# Regression To Trend: SPX 62% Overpriced!

July 2, 2013

At the end of June the S&P 500 index price was 62% above its long-term trend, down from 65% above trend 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 1.73%.

The peak in 2000 marked an unprecedented 152% 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 11% below trend briefly in March of 2009. But at the beginning of July 2013, it is 62% 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 around the 998 level. If the index should decline over the next few years to a level comparable to previous major bottoms, it would fall to the 450-500 range.

Footnote on Calculating 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, the monthly average of daily closes last month was 1618.77. The Growth function value for the month was 998.20. Thus, the former divided by the latter minus 1 equals 62.17%, which I rounded to 62%.

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