What is the derivatives market in layman terms

Why buying an inverse ETF doesn't produce the same results as shorting the ETF

For example, let's say the ETF is currently priced at $ 100. Suppose the next day it increases by 10% (to a price of $ 110) and the next day by 5% (to a price of $ 104.5). In these two days, the ETF made a net gain of 4.5% compared to the original price.

The inverse ETF reverses the daily gains / losses of the basic ETF. For the sake of simplicity, let's assume that the inverse ETF also starts at a price of $ 100. On the first day it drops by 10% (to 90 USD) and on the second day by 5% (to 94.5 USD). Thus, the inverse ETF had a net loss of 5.5% in the two days.

The specific dollar amounts do not matter here. The result is that the ETF ends up at its original price and the inverse ETF ends up at its original price. A similar example is given here.

As suggested in your offer, this is due to compounding. A gain of X% followed by a loss of Y% (composed of the profit) does not generally mean a loss of X% followed by a profit of Y% (composed of the loss). In simpler terms, if something loses 10% of its value and then gains 10% of its new value, it will not return to its original value because the 10% it gained was 10% of its decreased value, so not enough to to bring it all the way back to the top. If it gains 10% and then loses 10%, it will easily fall below its original value (since it has lost 10% of its newly increased value).