The wisdom of crowds -- growth rate in P/E ratio has contributed nothing to long-term stock-market returns

When you invest in a share of stock, you earn an annual return equal to, roughly, the sum of dividend yield, growth rate in earnings per share, and growth rate in P/E ratio:

\[
annual\,return=dividend\,yield+g_{eps}+g_{p/e\,ratio}
\]

(This formula is from my book, Investing in Dividend Growth Stocks. If you do not have a copy, you may be able to view the relevant pages, 7 through 10, at Amazon, here.)

Dividend yield assumes dividends are paid at the end of the year. Growth rates are defined as change divided by starting value, thus:

\[
g_{eps}=\frac{change\,in\,eps}{eps\,at\,start\,of\,year}
\]

and

\[
g_{p/e\,ratio}=\frac{change\,in\,p/e\,ratio}{p/e\,ratio\,at\,start\,of\,year}
\]

Our definition of annual return states that annual return is dividend yield (with dividends paid at the end of the year) plus a contribution from capital changes -- equal to growth rate in earnings per share plus growth rate in P/E ratio.

The purpose of this post is to show that, historically, of the contribution from capital changes to annual return, almost all has come from growth rate in earnings per share. That is, growth rate in P/E ratio has contributed almost nothing.

The following chart shows beginning-of-year P/E ratios for the S&P 500 between 1 January 1900 and 1 January 2016:

(The data for this chart comes from http://www.multpl.com/table. The 1 January 2016 P/E ratio is an estimate. P/E ratios are based on prices divided by trailing 12-month earnings per share. The median P/E ratio is 14.73; the mean, 15.77.)

More relevant to us, here, is change in P/E ratio. The following chart plots annual change in P/E ratio, 1900 through 2015:

Median annual change over this period, -0.085, is essentially 0. Mean, +0.076, is essentially 0 as well. Historically, therefore, on average, change in P/E ratio essentially equals zero. 

(Change in P/E ratio depends on period studied. Nevertheless, it is still quite small over most reasonably long periods -- exceptions such as the 1990s notwithstanding, though we all know what happened thereafter.)

As a consequence, growth rate in P/E ratio is essentially zero, on average, as well:

\[
g_{eps}=\frac{change\,in\,p/e\,ratio}{p/e\,ratio\,at\,start\,of\,year}=\frac{0}{p/e\,ratio\,at\,start\,of\,year}=0
\]

Returning to our formula for annual return, the only contributions to long-term stock-market annual return are thus, on average, dividend yield and growth rate in earnings per share. Growth rate in P/E ratio, on average, essentially contributes nothing. Going a bit further, quoting from my book, page 10, which, as noted earlier, you may be able to view at Amazon, here: 

"Dividend yield has historically produced about one-third of market returns; capital gains, about two-thirds. Moreover, of the contribution from capital gains, almost all has come from growth rate in earnings per share. That is, over long periods, growth rate in P/E ratio has contributed nothing. Sometimes, it has added. At other times, it has subtracted. Net, it has produced nothing."

Funny how things worked out this way, almost as if scripted -- by some invisible hand, https://en.wikipedia.org/wiki/Invisible_hand. This happy circumstance is probably a testament to, by and large, the stock market operating properly -- the stock market, by and large, pricing things correctly. After all, if P/E ratio is on average correct, change in P/E ratio is on average zero. Occasionally, we have manias -- followed inevitably by panics -- but, averaged over time, the market gets it right, a vindication, perhaps, of the wisdom of (investing) crowds.