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Stock returns are (to a large extent) not inflation protected either.

Actually, to a large extent they are inflation protected.

The best fit for change in US corporate nominal earnings over a given long interval is .94x inflation + constant/year.
The 0.94 coefficient has a t-statistic of 3.55.
Figures from a study by AQR Capital.

Extremely high inflation is definitely a problem, but more because it
breaks the economy than because businesses don't/can't pass on price increases.
Just one more reason to stick to firms with great pricing power, though.

High inflation also hurts asset-heavy firms more than asset-light firms.
Counterintuitively you usually want the high price/book investments at those times.

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