It doesn't impact the point you're making but your example on page 1 isn't 100% accurate. After a 40% loss, and before the reverse split, the share price is $7.50 not $7.
The percentage gain required to break even is the same before and after a reverse split. Perhaps your error in concluding that it is more difficult is due to the initial "rounding" error.
It makes sense that percentage move is irrelevant to how many shares since we are starting with a total investment value that is identical in both cases.
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ProShares Is Doing "The Splits": What This Means For Volatility Investing Strategies
It doesn't impact the point you're making but your example on page 1 isn't 100% accurate. After a 40% loss, and before the reverse split, the share price is $7.50 not $7.
The percentage gain required to break even is the same before and after a reverse split. Perhaps your error in concluding that it is more difficult is due to the initial "rounding" error.
It makes sense that percentage move is irrelevant to how many shares since we are starting with a total investment value that is identical in both cases.