Fintech with Todd
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Fintech with Todd

The Sound of Markets

Ding, ding, ding is the sound most closely associated with the New York Stock Exchange. Every weekday morning that bell tone signifies the start of trading and at 4:00pm the same bell closes the exchange.

The sound to start and stop trading was not always a bell. Originally it was a gavel. Later it became a gong. Not until moving to the current location of 18 Broad Street in 1903 was the gong replaced with a bell.

Besides the bell, the floor of an exchange was a noisy place. People shouting orders, emotional utterances, exuberant cries, and the general shuffle of controlled pandemonium echo through the room. However, those sounds are becoming silent as fewer of the players interact in person.

Sound and Markets

The new sound of the exchange is muffled computer fans while the market itself is a symphony of sound. Not an audible collection of notes but a post-modern movement of waves.

To illustrate, the following diagram is a chart representing the price movements of a stock over a period of time.

Now, compare that to a chart of sound waves over time from a collection of notes being played.

Both the music and the price chart represent waves and both appear to illustrate ordered patterns and cyclic behavior. A man named Ralph Nelson Elliot came to a similar conclusion during the late 1920’s. He found that markets cycle in waves as people experience the upward and downward swings of mass psychology.

Wave Theory

Elliot Wave Theory as the theory became known is based heavily on Newtons Third Law of Motion which states, “For every action there is an equal and opposite reaction.” Elliot concluded that for every price movement, up or down, there was a counter movement pulling in the opposite direction.

That does make sense as making a sell requires a buyer. Thus for all the people wanting to own a stock, there is another who want to sell at the same time. Elliot discovered there are five waves in the direction of the main trend followed by three correcting waves in what he coined a 5–3 move.

The 5–3 move remains constant even thought the timeframe may very as illustrated below.

Waves (1), (3) and (5) actually affect the directional movement. Waves (2) and (4) are counter trend breaks. The two breaks are apparently a requisite for overall directional movement to occur. Elliot discovered that the stock market was always in one of these 5-phase patterns.

Analysis at New Zeland’s PNG conclude, “Waves come insteps, the smaller being the building blocks for the larger. The waves link together to form larger versions of themselves, and they also link together to form the same patterns at the next larger size, and so on. Some of the largest wave patterns span hundreds of years, while some of the smallest span a few hours.”

This theory appears to provide a trader with a good probability of what the market will or will not do next — advertised as greatly reducing speculative risk. Surprisingly, the mathematician famous for fractals, came to similar conclusions as Elliot. Mandelbrot, however, concluded that markets are much more random than few ever realized and ultimately impossible to predict.

Random or Predictable

It is clear that markets, like oceans and sound, move in waves. The question is who is correct? Are this waves random as Mandelbrot suggests or predictable as concluded by Elliot? The answer may come down to the timing of their study. When Elliot was doing his research in the 1920’s, the stock market was much smaller and manual in it’s transactions. Contrast that to Mandelbrot’s last works over the early 2000’s and it could be the result of studying two different markets.

Perhaps it is an evolution of markets as human participants are replaced by computers that movements become more chaotic. Maybe it is the result of computer based decision making shedding light on humans’ ignorance of the entire heuristic.

Before going to far down this hole, it is important to note that Mandelbrot began by studying cotton prices from the 19th and early 20th century. He concluded in a 1963 paper that these prices do not follow the bell shape curve of a normal distribution. Elliot did not subscribe to the normal distribution either and may have agreed with the paper.

When one reads a paragraph into a computer recorder and watches the waves generated by their voice, a pattern is generated. However, reading the same paragraph again will show differences between the two. Repeating the experiment will continue to change the pattern as the speaker starts to memorize the words, anticipate the changes, and create a rhythm of speech.

Is it likely that as markets evolve, the patterns change as the sound of one reading cold versus practiced? Was Elliot correct in 1920 but due to changes in technology is no longer applicable today? Perhaps both Elliot and Mandelbrot are correct — one from the perspective of a market analysis and the other as a mathematician.

Mandelbrot Model

Mandelbrot discovered that fractal mathematics could be used to mimic market behavior. This model is based on 5 rules: markets are risky, trouble runs in streaks, markets have personality, markets mislead, and market time is relative. It was meant as a framework for reducing risk and shares many similarities with Elliot’s Wave Theory.

Rule 1: Markets are risky

Extreme price swings are the norm in financial markets — not aberrations that can be ignored — Benoit Mandelbrot

The first rule is really an iteration of his 1963 conclusion that prices are turbulent and do not follow a bell curve. Anyone who has traded real money probably experienced this one — especially in immature markets such as the crypto exchanges.

Rule 2: Trouble runs in streaks

Market turbulence tends to cluster. — Benoit Mandelbrot

His second rule deals with the fact that turbulent prices lead to more chaotic conditions for some time. Similar to oceans, if the market opens choppy it is likely to continue that way.

Rule 3: Markets have personality

When investors, speculators, industrialists, and bankers come together in a real marketplace, a special, new kind of dynamic emerges — greater than, and different from, the sum of the parts. — Benoit Mandelbrot

Rule three makes a bold claim that markets move at a rate and sometimes direction beyond the events, people, and news effecting them. This is often contrary to much investment advice. However, Mandelbrot’s study is backed by solid evidence that markets have unforeseen forces moving them in ways sometimes contrary to human intuition.

Rule 4: Markets mislead

Patterns are the fool’s gold of financial markets. — Benoit Mandelbrot

The fourth rule ensures with mathematical certainty that patterns in market pricing are the subject of human imagination. This is contrary to Elliot in that he believed markets have predictable patterns but in unpredictable time. Mandelbrot goes further to conclude the bubbles and crashes are the result of erroneous human behavior acting on fictitious patterns.

Rule 5: Market time is relative

[M]arkets as operating on their own “trading time” — quite distinct from the linear “clock time” in which we normally think. — Benoit Mandelbrot

Mandelbrot’s rule five is inline with Elliot as they both agree in a non-clock time for markets. Elliot concludes patterns exist in short periods and larger ones over the span of one-hundred years. Mandelbrot concludes volatility is the driver for market time and dedicates much ink to the subject.


In building a deep learning trading system, it is important to avoid human pre-conception. As a student of Mandelbrot, one is tempted to throw out the theories from the past. However, this is proving valuable study as a means of formulating the questions desired to be answered by the machine.

It is tempting to build a machine learning system hard-coded with Mandelbrot’s theory. However, if the AlphaGo team built their machine based on the best human players, it would not of been able to beat them.

The prudent course of action on finding definitive answers to market theory is to create a machine capable of discovering the truths for itself. That way it is no limited by human pre-conceptions.

Thank you for reading.



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