Novelty, Unicorns and the Stressed Investor

Bad Hair Days

There’s a Groundhog Day effect in financial markets: wait long enough and another crisis will occur and everyone will be stunned and surprised. In fact they’ll be just as stunned and surprised as they were the last time one occurred. We’ve the attention span of a distracted goldfish when it comes to noticing the disconcerting regularity of market mishaps.

But although market upheavals are frequent they’re not so frequent that we get used to them. The steady state is a constant background hum of noise punctuated by occasional bouts of excitement over some stock or other. When a crisis occurs it’s a novelty – and for most of us our response to novelty is to get stressed, and then run around like our hair is on fire. By and large, I'd observe, this is not optimal investing behavior.

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Eat Your Stocks

Much Ado About Nothing?

Scientists study stuff which exist: physicists the physical laws of nature, biologists the nature of life and psychologists the human mind. Economists, on the other hand, study money: which is surely a figment of the human imagination.

Given the ephemeral nature of the subject it’s a wonder that there’s any mileage in spending any effort on the subject at all, but huge amounts of time and money are expended in doing so. So if money is fundamentally unreal, what the hell is economics all about?

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Memes, Money, Madness

Meme Machines

The appearance and disappearance of investment themes over time is a fact of life – remember “you can’t lose with the railways”? Me, neither, but in the 1840’s it was a guaranteed winner until it wasn’t.

Other dubious ideas have more legs, like the Efficient Market Hypothesis and the theory that most analysts can figure out which shoe goes on which foot. All of these ideas influence markets and participants and help move prices, sometimes with startling synchronicity. A popular theory of how this happens is based on the idea of the meme, a cultural equivalent of the gene, propagating itself through human brains and influencing group behaviour. So are we meme machines, buying stocks at the whim of transient ideas?

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Cyclical Growth, Form and Fibonacci

Ancient Ideas, Modern Setting

As an up-to-date in-your face sort of blog we like to make sure our readers are well informed about the financial world as we see it. So, starting back in Ancient India in 200BC and taking in medieval Italy and some early twentieth century anti-Darwinian evolutionary thinking let’s take a look at plant growth and snail shells, how twentieth century humanity’s inclination to see the Man in the Moon translates into modern financial theory and why physics may simply be wishful thinking.

At the root of this journey is a simple mathematical progression named after a man who never discovered it and was more concerned with accountancy than trading. Still, he’s still remembered a millennium after his death, which is more than most of us can ever aspire to.

The Golden Ratio

In 1202 the Italian mathematician Leonardo of Pisa, aka Fibonacci, wrote Liber Abaci, a book which has three claims to fame in financial circles. Firstly it was one of the first books to introduce the Arabic numbering system to the West. Secondly it laid out the foundations of modern bookkeeping. Thirdly it presented the number pattern known as the Fibonacci sequence, although this had been known long before by Indian mathematicians. Only the latter has little significance in the development of science and business but, naturally, it’s the one that’s received the most attention.

The Fibonacci sequence is that that which starts with 0 and 1 and proceeds by adding the previous two numbers in the sequence to create the next one. So you get: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc, etc. Divide any Fibonacci number by the one below it and, as you get higher up the sequence, you get closer and closer approximations to the so-called golden ratio of 1:1.618.

Fibonacci in Living Form

As a piece of pure mathematics the sequence is unremarkable until you start digging around in the real world and find it appears regularly in nature. It can be found in many forms – in the arrangements of leaves around a stem, in the structure of sunflowers and pine cones and the shape of snail shells. The appearance of the golden ratio in nature has led many people to suspect that it embodies some kind of mystical significance. These people are idiots, of course, but idiocy has never been a bar to success in this world.

The true explanation for the presence of the Fibonacci sequence in nature was provided by D’Arcy Thompson back at the beginning of the twentieth century. In an age where evolution was accepted but the genetic code underlying it was not widely known Thompson was not alone in trying to find alternative explanations for natural selection. In the unique and beautifully written On Growth and Form he showed how many of nature’s creatures were adaptations of simple geometry rather than difficult evolutionary changes.

Essentially, Thompson argued that there were a few geometric forms suitable to life on Earth and by changing the morphology of these you could explain the majority of physical animal shapes. As an example, he showed how changing a few physical parameters could generate the whole range of different crab shapes found in nature. On a similar note, he showed how the golden ratio is the best physical adaptation to the shape of snail shells.

