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

  • Written by Syndicated Publisher No Comments Comments
    May 5, 2015

    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.


    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%.

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    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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    Footnote on Calculating the Regression: The regression on the Excel chart above is an exponential regression to match the logarithmic vertical axis. I 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.

    Images: Flickr (licence attribution)

    About The Author

    My original dshort.com website was launched in February 2005 using a domain name based on my real name, Doug Short. I’m a formerly retired first wave boomer with a Ph.D. in English from Duke. Now my website has been acquired byAdvisor Perspectives, where I have been appointed the Vice President of Research.

    My first career was a faculty position at North Carolina State University, where I achieved the rank of Full Professor in 1983. During the early ’80s I got hooked on academic uses of microcomputers for research and instruction. In 1983, I co-directed the Sixth International Conference on Computers and the Humanities. An IBM executive who attended the conference made me a job offer I couldn’t refuse.

    Thus began my new career as a Higher Education Consultant for IBM — an ambassador for Information Technology to major universities around the country. After 12 years with Big Blue, I grew tired of the constant travel and left for a series of IT management positions in the Research Triangle area of North Carolina. I concluded my IT career managing the group responsible for email and research databases at GlaxoSmithKline until my retirement in 2006.

    Contrary to what many visitors assume based on my last name, I’m not a bearish short seller. It’s true that some of my content has been a bit pessimistic in recent years. But I believe this is a result of economic realities and not a personal bias. For the record, my efforts to educate others about bear markets date from November 2007, as this Motley Fool article attests.
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