"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."
Thanks for clarifying the term.
I said: "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."
You said: "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."
Yes, the valuation of the stock price based upon future earning is not a question in my mind. I was not clear enough by what I meant by "consensus". By this, I mean the MARKET consensus on the stock price. That then gives the consensus on the appropriate P/E ratio.
I said: "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."
You said: "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 am familiar with the central limit theorem. My point was, (which I did not make explicit) the stocks at the low end of the P/E range were at 5, but the historic stock market cap to earnings ratio is is at .5--how can that be? If the low end of the sample is 5, surely the average will be higher for the entire market? Why is the ratio so low, given the P/E ranges?
You can see why I said "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). "
This sample of the SP500 shows a P/E ranging from 5-45 over 130 years:
Given this large sample, how can the market capitalization ration be historically under 1?