Regression To Trend: A New Look At Long-Term Market Performance

Quick take: At the end of September the inflation-adjusted S&P 500 index price was 77% above its long-term trend, a decline from 84% 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 1.78%.

The peak in 2000 marked an unprecedented 145% 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 14% below trend briefly in March of 2009. But at the beginning of October 2015, it is 77% above trend, now a bit below the 84% to 93% range it has been hovering for the previous nine 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 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. 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 above the two deviations.