English: S&P 500 Index Logarithmic Chart’s Interesting Features.

While an S&P 500 to linear plot scale is good for analysis of the current year or maybe up to the past 2 or 3 years, beyond that a logarithmic S&P 500 chart is required. This is because it gives the same Y displacement for a certain percentage move up or down regardless of date. Moreover, a fixed compound interest percentage gain plots as a straight line on a logarithmic chart, which is very useful as the human is very good at judging and comparing moves above and below a straight line (versus the linear plot's exponential curve for same). The given chart with Y axis logarithmic values was computed using Excel. There is an upper cluster of lines as published i.e. with inflation and lower cluster of lines with INFLATION SUBTRACTED, (inflation data from http://www.usinflationcalculator.com/inflation/historical-inflation-rates/). The upper cluster has roughly parallel curves plotted using S&P 500 monthly MAXIMUM values for the upper line and MINIMUM values for the lower line (from Yahoo history https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC or daily data) and the X axis has 828 months from 1950 to current December 2018. With the upper and lower clusters are straight lines plotted as a trial-and-error BEST FIT to the S&P 500 curves they are with. The close parallel lines represent an effective 'thickness' of 5%, though plotted as two lines; this to copy the approximate monthly difference of the S&P500 monthly fluctuation. Best Fit of the straight line plot versus S&P 500 Max and Min curves is by accumulating the excess i.e. positive for the upper curve above the upper straight line and negative for the lower curve below the lower straight line giving an accumulated value going from 1950 onwards. Observing where the curves and straight line have roughly ZERO difference shows the lines match at some places; these places displayed as a dotted text box. The upper cluster straight line BEST FIT slope gives a compound interest of 7.5% per annum. The lower cluster straight line BEST FIT slope (without inflation) gives a slope of compound interest of 4.0% per annum. Based on numerous attempts to do the Best Fit these percentage numbers are believed to be accurate correct to 0.1%. In addition a further confirmation is that inflation over the period 1950 to present computes as 3.5% per annum compound i.e. the difference between the two slopes. Government debt and GDP plots are added as percentage to show relative displacement though the Y scale is not valid.

Logarithmic Chart's Interesting Interpretations

Firstly the upper cluster S&P 500 curves including inflation follow a straight line percentage gain much better than those without; therefore inflation somehow evens out the ups (gains) and downs (losses) of the S&P 500 without inflation. It is interesting to note (see curve including inflation) that for example, the 1955-69 post-war boom curve above the straight line 7.5%, is eventually negated by an 1974-86 loss period below the straight line, returning to the 7.5% slope and BTW also giving a zero accumulated value at the 1987/97 region. Also, the Internet Bubble from 1995, peaking way above the 7.5% straight line at 2000, is followed by drops, 2002 and especially 2009 below the straight line. Following the Bubble, while climbing from 2009 the curve stays under the line for many years, only returning to the 7.5% straight line around 2015/16. The given plot of straight line plot versus S&P 500 curve gives parity or excess equal to approximately zero at the beginning, i.e. 1950s, and middle 1987 to 1997, These places are represented as overlain dotted boxes and labelled. As shown by history on the plot, after the term maximum 15 years of an above or below excursion, the S&P 500 curve returns to the 7.5% Best Fit line.

In 2018 the curve and straight line are fairly matched, and the S&P 500 market plot shows neither a high or boom period, nor slow or recession period.