Random walks and butterfly effects on Wall Street

Field of play

Past price increases generate expectations

In this post I propose to tie together two related phenomena. First is the notion of random events. The second is the so called butterfly effect.

Many of the ideas in this post come from a 2008 book by Leonard Mlodinow titled The Drunkard’s Walk – How Randomness Rules our Lives. Mlodinow is an American theoretical physicist and mathematician who has written many books making science accessible to non-experts.

He writes in the prologue: “The title The Drunkard’s Walk comes from a mathematical term describing random motion, such as the paths molecules follow as they fly through space, incessantly bumping,  and being bumped by their sister molecules. That can be a metaphor for our lives, our paths from college to career, from single life to family life, from first hole of golf to eighteenth. The surprise is that the tools used to understand the drunkard’s walk can also be employed to help understand the events of everyday life.” (Mlodinow, 2008) p.xi

We will look at how this might apply to the stock market.

Incidentally, I’m well aware of Burton Malkiel’s A Random Walk Down Wall Street, first published in 1973 which sold over 1 million copies. I disagree with much of Malkiel’s book.

Mlodinow tells us that the butterfly effect was discovered by a weather researcher in the 1960s. In doing computer simulations he found that a small change in initial conditions created wildly diverging results. The phenomenon was dubbed the butterfly effect. Mlodinow writes: It is “based on the implication that atmospheric changes so small they could have been caused by a butterfly flapping its wings can have a large effect on subsequent global weather patterns. That notion might sound absurd – the equivalent of the extra cup of coffee you sip one morning leading to profound changes in your life. But actually that does happen – for instance if the extra time you spend caused you to cross paths with your future wife at the train station or to miss being hit by a car that sped through a red light.” (Mlodinow, 2008) p.194

Feedback effects, groupthink and influencers

Let’s think about whether butterfly effects can come into play in the stock market. When we think about this lets keep in mind the question of whether prices in the stock market always reflect the true intrinsic value of the security being traded.

A parallel question might be whether good music has intrinsic value. In both cases, humans are the judge and there are subjective elements. And it seems, we are influenced by what others think.

In 2006 researchers published a study of 14,341 participants who were asked to listen to 48 songs by bands they had never heard of. If they chose, they could download the songs. They also had to rate the songs. The participants were grouped into nine separate ‘worlds’. In each of the first eight worlds the participants could see how many times songs were downloaded by their fellow world mates, but not by participants in other worlds. In the ninth world, none of the participants could see data either from fellow ninth world mates or from other worlds.

If the intrinsic quality of the songs had determined the outcomes, each of the worlds would have roughly liked the same songs. The researchers found exactly the opposite. As Mlodinow explains: “…as one song or another by chance got an early edge in downloads, its seeming popularity influenced future shoppers. It’s a phenomenon that is well known in the movie industry: movies goers will report liking a movie more when they hear beforehand how good it is. In this example, small chance influences created a snowball effect and made a huge difference in the future of the song. Again, it’s the butterfly effect”. (Mlodinow, 2008) p.206 (emphasis added)

What strikes me is the parallel with the stock market. In the stock market there are various feedback loops at play. The simplest is that the price of every stock trade is published for all to see. These represent psychological anchors and lead by themselves to feedback and groupthink. Another is that analysts’ price targets and earnings estimates are widely disseminated. Then there is social media. There are other avenues of communication that can lead to feedback.  

It’s not just Tesla and meme stock prices that have seen these effects. Sometimes the consensus favours one company or sector (think tech or oil); a snowball or butterfly effect takes hold and prices sore. Then that stock or sector goes out of favour and another sector is hot. The effect can work in reverse. A well regarded company or favorite sector can fall off its perch and languish in woebegone lands, all caused by a butterfly.

More on feedback loops

Shiller writes: “In feedback loop theory, initial price increases … lead to more price increases as the effects of the initial price increases feed back into yet higher prices through increased investor demand. This second round of price increases feeds back again into a third round, and then into a fourth, and so on.” (Shiller, Irrational Exuberance, 2005 Second Edition) p.68.     

He adds: “In the most popular version of the feedback theory, one that relies on adaptive expectations, feedback takes place because past price increases generate expectations of further price increases. In another version of the feedback theory, feedback takes place because of increased investor confidence in response to past price increases. Usually such feedback is thought to occur in response not so much to a sudden price increase as to a pattern of consistency in price increases.” (Shiller, 2005 Second Edition)p.69

The idea of a feedback effect in human affairs is fairly well accepted. Ian Hacking, a professor at the Institute for the History and Philosophy of Science and Technology at the University of Toronto, in his profound “epistemological study of the social and behavioral sciences, with consequences for the concept of causality in the natural sciences,” which he titled The Taming of Chance, expresses the view that: “The human sciences display a feedback effect not to be found in physics.” (Hacking, The Taming of Chance, 1990, twelfth printing 2009) p.7.  (Emphasis added)  

Back to molecules bumping through space

The price of a stock or a price change in a stock or of a group of stocks can be part of a data series. Let’s think about whether this data series follows a drunkard’s walk. Is it like randomly bumping molecules?

As Hacking points out, we may look in vain for feedback effects in molecules.

The technical definition of randomness in a data series is that the data must be independent. No one argues that stock prices are random over the long haul. It is my humble opinion that stock prices are not even random in the shortest term i.e. from minute to minute or even from second to second. That is because every buyer knows the previous price at which a stock traded. Stock price changes over any short period of time may be truly unpredictable, but that does not mean they are random. They are not a series of independent data. I don’t think anyone would argue that you could use a data series of stock prices or stock price changes to create a list of random numbers.


Mlodinow’s essential thesis is that random processes are everywhere and impact our lives more than we realize. They may as Mlodinow suggests be a metaphor for our lives but we cannot apply the tools of randomness blindly to either our lives or the stock market. What I have tried to do in this post is to build on Mlodinow’s thesis and point out that we can apply some of the lessons we learn from randomness in science but that we must be careful in applying them to the stock market. The stock market is a complex adaptive system that operates with feedback loops. Blindly using models based on the motion of molecules to understand the stock market doesn’t get us there.


As an illustration of how the behavioral tail can wag the statistical dog in understanding the stock market, take a look at this post:

Does Wisdom of Crowds apply to earnings estimates, price targets, value estimates and stock prices?

On the shortcomings of math and models. Math and algorithms will give precise answers. And therein lies the problem. Check out this post:

Do quants with algorithms have an advantage over other investors?


You can reach me by email at rodney@investingmotherlode.com

I’m also on Twitter @rodneylksmith


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