Stock Market Weather and the Bouncing Ball Theory

In statistics, averages can be tricky. On a winning day, the S&P goes up on average 0.76% of the index, and on a losing day, it goes down 0.79%. The problem is, as people know, most of the time the market is relatively stable, but there are moments of violent volatility that can blow years or earnings in a few days or months. So averages are not really useful to understand stock markets. The goal of this article is to help readers have a clearer high-level view on how much and when the market is more likely to move violently.

Note: The following paragraph relies heavily on the notion of quantile. If you are unfamiliar with the quantiles used in the calculation, you might want to have a look at the appendix at the end of this article.

We have plotted the yearly price movement using an idea close to the standard deviation. In theory, when a dataset is normally distributed, a standard deviation of 1 ("std1") should represent 68% centered around the mean, a standard deviation of 2 ("std2") 95% of the data and 3 ("std3") 99% of the cases. Since stock data is not normally distributed, we used a proxy of this idea by assuming the median (quantile 50%) as being the equivalent of the mean. For std1 we took the value that stands on quantile 16% (50% - 68%/2) and quantile 84 (50% + 68%/2). For std2 values on quantile 2.5% (50% - 95%/2) and 97.5% (50% + 95%/2). Std3 being on quantile 0.5% and 99.5 (50-99%/2 and 50 + 99%/2). The result is as below.

The dotted lines represent the average values of std1, std2, and std3.

At first sight, we can see that the movement are uneven, most of the time the values are below the average, but the years the market moves beyond the average,  it moves on both sides. If we look more carefully, it seems every time the market moved violently happened when there was a financial crisis. I have added a line next to the biggest spikes and it fits almost perfectly. For the dot-com crisis, it started in 2000 but the market keeps on crashing in 2001 and 2002.

This is a rather intriguing phenomenon. One would expect to see very big negative changes during crisis periods, and big positive changes when the market goes up. The only explanation I could give to that phenomenon is that the market behaves like a bouncing ball. The higher it falls from, the higher it will rebound. Traders see that all the time. 

When it comes to market timing, most experts agree it is impossible to time it all the time. And nobody wants to try to "catch a falling dagger" as the trading saying goes. But this chart demonstrates that the basic idea of buying low and selling high is not completely absurd because the bigger the fall, the stronger are rebounds. Overall in falling markets though, the falls end up being stronger than rebounds. 

Stock Market Weather

Another more subtle observable phenomenon on the chart is that on these high volatility years, the std1 values are beyond std2 values of calm years. In other words, the top 64% values of high volatility year are beyond the top 95% values of low volatility years. Much like a storm accompanied by violent winds, these massive movements create ripple effects over many weeks or months. This cannot help a person to predict stock market crashes, but it can help predict how will the market behave in the aftermath. The market doesn't move in isolation with other events. When there is a violent movement, especially downward, more are to follow, both upward and downward. There are also circumstances where the market is going nowhere, either because of the absence of big players on the table, or the equilibrium of forces of the players, days with weak or no wind.

If we want to think in terms of "normal" in the sense of a normal distribution, most people are familiar with the idea of the average and some are familiar with the idea of standard deviation. Averages are good for situations where data is normally distributed, such as when the market weather is calm. Some systems are using rolling averages, EMA, etc, and most probably work well in normal circumstances. But it is very unlikely that these systems can withstand the violent storms with their crazy upward and downward volatility. 

Concretely for active traders, one of the consequences of the understanding of market weather is stop-losses. It is unrealistic in turbulent periods to keep stop-losses of the same size as in "regular" days. The amount placed can still respect the desired risk profile (the 1-2% rule), but it must be looser.

If we want to compare the stock market with the weather, it seems clear that the ideal trading periods are those with strong directional wind, but the reality is very often the wind blows in different directions, and sometimes, there are storms causing a lot of turmoil. An ideal system should be able to diagnose the weather and trade accordingly.  

Appendix : Quantile explained

In order to represent visually the stock movements,  we will have to delve into quantiles. If you are familiar with quantiles, you can skip this section 

Imagine a sequence of numbers 10 numbers from 1 to 10, sorted in ascending order:

• The top 20% numbers are 9 and 10
• The lowest 20% numbers are 1 and 2
• The number on quantile 20%, that would be 2
• The number on quantile 80%, that would be 2

The same idea applied to 100 numbers from 1 to 100, sorted in ascending order:

• The top 3% numbers are 98, 99 and 100
• The lowest 3% numbers are 1, 2 and 3
• The number on quantile 3% is 3
• The number on quantile 98% is 98 

10 numbers from -5 to 5, sorted in ascending order:

• The top 20% numbers are 4 and 5
• The lowest 20% numbers are -5 and -4
• The number on quantile 20%, that would be -4
• The number on quantile 80%, that would be 4

  The same idea applied to 100 numbers from -50 to 50, sorted in ascending order:

• The top 3% numbers are 98, 99 and 100
• The lowest 3% numbers are 1, 2 and 3
• The number on quantile 3% is -38
• The number on quantile 98% is 98