Thanks for the reply. My main concern was the definition of “stock market GDP”. I knew what GDP was—all production of goods and services in the US. That doesn't map clearly to either profits or revenues.
You are correct that one cannot “assign” a P/E ratio to a stock, group of stocks, or the entire market. Rather, it is a consensus decision of the entire market that assigns it.
There still seems to be a contradiction between the observed P/E ratios of stocks (5-100 is the rough range) and the observed capitalization to “market GDP” ratio (50% to 150%). I would expect the group to follow the individual stocks. Since it varies so wildly, I think I still don't have the correct definition of “market GDP”.
I never questioned that you knew that, of course.
Application to "stock market" requires some care. For GDP, the universe is all producers of a nation, and the GDP itself is the sum total of output of all members of that universe.
Similarly, the universe of "stock market" is a set of companies with given stocks --- SP500, for instance. The GDP of that stock market is the sum total of earning in that universe.
"You are correct that one cannot “assign” a P/E ratio to a stock, group of stocks, or the entire market. Rather, it is a consensus decision of the entire market that assigns it."
I am sorry I did not make that clear, but it is not the consensus issue. Even one decision-maker cannot assign the same price P given E, because his decision (P) is affected also by factors other than E, namely, ALL FUTURE EARNINS of the company (hence dividends, which are the cash flows received by the decision-maker that owns the stock). You probably know the formula for the valuation of the stock based on its dividend: it is the result of summation over all FUTURE periods, from 1 to infinity. [Of course, since we don't know the future, what enters the formula is the d-maker's BELIEFS about the future or, as practitioners refer to it, estimates of the earnings and dividends.
"There still seems to be a contradiction between the observed P/E ratios of stocks (5-100 is the rough range) and the observed capitalization to “market GDP” ratio (50% to 150%). I would expect the group to follow the individual stocks.
The opposite should be true. The larger the sample, the closer the observed value to the average over the sample. So if you measure something --- whatever it is --- and it varies over the range 5-100, you can be almost sure that the observed value for the entire sample is closer to the average. Formally, this is expressed by various versions of The Central Limit Theorem (it does have assumptions, and one has to make sure that those assumptions hold, but the intuition expressed by the Theorem is correct in most business situations). "I still don't have the correct definition of “market GDP”."
Your definition is the same as used by all analysts and S&P. When they report "P/E for the SP500 index," they take the total (sum) capitalization of the 500 stocks and divided by the sum of earning of those companies (trailing or projected). There is nothing wrong with that definition or that computation. It is the intuition that leads one to expect the ration to be close to 1 that lacks support.