Double Pendulums and Chaotic vs Random Market Behaviour

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15 Feb Double Pendulums and Chaotic vs Random Market Behaviour

Everyone would be very familiar with the pendulum. Take a weight and suspend it from a pivot. It is stationery while at rest. When it is displaced and released, gravity causes the pendulum to swing back and forth. Since the ancient ages, pendulums have been used for timekeeping.

The double pendulum is yet another interesting phenomenon. Instead of just one weight, what happens if we suspend another pendulum at the bottom of the first. Have a look at the following.

The pendulum moves in a seemingly hap-hazard manner, without any discernible pattern whatsoever.

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To make it even more interesting, here is what you get when you put together two identical double pendulums, but yet vary their starting point by a teeny weeny bit. The pendulums trace an entirely different path.


In the simulation on the right, the starting point of the blue pendulum is about 6 degrees above the x-axis.

Chaos and Randomness

According to physicists, the difference between chaos and randomness is that random behaviour has no deterministic qualities. That is, you cannot tell from previous physical conditions what is going to happen, whereas chaotic behaviour, despite seeming random, are actually predictable.

An example of this is our weather systems. Snow storms and typhoons, heat waves and droughts. They are the result of the interaction between the different elements of our climate. They may seem complex and entirely random to the beginner, but to the trained meteorologist they are deterministic in nature. In other words, given the right amount of information, weather can actually be predicted and forecasted with reasonable accuracy.

Going back to the double pendulum. To me, it is just a couple of swinging sticks drawing some (nice) patterns. To my untrained eye, it looks to be a totally random phenomenon. Yet, when presented with all the required information, physicists can calculate the movement of the double pendulum accurately. They are able to tell with great precision where the positions of the sticks will be at each moment in time.

A Random Walk down Wall Street

Princeton Professor Burton Malkiel published the classic A Random Walk Down Wall Street in 1973. He built upon the Efficient Market Hypothesis and argued that asset prices exhibit signs of random walk and cannot consistently outperform market averages.

Using research from other academics, he tore apart many investing strategies, going as far to suggest that stock prices follow a random and unpredictable path. The premise of the Random Walk Theory is that stock prices are totally random and that attempting to use past prices to predict future movement is futile. He goes further to state that it is impossible to outperform the market without assuming additional risks.

In our context today, Malkiel’s stand is that prices are random and not chaotic.

What do you believe in? 

If you are an investor and you assume Malkiel’s position, you would have purchased an index fund and let the overall market work in your favour. Of course, on the other extreme, if you are an investor that puts in zero analysis into your investing decisions, preferring to act on stock tips and gut feel, you are also serendipitously in this same camp.

On the other hand, if you practice Fundamental Analysis or Technical Analysis, choosing to study and gain knowledge of the companies before you purchase their stock, you are in a different camp altogether.

You are effectively saying that even though markets can be chaotic, but given the right amount and successful application of these information, you are able to predict the future movement of stock prices. Just like how physicists are able to calculate the exact movements of the double pendulum.

Which camp do you belong to?

TL;DR – There is a difference between chaotic systems and random systems. Chaotic systems appear random – they are actually not. If you practice technical and fundamental analysis, you believe that the market is chaotic and deterministic.

images: flickr George Iaonnidis, foriestseries



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