2020 Stock Market Index Update

It has been some time since I posted any updates to my stock market index analysis charts.  Now seems like a good time to follow up with my data-driven view of the equities investment environment.

My thesis for the behavior of the equities markets is that they obey stable long term exponential growth rules (constant annual percentage growth rates) with normally distributed perturbations around these rules.  Meaning that “normal” index values should be expected to vary within some fixed percent of the model values.  Over- and under-valued markets can then easily be observed because they fall outside of the expected statistical variation range.  The power of this approach is twofold.  First, it does appear to accurately reflect reality.  Second, it takes emotion and opinion out of one’s assessment of how the markets are doing.  Numbers here were updated as of April 3, 2020.

The coronavirus pandemic has caused quite a disturbance in equities.  But 65 years of Dow Jones Industrial Average index values show things in perspective.  The recent decline, while significant by any consideration, still leaves the index well within its normal variation while being just below the model expectations in absolute terms.  We have seen perhaps the largest points drop, but the recent fall hasn’t even been as significant as the response to 2008 financial crisis.


This is clearer if we just look at the last ~10 years.  The DJIA was bouncing around the upper limit of what we should expect when the pandemic hit.  This top limit is about 30% higher than the red line model value, so much of what was lost was “gravy.”  It was value that long-term investors shouldn’t use as a baseline.  Yes we all felt it in our 401(k) and IRA statements, but this shouldn’t impact long term strategies at all.


The DJIA is a small index, only 50 companies.  Let’s turn our attention to a broader index – the S&P 500.  The plot below shows that the S&P was not as aggressively flirting with its normal range, and remains in the green zone, like the DJIA, somewhat below it’s model value, but still comfortably so.


Again, looking at the last ~10 years shows this with more clarity.  It too has fallen, but the broader market shows a more tempered response, both in terms of its recent willingness to explore the top range of normal, and its response to the pandemic.


The NASDAQ is also broad like the S&P in terms of the number of companies in the index, but is focused primarily on tech stocks.  It has a much more aggressive growth rate (9.6% annual compared with 7% for the S&P), but has held the S&P-like tempered response to the pandemic.


For completeness, here is the last ~10 year view as well.  It is still well aligned with its long term trend, and its historical variations around that trend.


I always like to show these three indices together, along with their longer term model forecasts.  The NASDAQ continues on its trend to be on par with the DJIA in the 2040s (with index values on the order of 100,000) and overtake it in the 2050s.  This is always a plot that surprises people.  Note that neither the tech bubble of 2000, the financial crisis of 2008, or the pandemic response of 2020 have made any of these indices deviate for any significant length of time from their long term growth baselines.


Laws of the Markets Update

It has been some time since I last posted on my market index model.  Quickly, I was looking for an objective, data-drive method for evaluating the value status of the stock market.  Ten different people on the television will tell you ten different opinions of whether the markets are over valued or under valued or whether you should worry.  This is silly.  We have data, let’s use it.

You can read the older post for the details, but the essence is that the “wisdom of the crowd” in terms of investors and traders, knows where a given index should be and where their comfort levels around that number are.  It turns out the comfort levels lie within about 30% or so of that number, just drawing from statistics.  Over long periods of time, stock indices grow at constant annual rates; the day to day variations fluctuate around these long term numbers (and are probably completely unpredictable in any meaningful way).

Starting with the blue-chips, I have extended the model to take weekly Dow Jones Industrial Average data from 1935 until 10 December 2018.  For all the plots below, the red line is the model fit to the data, which is a 6.5% annual growth rate here, and the green zone around it is one standard deviation of the actual data around the model value – about 32 percent in each direction for the Dow.


My thesis here is that the green zone boundary, one standard deviation from the model value, is essentially a turnaround point – inside it reflects the “normal” variation in index value.  Broadly speaking, when the index value crosses into the red, the market will respond as though the market is overvalued, and when it crosses into the blue, the market will respond as though the index is under valued.

Recent events are agree with this thesis.  Below is the DJIA since 2010.  In 2018 it has been floating around the top of the “normal” zone (shaded grey in this plot), even crossing into being overvalued a few times, but generally not for very long.  Though the DJIA has taken a beating lately, it is well within its historically normal (throughout 85 years) range of variation.  The people who claim it is a bubble are not basing their claims on objective, historical reasoning.


How about the broader indices?  Below is S&P 500 back to 1935.  The green zone here is 30% of the model value, and it adheres quite a bit more closely to my turnaround rule.  That there are ten times more stocks in this index than the last one probably helps it behave better.


How is the S&P 500 doing lately?  The data from above are replotted below since 2010, just like with the Dow previously.  The S&P 500 is precisely where you would expect it to be from 83 years of data.


How about tech stocks?  The NASDAQ (1972 to present) has a wider standard deviation than the previous two, about 43%, mainly from the tech bubble (where it was trading at 3x the model value).  But note the NASDAQ is still tracking the same annual percentage growth line it’s been on for 46 years.


For consistency, below are the data since 2010.


You may ask how the actual index values are distributed around the model values.  Meaning, is the standard deviation a good metric?  Histograms of the percent deviation from the model are below for all three indices, with the first standard deviation colored green.  They aren’t perfect gaussian distributions, but they are clearly symmetric around the model.  You can clearly see, on the NASDAQ histogram, just how big the tech bubble was.


If you’re statistically inclined, the cumulative distributions make the case for the model quite well.  The green rectangle is one standard deviation horizontally and the vertical axis reflects the time spent at or below a given deviation.  The DJIA spends 65% of its time inside the box, the S&P 500 spends 70% there, and the NASDAQ spends 88%.


One last thing.  Since we have such well behaved data, we can take a little gamble and forecast a little bit.  Historically the average growth rate of the NASDAQ is almost 50% higher than the other two I’ve mentioned.  What should we expect in the future if decades of data continue to hold true?  Plotting them all together paints an interesting future.  That is, some time around 2050 the NASDAQ should be overtaking the DJIA.  And both the DJIA and the NASDAQ index values will be over 100,000 sometime around 2040.