager’s skill.

Illusion Created by Mean Reversion
So we see that mean reversion creates two kinds of illusions.

The first is the illusion of cause and effect. Out inherent tendency to look for what is causing a measurement to regress toward the mean, an exercise that is frequently fruitless.

The second is the illusion of feedback, which makes it seem like favourable feedback leads to worse results and unfavourable feedback leads to better results.

Michael Mauboussin, author of The Success Equation, writes in his book –

Understanding and using the phenomenon of reversion to the mean is essential in making sound predictions [decisions]… Reversion to the mean is most pronounced at the extremes, so the first lesson is to recognize that when you see extremely good or bad results, they are unlikely to continue that way. This doesn’t mean that good results will necessarily be followed by bad results, or vice versa, but rather that the next thing that happens will probably be closer to the average of all things that happen.

When I first understood the concept of mean reversion, a bulb went off in my mind. It was one of those aha moments of life. Suddenly I had an answer for a lot of unexplained observations around me.

Daniel Kahneman, the father of behavioural economics, had a similar experience when he saw the live performance of mean reversion. He says –

This was a joyous moment of insight, when I saw in a new light a principle of statistics that I had been teaching for years.

Remember, the only reason mean reversion happens is because of randomness. Anytime you hear that mean reversion is happening because of competitive forces, declining moat, etc. wear your lens of mental models and then investigate further.

In the current world of digital revolution and information explosion, it has become increasingly important for you to build a strong bullshit filter to separate the noise from real knowledge. Mean reversion is one such bullshit filter that should be an important node in your latticework of mental models.

Goes without saying that not every deviation from the norm is because of randomness or mean reversion. I would like to re-iterate here that relying on just one mental model to explain everything around you is dangerous. Don’t become the man who goes on nailing every problem with his single hammer.

Let me take the risk of being repetitive and tell you again – the best way to learn anything is to teach. I urge you to find few friends and partners with whom you can share these ideas. Because that’s precisely what I am doing right now, hoping that I get a better handle on these mental models.

Mr. Irrational joins me in bidding you goodbye till next week. Take care and keep learning!