# The fractal market …

What does this fern leaf and the stock market have in common?

Surprisingly, a lot!

For a start, this is not a drawing or photo of a real leaf … it’s a actually a computer-generated image derived from just a few short lines of computer code.

It’s a ‘fractal image’ – a branch of mathematics that uses randomness (with many similarities to ‘chaos theory’) to describe natural objects so that they look ‘real’ to the naked eye … again, using only a very simple mathematical formula!

The two most interesting things about fractals:

1. They are easy to generate – they are based upon replication of a very simple formula, over and over again. Order-in-Randomness takes care of the rest

2. As you scale up or down the picture looks remarkably similar ….. take the leaf to the bottom right and blow it up to full-size and you will see something very similar to this original image

What does this have to do with the stock market? Well take a look at the following two graphs:

These both indicate movements in the Dow Jones Industrial Average; what’s interesting isn’t the direction … it’s the shape …. they both indicate a random series of up/down movements in a general direction (that, too, seems to change randomly).

The interesting thing about these charts is that they are the same chart (almost)!

One is a 1 year view of the Dow Jones, the other a 3 year view (it should be easy to work out which is which!) …

… you see, as the IBM scientist who ‘founded’ fractal geometry (well, actually revived … it was ‘discovered’ in the late 19th century by a scientist named Julia) in the 80’s discovered, the stock market is fractal.

While the movement is seemingly random, each piece of market movement when enlarged looks very similar to the larger scale movements … so we have up/down movement in the stock market at every scale: daily, weekly, monthly, annually that actually behave quite similarly.

The frustrating thing is this: chaos theory abounds.

Chaos theory says that when systems become complex, a very small apparent change in one variable (i.e. number) can suddenly have a HUGE change on the whole.

It’s why they say that a butterfly flapping its wings in Japan can cause a hurricane in Louisiana …

You can’t think of a system (except in Nature) more complex than the stock market: thousands of stocks make up a market … each one is a real-live business generating revenue, controlling costs, dealing with market/economic/government changes on a daily, or even minute-by-minute basis.

The whole shebang can move up … down … or sideways. But, within each movement is the movement of each company’s stock. The price of each individual stock is fixed by the investors: are they net buyers or sellers in this micro-second (that’s how fast the stock exchange moves)?

Suddenly, one mutual fund executes it’s order to sell Company A and the effect is minimal, either on that company’s stock or on the market. But, on another day a ‘perfect storm’ arises (an announcement by the feds of a change in interest-rates; a war in the Gulf erupts; etc.) and that same sell-off triggers a panic.

Who can predict it?

Nobody … and, that’s the point … look at the charts: do you see anything that looks remotely predictable in that lot?

Do you want to bet your financial future on where the stock market is heading, even for the next 3 years?

I don’t … but, I do know that while the market can (and, does) move dramatically & randomly, there is an underlying force driving it relentlessly upwards:

The companies that make up the market are producing widgets, and inflation is always making the price of widgets go up/up/up (with an occasional, but only short-term pull-back) inevitably pushing their profits (hence stock price) along with it … where inflation goes, the stock market will surely follow … eventually.

But, who can say exactly when?!

So always be a buyer and holder … never a seller be.

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## 5 thoughts on “The fractal market …”

1. Great definition of chaos theory as it applies to the stock market Adrian. And not only is it best to be a buyer and holder, but what better time to buy more than now!

2. You are referring to the fractal work by Benoit Mandelbrot. His book, The (Mis)Behavior of Markets, is a must read if you are interested in market mechanics.

3. @ Thomas – At the time it was the fractal work of Mandelbrot that interested me rather than the markets! But, I do remember the references to his market work, even at that time ….

4. Well at some time you gotta be a seller, right? Unless you are going to live off the dividends! That is the “buy and hold” strategies achilles tendon. Now, don’t get me wrong I have been buying and holding certain stocks for a while with great success. But, just as you can learn how to be a good real estate investor by paying attention to the proper metrics, you can learn to become a good stock investor by paying attention to the metrics! There are many folks who “trade” stocks to great returns (learning how to leverage stocks to improve returns is a learned skill).

Now, do I think it is much easier to use leverage in real estate investing to get to that needed return, therefore it should be the place most investors concentrate their efforts. But, there are many ways to produce great returns! Buy low and take profits when they appear is certainly another way!

5. @ Shafer – selling a minor portion of a great-but-low-dividend stock each year – in order to convert to cash to live off – is fine. And, for tax reasons, it’s probably even better than owning a dividend stock …. compare the capital gains tax on the former versus the income tax on the latter 😉