Patterns in Random Numbers

At iTulip they had an interesting posting regarding the currency markets.

We are fast reaching a stage at which elegant quantitative models won’t determine who survives, in fact, those that tend to rely on models in this environment may be most likely to be shining shoes sooner rather than later.”

Really, you mean you CAN’T PREDICT? Who would have thought? Seriously, I have been talking about this time and time again (1,2,3). I might be a newbie at this, and I might not have all the credentials of a full time quant. BUT, after a year of doing algorithmic trading I have learned that you cannot and should not predict the market.

Creating a model that fits on the market is building a model to fit noise. Let’s say you are flipping a coin. Here is a potential string of random results (H = heads, T = tails).

HTHTHTHTHTHTHTHTHT

Yet is this string really random? No, I injected a pattern of HT and HT, and so on. You would argue this is not random and that random looks random for a better word. But random has an interesting side effect, and that is randomness clusters.

In Fooled by Randomness (pg 168-171) Taleb noted that Professor Karl Pearson said that random data does not look random.

“A single random run is bound to exhibit some pattern — if one looks hard enough.”

Randomness gives the appearance of patterns, but it is really clustered noise. Many times true randomness looks like there is some pattern, some process. To illustrate, take a history of lotto numbers, and then generate a graph of boxes where each horizontal line is labeled 1 to maximum value of lottery. Then get a years worth of lottery draws and fill in the boxes. Take a step back and look at the drawn numbers. It feels like the numbers follow some sort of pattern.

When people look for patterns in the market they are looking really hard to find a way of beating the market. But since this is random, or pretty close to random noise you are looking for patterns where there are none. 

I make the assertion that the market is random because you have counter parties. The market is a constant struggle of up and down because people can make money by watching you fall. It is like judo where you can use the weight of the other person to win. Thus no single move is a winner, and no single move is a looser.

Getting back to the clustering of random numbers. Clustering means that when random events occur they tend to occur multiple times in a row, and then will not occur for an undetermined time. The following example is a form of clustering.

HTHHHHHHHHHHTHHTHHHTTTTTTTTHHTTTHHHHHTTT

The random string does look like it contains patterns, but there aren’t any. So knowing that random numbers cluster can I trade and win? Absolutely. It’s called trend following.

Let’s break down the term Trend Following into its components. The first part is “trend”. Every trader needs a trend to make money. If you think about it, no matter what the technique, if there is not a trend after you buy, then you will not be able to sell at higher prices…”Following” is the next part of the term. We use this word because trend followers always wait for the trend to shift first, then “follow” it.

But here is a problem. If people know that there are trends then they could profit from playing the counter side to a trend. Yes that is possible, but it is also a dangerous game. It is like saying, “Hey I know Mother Nature will flood this place, but I know how to beat Mother Nature.” Maybe most of the time you can beat Mother Nature, but there are one or two times where you will be wiped out. Thus to play the counter side of a trend follower you better have big kahunas.

When building an algorithmic trading systems it means you should not try to put more intelligence into the market than there is. For example, are you using a scanner? Are you using a scanner to latch onto a wave? Or are you using a scanner to match for a stock that fits a pattern? Because if you are scanning for patterns then I am thinking you are trying to fit a pattern onto noise. 

What’s my strategy for trading? When I go long I buy low, and sell high. When I go short I sell high and buy low. Sounds too easy? But, that is my strategy. I have learned that simplicity does not equal understanding. We want to complicate things with other factors and conditions, but the reality is that those other complications don’t help clear the confusion.

Hello There Mr Roboto!
(the song and era says it all... http://www.devspace.com)

Wednesday, Aug. 8, 2007 by Christian

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3 Comments Add your ownSubscribe

  • 1. EZ  |  August 11th, 2007 at 12:23 am

    Great article. I would definitely agree. It seems that a fundamental philosophical tenet technical analysts or chartists hold is that market does not adjust to information as rapidly as we would think, meaning it is not really an ‘efficient’ market. As a result, they can supposedly recognize these patterns and potentially incur great profits.

    I don’t have any experience with this kind of thing, but it seems absurd that besides charting, a quantitative model could take into account the subjective human element where it would have to account for the reactions of a multitude of investors in real time. Burton Malkiel in ‘A Random Walk Down Wall Street’ mentioned how a coin flip developed what I believe was a ‘Head and Shoulders’ pattern. He then proceeded to show this to a chartist who excitedly said it should be purchased immediately. Needless to say, the chartist was pretty pissed off when they found out it was produced by a coin flip!

    It’s also interesting to note the trend with some of these MIT Physicists turned Hedge Fund managers turn up on the Street. Let’s face it, particles abide by certain fundamental laws of physics, unlike the behavior of the masses, so I’m interested in how exactly they are applying their expertise.

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