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You don't have to do an inflation adjustment on an instantaneous earnings-related rate. A firm with 10% ROE is likely to have 10% ROE the next year with smaller dollars. With a shrunken yardstick you get bigger R and proportionally bigger E as well: the same ratio.

I don't think this is necessarily true.
E could increase much more slowly (proportionally) due to inflation than R.
Let's take an example.
Beginning assets = \$100 monetary, \$200 non-monetary (book value with no depreciation).
Liabilities = 0.
Beginning equity = \$300.
No inflation.
Earnings = \$100.
Ending equity = \$400 (all earnings go to retained earnings.)
If we calculate ROE on the average equity, it comes to 2/7 (\$100/\$350) = 28.57%. On the beginning equity, it is \$100/\$300 = 1/3.

Now assume 10% inflation (not hyperinflation which will trigger asset re-evaluation and change in equity.)
Beginning equity = \$300.
Earnings = \$110.
Ending equity = \$410.
Average equity = \$355.
ROE = 110/355 = 30.985% ~ 31%. On beginning equity, ROE = \$110/\$300 > 1/3.

If you have to restate assets to \$100 (monetary) + \$220 (non-monetary) = \$320 then your ending equity will be \$320 + \$110 = \$430.
Average = \$365. ROE = 30.1369%.

Conclusion:
IF all net assets (assets - liabilities) are non-monetary AND you calculate ROE on beginning equity AND there is no depreciation, THEN your statement will hold true.

In our case, assume \$300 assets = \$300 equity at the beginning, and no cash, and no depreciation charges; then at the end both would be valued at \$330, not counting the recently added \$110 in earnings, and ROE will remain at 1/3 = \$110/\$330.

Otherwise, ROE will increase with inflation.

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