Order Out of Chaos

The existence of Fibonacci sequences and the golden ratio in nature is therefore not the result of some divinely inspired meddling but the process of natural selection figuring out the best forms for survival. It so happens that Fibonacci numbers offer the most optimal form of growth or packing for certain creatures and that natural selection has, though its normal process of trial and error, figured this out. It’s not that the golden ratio is “out” there, it’s simply that nature finds an efficient way of managing its resources to best effect.

Indeed the golden ratio is a trend rather than a fixed rule. Many flowers, for instance, don’t use Fibonacci numbers and the oft-quoted “fact” that the golden ratio defines the proportions of a human is simply wrong. In fact, judging by the preference of artists down the ages, it’s not even the preferred ratio of human beauty. Statements alleging that the golden ratio is everywhere and unavoidable are, simply, nonsense propagated by mystics and financial theoreticians. Not that there’s much difference between the two, usually.

Elliot Waving Not Drowning

The appearance of this mathematical sequence in nature, however, convinced many people that there was something special about it. As we’ve seen in recent times there’s no industry more attracted to mathematical solutions to complex problems than the financial sector and this isn’t simply a recent trend. The search for the magic formula for making money with no risk and less brainpower has been around for about as long as money has.

Back in the 1930’s Ralph Nelson Elliot developed a technique for forecasting market price movements which he, at some point, decided was based on the Fibonacci sequence. The principle of the Elliot Wave is that collective human psychology drives moves from mass optimism to mass pessimism and then back again. In Elliot’s reconstruction the ebb and flow of the markets is done in an eight step process, five up and three down, ranging over timescales from minutes to a grand supercycle of multiple centuries. According to Elliot the Fibonacci numbers simply appeared out of his theory, although there’s no known underlying principle to explain this. It’s just the way the world works, presumably: shake your chakra, baby.

For reasons we don’t quite understand humanity seems to have a drive to see cyclical behaviour in nature. Going all the way back to Ancient Greece the circle was viewed as the symbol of perfection and a whole model of physics was generated out of this, complete with circular orbits around the Earth. When the universe failed to play ball with the theory, by making planets seen from the Earth go backwards the scientists naturally refused to change their theory and instead developed an elaborate and wondrous system of epicycles, circles within circles.

Epicycles in Finance

Of course, the model was wrong, being based on a false premise, just as models of stockmarket behaviour based on Fibonacci sequences are wrong. The golden ratio exists in nature because it’s the optimal solution to specific problems, not because the universe is designed that way. Our projection of pure mathematics onto the universe’s haphazard geometric best fit engineering solution seems like as good a metaphor as any for the way that modern physics is trying to understand how our universe is put together. Instead, maybe it’s just the only way of making the damn thing work.

In Elliot’s work and the development of multiple other stockmarket cycles – Kitchin, Kuznets, Kondratieff – we see humanity trying to impose order onto chaos. It’s in our nature to try to find patterns, because we’re pattern matching creatures: it’s our way of structuring the world around us. Sadly this often plays us wrong, causing us to see a Man in the Moon, castles in the clouds and cycles in stockmarkets.

Spurious Stockmarket Structures

Many of the more recent market failures have been caused by attempts to model stockmarkets on the assumption that there’s structure underlying them. This spurious quest for structure and precision where none really exists is dangerous for investors. From time to time any theory will work – possibly because enough people believe it, possibly by chance. Inevitably, however, all theories will melt into oblivion in the crucible of market madness.

Those ancient Indian mathematicians knew a thing or two, but they didn’t know about stockmarkets. Remember – the truth isn’t out there, it’s inside us. Trusting in invisible sequences in random systems won’t always be successful, even if those sequences genuinely appear in nature. Systems including humanity will never obey nature’s simple physical laws.


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Sexual Trading

Contagion in Markets

It’s often remarked that stockmarket manias and panics are contagious, as though there’s some virus spreading through the markets, infecting the participants and causing their irrational behaviour. Of course, this is usually meant as a metaphor rather than something to be taken literally – it’s a nice conceit that there’s a disease “out there” causing us to all do stupid things all together.

However, humans are social animals, we live in social networks and networks are prone to attack at their weakest points. Models of how real and virtual diseases spread – the study of epidemiology – can give us clues as to what’s really happening when everything goes screwy. And it turns out that the more connected we are the more danger we’re in.

