Understanding the Market in a Statistical Way

By Lawrence

Have you ever spent time studying how the market you trade behave statistically? Here is an example showing some interesting behaviour that is ignored by many traders.

Statistic Concept of Runs

A Run in statistics means the repetition of the same event for multiple times. For example, if the market you trade has closed higher than the previous close for 5 consecutive times, then we call this a run of higher close for 5 times.

As you see, there are many things that you can measure by runs. For example, the number of times a market is making higher highs, lower lows, etc. can all be measured and analyzed through the distribution of runs.

An Example – Distribution of Runs on S&P 45-minute Bar Over the Last 10 Years

Here is a distribution chart of the S&P Index Future in 45-minute bars.

I have measured the distribution of the runs for the following items,

1. higher closes
2. higher highs
3. higher lows

Take a look at the chart,

SP 45MinRun

The horizontal axis is labelled with the # of times the condition(s) were met. For example, When the S&P 45-minute bars has made consecutive lower lows for 3 times, it only happens 5% of the time.

The graphs you see here are all belonging to the classic binomial distribution. In classic text books, the examples are usually based on 50/50 probability for the complimentary events. In our situation, the down side statistics (i.e. lower low, or lower high, etc.) is slightly weaker than 50% while the up side statistics (i.e. higher or equal low, or higher or equal close, etc.) are stronger than 50%.

What Does the Graph Tell Us?

First, we are looking at three (3) almost perfectly distributed graphs based on their complimentary events. Complimentary events are events that have their probability add up to 1.

Second, the S&P 500 Index Future demonstrates a very strong tendency to revert to the means of each distributions graphed. In short, the S&P index does swing back and forth around the mid-points of the 3 distributions I have presented.

Third, based on our research, S&P Index Future demonstate this same behaviour from daily bars all the way down to the 15-minute time frame.

Exploiting the Distrbutions

For discretionary trader, the statistical behaviour of the underlying instrument is an independent confirmation from his/her usual technical analysis tools. The odds of a reversal from an extreme price level is increased significantly when the distribution reading is confirming the bias.

For a system trader, have you ever used runs distribution as a filter for your trading systems? It is one of the rare tools that can improve a trading system without causing curve fit issues.

In short, if you trade 15-minute time frame, with a long position, then it is pretty obvious that after 3 bars of consecutive higher closes, even if you are not closing out your position, it is very important that you have a proper stop order in place to protect your position.


There are many ways to study the markets you trade, by incorporating statisitical bias into your trading decisions, you should be able to trade smarter.