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I am REALLY struggling to understand why it makes sense to assume future real EPS growth for the S&P 500
will be more similar to the two periods you mentioned, 1975-2005 & 1935-1975, rather than what we've seen since 2005.

The recent upswing in the rate of real profit growth is transient statistical noise, due to the big recent "kinda cyclical" upswing in net margins.
That's ultimately just a transient thing, because net margins can't grow faster than sales without bound.
Even if they stay high for a long time, we'll see that the rise was a one time thing, not a new higher growth rate.

Real aggregate profits over time won't grow any faster than real aggregate sales, which won't grow any faster than real GDP, which seems to grow at around 2%, give or take.

Net margins have high decades and low ones, but the range is ultimately bounded.
Thing of aggregate net profits as mainly tracking aggregate sales, which are relatively smooth, plus or minus squiggles for profitability variation through time.

I would have to assume real EPS growth rates that low (<3.5%) will require some mix of the following:
• Normalized nominal returns on equity being much lower than 11.8% going forward. (maybe due to higher future effective corporate tax rates or something else?)
• Significantly higher dividend payout ratios and lower earnings plowback (retention) ratios reduce future nominal EPS growth rates.
• Future inflation is way higher than 2% and dragging down the real EPS growth rate.
• Some other factors that I missed?

Not really.
All it would require is sales growing at around the same rate they have been, and net margins NOT continuing to rise to ever higher levels.
(recent numbers are the highest in decades, about 1950 depending which precise figures you use)
S&P 500 real sales have risen at 2.0%/year since late 2002.
S&P 500 real sales have risen at 2.0%/year since mid 2012.
Only 1.27%/year since the end of 1999.
So, if net margins flat line at this high level and sales continue to grow at around that 2% rate, profits will grow at that rate.
If net margins mean revert at all, profits will grow more slowly while that happens. Potentially a lot more slowly.
It's not rare to see a decade of no growth in real (smoothed) earnings per S&P 500 point.

Separately, you can't compare the real EPS growth figure to the ROE directly.
There are a few extra moving parts.

Please let us know why we should NOT assume real EPS growth rates will continue to be higher (3-6%) going forward for the broad US Index than they have been historically (2-3%)

In short, it simply can't happen unless either net margins keep rising and rising, up beyond 100% of sales, or sales growth picks up well beyond historical norms.
Which would require GDP growth to pick up to almost unheard of levels.
Sales growth has in fact been pretty good just lately, but that seems to be mostly recovery from a Loooong stretch of doldrums.
The pre-credit-crunch real sales level wasn't exceeded till March 2018.
So the rates over long baselines are probably a better guide, as above.
Which makes sense...they're close to real GDP growth figures.

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