The Nature of The Beast: How The Stock Markets Work.

This write-up is not about the mechanics of buying and selling individual stocks. This post is about the fundamental nature and behavior of the stock markets.

What Is "The Stock Market"

A stock market, or stock exchange, is a place where a large number of individuals and organizations come together to freely buy and sell shares in corporations. What is being traded is currency, such as U.S. dollars, for shares in corporations. Currency for shares or shares for currency.

Examples of stock exchanges are the New York Stock Exchange, Frankfurt Stock Exchange, London Stock Exchange and the Tokyo Stock Exchange.

While there are many different measures of a stock market, the most popular is some average of many different stock, or share, prices. These averages are called stock indexes. For the United States, two important stock price averages, or indexes, are the Dow Jones Industrial Average, or DJIA, and the Standard and Poor's 500, or S&P 500. The DJIA is an average of 30 large U.S. corporations, while the S&P 500 is an average of 500 corporations.

From here on out, I will use the S&P 500 as a good representation of the average price of a large number of U.S. stocks.

The S&P 500

Below is a graph of the S&P 500 from 1957 to 2020. The y axis, or left hand side, in the average S&P 500 values for each month. The x axis, or bottom, is time.

The first thing you will notice is that over long periods of time, the S&P 500 generally goes up in value (price). There are, however, shorter periods of time where the price falls significantly.

Now, let's start tearing the S&P 500 apart to see how it behaves.

Let's Predict the Stock Market

If we try to predict the stock market, we can start to get an idea of how the beast behaves. The simplest method to predict the stock market is with the naive forecast. In a prior post, I described the naive forecast and why it is important. Click here to jump back to this post.

In short, the naive forecast says tomorrow will be the same as today. The S&P 500 will be the same next month as it is this month. If we use this very simple model, how right or wrong will we be? Well let's see.

How Wrong Are Our Predictions

Let's define "error" as the difference between actual and predicted, or error = actual - predicted. The error of the naive forecast is simply the difference from one month to the prior month.

Below is a history of the error of the naive forecast of the S&P 500 since 1957. The left hand side is the error and the bottom is time. This plot is also just the change in the S&P 500 from one month to the next.

It seems that over time, the changes in the S&P 500 get bigger (or the error becomes greater). In 1957, the range of the errors was 4.5 points (from highest to lowest) while in 2019 the range of the errors was 247 points.

As the value of the S&P 500 gets larger and larger, the size of the changes in this stock index also get larger.

The S&P 500 Through a Different Lens

Let us look at the S&P 500 through a different lens to see what it might show. Instead of the actual values of the S&P 500, let's look at the logarithm, or log, of the values, as the logarithm is a method used to shrink large numbers.

Now our precious stock market index looks like this:

It appears that over long periods of time, the logrithm of the S&P 500 is more-or-less a line (albeit a wonky line). Let's put a line through it and see what it looks like.

Now if we go back and look at the naive forecast of the logarithm of the S&P 500 instead of the absolute values of this index, what will have changed? Below is the error of the naive forecast of the log S&P 500 from 1957 to 2020.

The graph above is also just the difference in the logarithm of the S&P 500 from one month to the prior month. This difference in the log of the S&P 500 is also almost the same as the percent difference in the S&P 500.

When using the absolute values of the S&P 500, the errors seemed to get bigger and bigger over time. However when using the logarithm of the S&P 500, now the errors are more or less consistent over long periods of time.

This leads to an important conclusion:

For historical comparisons, the percent difference in a stock index should be used. Do not use the absolute difference.

While this has been demonstrated for the S&P 500, this conclusion also holds for all stock indexes, both U.S. indexes and international indexes (such as the DAX, Hang Seng or Nikkei).

While a 1000 point drop in the Dow Jones Industrial Average in 2020 is bad, a 1000 point drop in the DJIA would have been catastropic in 1982 when this stock index was only around 1000 points.

How Does The Beast Behave?

From here on out, I will use a number of tools to describe how the stock market behaves. One of these tools is a histogram. A histogram is a plot of the frequency of observed values over the range of these observed values. It is frequency (or count) versus value.

Below is a histogram of the errors in our naive forecast of the logarithm of the S&P 500.