Probability by the Numbers

As professional traders we believe it is important to use as many tools that are available to try and stay in front of this market to give us an edge. One such tool is to data mine previous market behaviors and compare them with current market dynamics. At the very least you should have a guide map of possible future scenarios. In this article we are going to discuss some of the characteristics of the markets which have occurred in the past in one form or another.

Let’s get started by looking at the S&P’s return distribution. Since 1960, the S&P has returned an average of 8% per year with a standard deviation of 17.0%. If you are not familiar with the statistical terms, just think of Standard Deviation as a means to measure the dispersion of data around the average. In theory, 70% of the time markets will be within one standard deviation from its average.

This means, one could expect the index to return between -11% (8%-17%) to +25% (8%+17%) on any average year. Extreme cases are when market returns are noticeably below or above the -11% to +25% band. Extreme readings are not sustainable in the long run and need careful analysis.

To better understand the above concept we have constructed Chart 1 below which shows the frequency of returns (stated in percentage) since 1960.  For example the third bar from the right shows that the market historical returns between 10% to 25%,occur 34% of the time.

Now, if you recall from our previous article, In 2013 the S&P‘s total return including dividends reinvested was almost 32% (The index rose by approximately 29%). You will also notice that on a historical basis, a return above 29% occurs only 8% of the time. This could suggest that last year’s growth was an extreme case and requires further investigation. It’s also interesting to note that according to this chart; market returns between -12% to 25% occur 70% of the time.



The same message can be concluded when you plot the frequency of Price to Earning (P/E) ratios. Chart 2 below shows cyclical adjusted Price earnings ratio since 1907. As you can see, 76.8% of the time the market traded at a P/E ratio between 10 and 24. The current P/E ratio of 25 is clearly a stretch as anything above 24 occurs only 9.7% of the time in the past 114 years.



Now that we have determined that the markets are starting to look overstretched, our next step is to look back and see what happened each time the markets printed an extreme reading. To do this, we need to isolate those particular years when the market went up by 29% or more and recorded the next year’s performance. We first checked the data set from 1960 onwards and found only 3 periods with 29% or more growth. Obviously drawing any conclusion from only 3 matches would not be a sizeable population of data and therefore we extended our time horizon to 1907 and repeated the above process.

In the larger time frame we found 12 occurrences, the results are summarized in Chart 3 below. This shows that after a 29%+ rise in the previous year, the market rallied the following year 77% of the time. What this tells us is that whilst a 29%+ growth year seems overstretched by its PE factor, It could be more a sign of positive momentum rather than a sign of market exhaustion.

CHART 3 - RETURNS_following


While Chart 3 is sending some bullish messages for 2014, it is important to note that this chart has not accounted for the noticeable -3.4% drop in January 2014 when equities were overvalued by historical P/E readings which is what has occurred this time.

To address this issue, we adjusted our finding to identify all those years that:

A)     the market has dropped 3.4% or more in January and

B)      the market P/E was at 25 or more at the beginning of the decline

and then recorded the market returns 12 months after each instance of the above event.

Results are summarized in the Chart 4 below. We can see that a monthly drop in January of 3.4 % or more while P/E ratio is 25 or higher, has a 70% chance of initiating a bearish trend for at least 12 months. This is a very important finding as it captures the current market dynamics.



Continuing with our study, we also wanted to identify the months that were historically strong or weak. This can potentially help us with our timing whether we take a bullish or a bearish view for the rest of 2014.

Chart 5 below summarizes the average returns each month since 1960. According to this chart: January ,March ,April ,Nov and Dec have historically been strong and equity positive. On the other hand, the periods between May to October have traditionally been weak allowing for market corrections.




Historical market statistical patterns and behaviour can play an important role in understanding current market dynamics. While in this article a slightly bearish outlook may be identified by Chart 4, it also alerted us that if for whatever reason markets decided to go in the other direction, we may end up seeing a rather strong year again in 2014 as identified in Chart 3. This indicates that traders should be ready to change direction if and when required, be it long or short.

One thing we would like to point out is that once the numbers don’t add up anymore than this may indicate a time to rethink your strategy.

At Trade View, we look at how the markets behave based on historical patterns by using a mathematical approach to define absolutes. The reason for this is that markets are traded by humans and humans tend to follow patterns. We also feel that history may repeat but not necessarily act in the same way due to the ever-changing nature of the financial markets and systems. The best example of this can be seen by the introduction of algorithms and HFT (High Frequency trading firms) which use mathematics to define rules.

We do however feel that it is important for a trader to be familiar with historical patterns which should help give the trader a much needed edge in these current choppy and over inflated conditions.

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