Regression to Trend: Another Look at LongTerm Market Performance
June 1, 2017
by Jill Mislinski
of Advisor Perspectives
Quick take: At the end of May the inflation-adjusted S&P 500 index price was 99% above its longterm trend, unchanged from the previous month.
About the only certainty in the stock market is that, over the long haul, over performance turns into
under performance and vice versa. Is there a pattern to this movement? Let's apply some simple
regression analysis (see footnote below) to the question.
Below is a chart of the S&P Composite stretching back to 1871 based on the real (inflation-adjusted)
monthly average of daily closes. We're using a semi-log scale to equalize vertical distances for the
same percentage change regardless of the index price range.
The regression trendline drawn through the data clarifies the secular pattern of variance from the trend
— those multi-year periods when the market trades above and below trend. That regression slope,
incidentally, represents an annualized growth rate of 1.80%.
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The peak in 2000 marked an unprecedented 139% overshooting of the trend — substantially above the
overshoot in 1929. The index had been above trend for two decades, with one exception: it dipped
about 15% below trend briefly in March of 2009. At the beginning of June 2017, it is 99% above trend,
exceeding the 68% to 90% range it hovered in for 37 months. In sharp contrast, the major troughs of
the past saw declines in excess of 50% below the trend. If the current S&P 500 were sitting squarely
on the regression, it would be at the 1205 level.
Incidentally, the standard deviation for prices above and below trend is 40.7%. Here is a close-up of the
regression values with the regression itself shown as the zero line. We've highlighted the standard
deviations. We can see that the early 20th-century real price peaks occurred at around the second
deviation. Troughs prior to 2009 have been more than a standard deviation below trend. The peak in
2000 was well north of 3 deviations, and the 2007 peak was around two deviations, below the level of
the latest data point.
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Footnote on Calculating the Regression: The regression on the Excel chart above is an exponential
regression to match the logarithmic vertical axis. We used the Excel Growth function to draw the line.
The percentages above and below the regression are the calculated as the real average of daily closes
for the month in question divided by the Growth function value for that month minus 1. For example, if
the monthly average of daily closes for a given month was 2,000. The Growth function value for the
month was 1,000. Thus, the former divided by the latter minus 1 equals 100%.
Footnote on the S&P Composite: For readers unfamiliar with this index, see this article for some
background information.
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