I find myself struggling to succinctly express the concept of gain or loss percentages that are equivalent in the sense that they are reciprocal. For instance, take the following sentence:
An investor with log-utility will experience the same magnitude of utility change for a gain or loss of a certain percentage of wealth.
What is intended is that the investor would lose as much utility from a 20% decrease in wealth as they would gain from a 25% increase (because (1+25%)=1/(1+-20%)). Obviously, I can say "change in log" but that makes the above sentence feel redundant. And I could also say "for percentage gains or losses that are reciprocal when added to unity", but that's pretty verbose. Is there a nice succinct term/way to express this idea of "same" reciprocal percentages?