Recovery from a loss
Why does undoing a percentage loss require a larger percentage gain than the loss itself?
In plain words
A percentage fall shrinks the base on which any later gain is measured, so the gain needed to return to the starting value is always larger than the loss that caused the fall. The bigger the loss, the more this asymmetry matters.
Why it matters
Depth matters as much as direction when assessing risk. A market far below a previous peak needs a very large percentage advance simply to get back to even, while a position sized before the fall may have lost far more than its owner expected.
In a real week: ETH, week of 3 March 2025
In the week of 3 March 2025, ETH fell 19.77%, from an open of 2518.12 to a close of 2020.41, so undoing that fall requires a gain larger than 19.77%. ETH also closed 50.56% below its 52-week high, meaning an advance far larger than that decline would be needed to return to the peak. The week ranked in the 5th percentile of ETH's 368 weeks of history.
A common mistake
Thinking a loss of a certain percentage is fully reversed by a gain of the same percentage. Small losses mislead less than large ones, where the gap between the two widens sharply.