**Quick take**: At the end of August, t*he inflation-adjusted S&P 500 index price was 131% above its long-term trend, down from July.*

About the only certainty in the stock market is that, over the long haul, overperformance turns into underperformance 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 1.94%.

At the time, the peak in 2000 marked an unprecedented 115% overshooting of the trend — substantially above the overshoot in 1929 (78%) and in 1901 (92%). In recent years, we have seen the index get as high as 177% above the trend (2021). The index has been above trend for nearly three decades, with one exception: from October 2008 to August 2009 the index dropped as low as 26% below trend.

At the end of August 2023, it is **131% above trend**. 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, its value would be 1932.

Incidentally, the standard deviation for prices above and below trend is about 44%. Here is a close-up of the regression values with the regression itself shown as the zero line. I've highlighted the standard deviations in red. 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 trend experienced third standard deviations (3SD) above the trend from December 2020 to April 2022, even reaching as high as 4SD for one month in November 2021. The trend quickly fell back down to the 2SD range previously seen at the turn of the century. Recently, the trend crawled just above 3SD but the latest data dropped it back to 2SD above the trend.

ETFs associated with the S&P 500 include: iShares Core S&P 500 ETF (IVV), SPDR S&P 500 ETF Trust (SPY), Vanguard S&P 500 ETF (VOO), and SPDR Portfolio S&P 500 ETF (SPLG).

**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 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.

**This article was originally written by Doug Short. From 2016-2022, it was improved upon and updated by Jill Mislinski. Starting in January 2023, AP Charts pages will be maintained by Jennifer Nash at VettaFi | Advisor Perspectives**

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