1. S&P 500 is overvalued and likely to get very low (say 0-3% nominal returns over next 5-10 years)
2. Berkshire would very likely give 6-7% real returns (say 8-9% nominal returns over next 5-10 years)
3. Berkshire would outperform S&P 500 at most by 0-2% longer term (similarly over next 5-10 years)

Since all three cannot be true at the same time. What gives?

Rephrase a bit to add the reasons, and the problem goes away.

1. S&P 500 is overvalued and likely to get very low (say 0-3% nominal returns over next 5-10 years) mainly because it's likely that valuation levels will not rise, and may fall a bit. There will be a headwind for earnings based value for a while as the trajectory of profit growth slows due to higher real interest costs hitting companies that have debt.*
2. Berkshire would very likely give 6-7% real returns (say 8-9% nominal returns over next 5-10 years) because that's a pretty reasonable expectation for the growth in value per share, and it's reasonable to assume that valuation levels won't change much because they aren't stretched right now. Higher real interest rates don't hurt Berkshire measurably.
3. Berkshire's underlying business results would outperform S&P 500 at most by 0-2% longer term (similarly over next 5-10 years) because the underlying businesses are in both cases so large and diversified.

Personally I might not pick those specific numbers, but phrased this way there is no particular conflict among the ideas.

I expect both choices to be hit with a headwind at some point in the next few years with a rise in headline US corporate tax rates. For now I'm assuming the headline rate will rise from 21% to 25%. Not fatal, but a measurable hit to value. This doesn't worry me--Berkshire has had a recent stretch of unusually good business results, so a short stretch with below-average growth in observable value would not be a shock. e.g, my valuation metric for Berkshire shares rose at inflation + 11.6%/year in the five years to 2021. That's not normal.**

Jim

* 19% of the S&P 500 net profit growth rate in the last 30 years came from falling interest costs. If those costs rose back to prior levels in the next while, that would be a corresponding slowdown in the profit growth rate. The rate of profit growth has been historically an outlier in this period at inflation + 3.8%/year, of which 0.72%/year was falling interest costs. If there were a rise in interest costs from here instead of a fall, other things being equal, the changing interest cost would be a drag instead of a boost and net profit growth rate to come would be 2.36%/year. It is possible that Mr Market would not give the same valuation levels to a collection with earnings rising at less than 2/3 the recent rate.

** "In a garden, growth has its season. First comes spring and summer, but then we have fall and winter. And then we get spring and summer again." --Chance, the gardener

Jim