Ugh. So this is a pain, because the P/E should converge to the market average P/E. *But that depends on what decade you're living in*. It'll run at 20 for a decade, and it'll run at 10 for a decade, and it'll run at 5 for years. Very very much dependent on giant, global, macro factors. Very very very long run, 15 seems correct, but people's entire lives can be over before it reverts.
I've been trying for a while to only buy stocks which can survive an overall market average P/E reversion from the current highs back down to 10.
S&P 500 PE Ratio - 90 Year Historical Chart
Here's a nice chart for SP500 PE going back to 1929. The average PE is about 16. Retrosoective PE is largely viewed as indicator of market health, whether it was undervalued or overvalued. But to have any sort of prospectove view, you've got to make assumption as pick a number.
We are also making a very strong assumption about the long term health of the global economy specifically that GDP will grow at 3.5%. Whatever we may choose as our long term PE ratio, we do well to make sure that is is at least mathematically consistent with our choice of discount and GDP growth. Assuming 10 P/E, we get discount = 1/10 + 3.5% = 13.5%. This is a fairly high discount, but a time in which P/E is 10 while the economy grows at 3.5% is either very pessimistic about stocks or suffering from high interest rates. At 16 P/E, discount is 9.75%.
Of course, while we're reviewing options for a long term PE ratio, we may as well consider GDP as well. Here is a good source (GDP growth (annual %) | Data). So over the last 40 years average growth has been about 2.7%. Combining this with 16 P/E, discount is 9%. So this seems about right. My outlook on the global economy is much more optimistic than 2.7% growth. In particular, I believe that renewable energy will usher in an era of low energy cost. (It has to be cheaper if it is to ever displace fossil fuels.) Specifically, energy poverty will be addressed in unprecedented ways (solar and battery based microgrids). This will unleash tremendous growth in the developing world. Hence, I am personally optimistic about 3.5% long-term growth. I'd love to get some reaction to this.