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Regression to Trend: A Perspective on Long-Term Market Performance

May 2, 2011 Monthly Update

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) to the question.

Here’s a chart of the S&P Composite stretching back to 1871.

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The chart shows 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 1.71%.

The peak in 2000 marked an unprecedented 157% overshooting of the trend — nearly double the overshoot in 1929. The index had been above trend for nearly 18 years. It dipped about 9% below trend briefly in March of 2009, but at the beginning of April 2011 it is 45% above trend. 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 hovering just above 900. If the index should decline over the next few years to a level comparable to previous major bottoms, it would fall to the low 400s.

Check back next month for another update. Footnote on Calculating Regression: The regressions on the Excel charts above are exponential regressions to match the logarithmic vertical axis. I used the Excel Growth function to draw the lines. 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, the monthly average of daily closes for April was 1331.51. The Growth function value for the month was 912.11. Thus, 1331.51 divided by 912.11 minus 1 equals 45.98%, which I rounded to 46%.

Footnote on the S&P Composite: For readers unfamiliar with this index, see this article for some background information.

View the original article on dhsort.com

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