Identification of bubbles as a case in point
For the last thirty years I have been using charts to understand the stock market. I see some usefulness in trying to gain small insights into trends, cycles and some other patterns in individual stocks and in the stock market in general. The only claim I make for charts is that they help investors to visualize data.
I say that with some trepidation because charting has long been identified with traders and speculators and thus looked down on by real investors. It has also been roundly criticized by Benjamin Graham, Warren Buffett and many academics.
Ironically it is the academic school of mathematical economists with skills in mathematics and statistics, who brought us the EMH (Efficient Market Hypothesis), who have been most withering in their criticism of charting. They have largely called it witchcraft or some other such dismissive criticism.
Taming masses of data
Investing is a field that is necessarily strewn with masses of data. The data include prices, trading volumes, financial data, economic data and so on. Even random data, such as the results of flipping a coin one hundred times, are susceptible to recording and analyzing. Mathematics has supplied two valuable ways to tame masses of data. These are statistics and graphs. Sadly, both are frequently misused and as with many tools that simplify things, they are often more difficult to use effectively than they seem and can often mislead.
Graphing of data has been around for hundreds of years and generations of scientists have developed skills in sussing out what can be learned by inspection (a learned skill) of a graph. A graph is a plot of data on a piece of paper or computer screen. There are usually two axes, the x-axis which is horizontal and the y-axis which is vertical. We typically plot two series of related data on a graph. A stock chart typically plots prices on the y-axis and time or date on the x-axis. The two axes intersect at the origin. The points on the chart represent the relationship between the series of data. Each point is called a coordinate.
The following figure of a simple chart comes from Statistics Canada.
42 Parts of a Graph
Much as charts can be invaluable for visualizing data, they can, like statistics, be very misleading. It seems framing or misframing can be at work. For more on framing see here. Whether wittingly or unwittingly a chart can frame how we look at the visualization of the data. Framing can mislead us. If the y-scale doesn’t begin at zero, is there a good reason? Does this give a misleading impression of variability of the y-data? For example, if the y-scale showing price begins at $20 and ends at $25 dollars this emphasizes volatility. One of the most common errors with the use of stock charts is to fail to use semi-log plotting on the y-axis.
It’s a chart crime we see all the time. Let me illustrate this in the context of using charts to help us identify bubbles. One of the characteristics of bubbles is the exponential curve of their ascent. Another is the avalanche shape of the collapse that follows.
Prof. Al Bartlett has told us: “The greatest shortcoming of the human race is our inability to understand the exponential function.” Professor Bartlett (1923-2013) was Professor Emeritus in Nuclear Physics at University of Colorado at Boulder. http://www.albartlett.org/
Understanding exponential functions is critical to understanding any stock chart.
The rise of the Nasdaq in the late 1990s was clearly a bubble. Can we identify this on a chart? The answer is yes, but, the correct kind of chart must be used. Let us compare the shape of a plot of the Nasdaq 100 in the late 1990s using the two different formats– arithmetic chart and semi-log chart.
The following chart is a long term chart of the Nasdaq 100 index plotted with an arithmetic y-axis.
23 NASDAQ 100 Index arithmetic plot
The rise from 1990 in the arithmetic plot shows a dramatic, apparently exponential, rise. Prices are accelerating. That much is obvious. But it is impossible to know from inspecting the chart whether the rate of change of prices is increasing. The index price level is on the vertical y axis and the reader can see that the numbers increase in increments of 100 all the way up the right side. Each increment of 100 is equally spaced. That is, the Nasdaq index is depicted in a linear or arithmetic plot.
The following is a long term chart of the Nasdaq 100, plotted for the same time frame as the previous chart but on a semi-log chart. For more on semi-log charts see the Appendix 1: A glossary of special terms and phrases.
24 NASDAQ 100 Index semi-log plot
The rise from 1990 shown in the semi-log chart is not as dramatic. But, the blue lines help to show that the steepness of the curve is increasing as the 1990s unfold. This increasing steepness can be seen simply by inspecting the chart. The index price level is again on the vertical y axis and the reader can see that the numbers on the right scale do not increase in equal spacing. What is constant is that the percent increase from each number to the next is equally spaced. So, the space or distance from 500 to 1000 is the same as the space or distance from 1000 to 2000. It is called semi-log chart because only one of the two axes is on a log scale. The x axis is linear.
The crucial thing to know about a semi-log chart is that if the rate of increase is the same year after year the chart will show a straight line. That is, if the stock market is increasing at a rate of 10% per annum over many years, a chart of its prices will show a straight line. As well, the slope or steepness of the chart line will depict the 10% rate of increase. That is, a rate of increase of 15% a year would show a steeper slope and a rate of increase of 5% a year would show a less steep slope. But, this only works on a semi-log chart. This is why I said above that inspecting charts is a skill.
If the stock market is increasing at 5% per annum for a period of time, then accelerates to a rate 10% and then accelerates again to 15%, this is an exponential increase. That is, the rate of increase is itself increasing. This can be seen on a semi-log chart as a line that is curving upwards and getting ever steeper, as in the Nasdaq semi-log chart of the late 1990s.
The price of gold showed the same shape in the bubble of 1968 to 1980, as did the Japanese stock market from 1980 through 1987.
Here’s the point: If the steepness on a semi-log charts is increasing (as illustrated by the increasing steepness of the three blue lines on Nadaq semi-log chart above) this is some evidence of a bubble.
If the steepness of the blue lines on the arithmetic chart (as illustrated by the increasing steepness of the blue lines on the Nasdaq arithmetic chart above) this tells you nothing.
Example of misleading plot
The financial press, analysts’ reports and authors regularly use linear y axis charts. Sometimes little harm is done when the time period covered by the chart is small. But, as the time period increases the distortions of the chart increase. These charts tend to exaggerate recent prices and understate older prices. This can be seen in Figure 1.1 of Professor Shiller’s Irrational Exuberance (Shiller, 2005 Second Edition).
25 Shiller S&P 500 arithmetic plot
Shiller’s Figure 1.1 shows a towering price peak in 2000. This peak can be compared in size with the peak in 1929 which is a relative dwarf. The preface to the first edition of Irrational Exuberance, published in the spring of 2000, says, after referring to the fields of economics, psychology, demography, sociology, history as well as conventional financial analysis: “I marshal the most important insights offered by researchers in these fields. Taken as a whole they suggest that the present stock market displays the classic features of a speculative bubble: a situation in which temporarily high prices are sustained largely by investors’ enthusiasm rather than by consistent estimation of real value.” (Shiller, 2005 Second Edition)p.xviii. Regarding the chart, he says: “The spiking of prices in the years 1995 through 2000 has been most remarkable: The price index looks like a rocket taking off through the top of the chart, only to sputter and crash.” He goes on: “No price action quite like that around 2000 has ever happened before in the entire stock market history shown in Figure 1.1.” (Shiller, 2005 Second Edition)p.4.
His conclusion that there was a bubble was correct. His observation on price action is overstated. His use of the chart in Figure 1.1 is not valid evidence the way it is plotted. It exaggerates the rise in the 1990s. A semi-log plot of the same data would show an exponential rise, just not as dramatic.
When we are concerned that the stock market might be in bubble territory we can look for a sustained exponential rise on a semi-log chart. This would only be one bit of evidence to consider.
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