Last month Luca Varani, a biophysicist from Switzerland, emailed me with some interesting comments about the regression trend lines in this commentary on historic market price and dividends. He wrote:

I have a hard time believing the post 1982 regression line. I believe that the similar trend lines through the 20s and 60s do make a strong point. It is equally difficult, however, for me to believe that everything has been the same for 139 years. After all you are using an arbitrary start point (yes, I know it's the earliest, but still arbitrary); for instance, fix your initial measure at the bottom in 1920 and, I suspect, you will have a different trendline to compare with.

First, a quick note on the regression trend lines in my charts. Since I use a logarithmic y axis for the market price, the Excel-drawn regressions are of the exponential variety. The lines essentially bisect the monthly values using the least-squares method so that the total distance of the data points above the line equals the total distance below. The regression, then, is sort of a hypothetical equilibrium, but it by no means implies that everything has been the same for the past 139 years. On the contrary, the market rarely hovers around the long-term trend. My main point in the earlier commentary was to suggest that the 1982 bull market was not the start of a new economic order but a reversible trend similar to historic market cycles.

The two thumbnail charts (click for larger versions) have regressions drawn through the secular bull and bear markets in the S&P Composite over the past 139 years. For the mathematically inclined, I've included the regression equations and R-squared. To calculate the annualized slope of the regression trend, I've multiplied the coefficient highlighted in color (red or blue) by 12 (monthly data) and formatted as a percent.

The table below combines the data from the charts. I've also added a more conventional measure of performance, annualized returns, with and without dividends reinvested for each of the secular periods. For these numbers I used the fabulous tool on the Political Calculations website (click the link and scroll down).

For each trend, the closer R-squared is to 1.0, the better the fit. For example the bull regressions for the Roaring Twenties, the 1949 "baby boom" bull and the 1882 "adult boomer" bull are close fits to the regression. In contrast, the bear market regressions are relatively poor fits, which is not surprising in light of the much higher volatility during secular declines (see this table). Thus, the extreme volatility of the Great Depression gives us a very low R-squared. Had I plotted the regression through the 32-month crash of 1929, it would probably have been closer to 1.0. The regression since 2000 has an even lower R-squared — not surprising given the back to-back cyclical bears in which the S&P 500 experienced nominal declines of 49.2% and 56.8% in less than nine years. The accompanying table also documents the secular annualized returns, with and without dividends.

As I've pointed out before, even though our data stretches back nearly 140 years, there have been too few of these mega-cycles to make firm conclusions or reliable forecasts. But by drawing a regression through the data and one for each of the major bulls and bears, we get an inkling of the potential magnitude, duration and frequency of these secular trends.