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Stocks have returned 6.5% real (Siegel's constant) yet GDP and aggregate real sales have not risen
by that for a long time (since the 1960s).
The way to reconcile these is greater retention ratio, expanded P/Es, higher margins.
... So I don't see why profits would not grow a lot faster than sales.

I think you have to think a bit more clearly about how the market works.
The rate of return on stocks is not expected to be, and is not, the rate of rise of the value of the market index.
Each year you get the earnings on your holdings, not the rate of increase of the earnings of the holdings.
Over the very long run, real broad market earnings rise something near 2%/year, not 6.5%/year.

Historically speaking, Siegel's constant of around 6.5% real return comes from the sum of numbers like 1.5-2.5%/year real earnings growth for the index plus 4-4.5% current dividend yield.
If you're not getting dividends similar to that, you're not going to get real total returns near Siegel's constant.

The value of the index tracks the real cyclically adjusted earnings of the index, which typically rises around 2% a year, give or take.
Absent changes in valuation multiples, in any given holding period your real total return equals the rise in the index value plus your dividend yield.

Dividend yield are under 2%/year now, so even with no change in market valuation multiples you should expect maybe 4%/year in real total returns.
And less, if valuation multiples drop a bit in the direction of historical norms.

The bigger point:
Profits can't rise as a percentage of sales over time, except in the "up" portion of cyclical variation.
Even a thousand years from now, profits will not exceed 100% of sales. Probably never more than 20%, at a guess.
As real GDP generally rises only in the vicinity of 2%/year, that's the best net profits do as well, over the long run.
Hey, be a huge optimist, say 3%.

If real earnings are rising at <<3% a year and dividends are getting you <<2% a year, you have no reason at all to expect a real total return from the broad market of more than <<5%/year.
Anything better than that is likely transient and cyclical multiple expansion.
We've seen a lot of that lately.
And it might be much worse in a plausible stretch of multiple compression.

If you want to reverse engineer reasoning to support an expectation of higher returns, you need a sustained and much higher rate of real GDP growth than ever seen, and/or ever rising net margins beyond their current 70 year highs.
Those aren't likely, so real total returns for the broad US market over 4-5% aren't likely.
I think anything over real 3%/year would be a wonderful result for the next 5-10 years.

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