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Both UVXY (https://www.etf.com/UVXY) and SVXY (https://www.etf.com/SVXY) track the first- and second-month VIX futures positions. SVXY, however, is an inverse tracker while UVXY is not. What I don't understand is if they both track the same thing, why are their trends so out of line (accounting for the inversion, obviously).

More specifically, UVXY reacted sharply in March 2020 because of the pandemic (as expected) and then relatively quickly settled back down to 2019 levels. SVXY also reacted sharply in March 2020 because of the pandemic (as expected) but has not returned anywhere near its 2019 levels (like UVXY). Why is this?

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An inverse tracker does not necessarily have the inverted long-term return as an equivalent non-inverted tracker.

Let's take two tracker, N and I. N is a "normal" tracker and I is an inverse tracker of index X. All three start at a value of 100.

On Day 1, X goes up 10% to 110. N also goes up to 100, and I goes down to 90 (-10%).

On day 2, X goes down 9.09% to 99.99. N also goes to 99.99, and I goes up 9.09%.

I's value is now only 90 * 1+(9.09%) = 98.18!

How can this be? if the up and down movements get the index back to where is started, why didn't the inverse index also go back to where it started?

It's because it takes a larger relative gain to recover from a loss (and a smaller relative loss to wipe out a gain). In other words, the effect of compounding negative returns is higher then the inverse of compounding equivalent positive returns.

So inverse ETFs do not follow the inverse returns long-term. That's why inverse (and leveraged, for similar mathematical reasons) ETFs try to warn you in multiple ways that they are designed to mimic the inverse of daily returns. It does NOT give you inverse (or leveraged) returns over multiple days because of this mathematical effect of compounding returns.

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