Is a dollar gain truly equal to a dollar lost?

Question

Under the context of the asymmetrical nature of gain to a loss, as shown below, is 1 dollar gained truly equal to 1 dollar lost?

If not how would you go about calculating the equalization ratio at a given point?

Answer 1

By computing the inverse of the loss. Down x% requires a gain of $(\frac{1}{1-\frac{x}{100}}-1) * 100%$ where one could plug in various numbers to the formula. For example:

Down 50% would be a loss of half which in the formula results in 100% which is a 100% gain to get back to even.

Answer 2

The chart demonstrates that $\frac{x}{1-x}\ne x$ for nonzero $x$, so a percent drop needs to be paired with a larger percent increase to 'even out'. But a dollar lost requires just a dollar to go back to the original amount.