Regression To Trend: A Perspective On Long-Term Market Performance

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. I’ve 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 1.77%.


The peak in 2000 marked an unprecedented 146% overshooting of the trend — nearly double the overshoot in 1929. The index had been above trend for two decades, with one exception: it dipped about 13% below trend briefly in March of 2009. But at the beginning of May 2015, it is 93% above trend, unchanged from the previous month. 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 around the 1086 level.

Incidentally, the standard deviation for prices above and below trend is 40.6%. Here is a close-up of the regression values with the regression itself shown as the zero line. I’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 above the two deviations — as is our current level.

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Quick take: At the end of April the inflation-adjusted S&P 500 index price was 93% above its long-term trend, unchanged from the previous month.

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Author: Travis Esquivel

Travis Esquivel is an engineer, passionate soccer player and full-time dad. He enjoys writing about innovation and technology from time to time.

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