Rod Steiger’s Network

Most people are aware of the Kevin Bacon game which measures actors by how close they’ve come to acting with the prolific star of Flashdance. Someone who’s acted in the same film with Kevin has a Bacon number of 1, someone who’s acted with someone who’s acted in the same film as him has a number of 2, and so on. By tracing out this network researchers have been able to piece together the network of social connectedness amongst Hollywood actors. In fact it turns out that Mr Bacon isn’t anywhere near the most connected actor, and the thesps should actually be linked by the Rod Steiger number.

What’s really interesting, however, is what happened when the researchers looked at how the actors were connected. It turned out that the average actor has an average number of connections but that a few, key, thespians held the network together. These critical “nodes” had far, far more connections than most of their fellow luvvies. If you think of this as a network, then if you could somehow remove the key players then suddenly the whole thing would fall apart.

Scale Free Networks

It turns out that this is a decent model for the way most social networks link and, in particular, for the way diseases spread. Epidemiologists have a real interest in understanding this because they’re interested in figuring out how to prevent the spread of diseases like AIDS. When a bunch of researchers from Stockholm and Boston studied the Web of Human Sexual Contacts they discovered a network that looks an awful lot like that of the actors. Preventing the spread of sexually transmitted diseases turns out to be difficult because not all of the people have the same importance within the network: the especially promiscuous individuals – the critical nodes – were the key. Targeting these people successfully could stop the disease transmission, but a failure to do so would see re-infection occur again and again.

Networks like these are known as scale free, because there’s no pattern to how connected each node can be – to be precise, the distribution of connections follows a power law. It seems that the worldwide web has the same pattern. A few, very popular websites, are linked to with a frequency that’s way in advance of the average site. These sites are our critical points for disease transmission when some problem sweeps the information highway. And herein lies the next clue to the epidemiological model of stockmarket madness.

Markets Are Social Networks

Markets are inherently comprised of traders, agents communicating with each other, doing deals. Some of these agents are our supernodes, the critical people holding the vast majority of the network together. If these nodes get infected then we can surmise that all of their unimmunised contacts also get the virus. Which is why we have nothing to fear but fear itself.

Interestingly this research suggests an amendment to efficient markets theory rather than an alternative to it – a reminder that econophysics research like this comes from a background of rational theory rather than empirical observation. The development of scale-free networks from models of interacting traders has been observed by Tseng, Chen, Wang and Li, who posit a concept of zero intelligence traders in their models. This, of course, may be rather closer to the truth than they imagine, but the argument is that the scale-free nature of the network emerges from market structure, not trader interaction – aka, the Efficient Market Hypothesis.

On the other hand a paper from Rossitsa Yalamova suggests that extreme market events are a result of the coordination of trader activities due to synchronisation of trading rules through a relatively small number of highly connected individuals. As she states:

“I argue that stock price correlations actually reflect coordination of traders activity that might be initiated by different factors related to news or noise. At the end what determines price changes are trading orders. Therefore, I propose that price changes actually measure the interaction strength among traders especially in extreme events situation.”

Infection and Connectedness

So, if the key market nodes get infected then all we need to assume is that other people will copy their behaviour. From this it’s easy to deduce the spread of waves of buying and selling or, at extremes, manias and panics: the contagion that can spread through networks of this type is greatly exaggerated by these critical points getting infected. The same is true of the internet where computer viruses can survive long after they should have been destroyed – the ability of any critical node to re-infect swathes of the internet is the problem. It’s like one of our promiscuous lovers refusing to use any protection despite the clear evidence that they’re a danger to their partners.

So it is in markets, and modern technology makes it worse. The days when the average non-professional trader, working from home, was disconnected from the critical nodes has long gone. The critical nodes are out there on the internet, like giant spiders, spinning their webs, entrapping their clients and claiming their victims.

Immunise Yourself or Perish

Of course, there’s no getting away from the promiscuous purveyors of popular trading ideas, and the ever present global media, which likes nothing more than to feed off the extremes of human reaction: there’s no exciting copy in news that the stockmarket isn’t crashing or booming. So each of us has to take action ourselves, to seek out and immunise ourselves.

Worse, we need to desensitise ourselves to the opinions of those we work with or discuss ideas with. Danger lurks in listening to the authoritative ideas of anyone, but especially in social situations where herd like behaviour can develop: internet bulletin boards are a particular danger, although even simple investment clubs may be risky.

Developing a sceptical frame of mind when it comes to do with anything about investing is probably a good idea. As the old adage has it, you’ve got to buy when the blood is running in the street, even when it’s your own. You can’t bet against the market when all you’re doing is listening to what the market’s telling you: as anyone who sold stocks in early 2009 can tell you.


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