I actually just showed you one example. It can work exactly the opposite way as well depending how the underlying moves, so you can end up with a scenario where, in my example, the inverse ends up much higher than the underlying after a round trip to the same point. Its really worth the time to play on excel, it was eye opening for me. The bottom line is that you can't depend on one side to approach zero, so just shorting both doesn't work. And I'll save everyone the effort, even if you rebalance daily all the ETFs are actually pretty efficient about tracking the percent change in the underlying so you can't profit off shorting both and taking advantage of slippage and costs in their internal trading. There is some of that, but your daily rebalancing costs dwarf them.
I've read that paper actually, when I did a deep dive on this subject a couple years ago. While it does address the path dependency of returns, any complicated math regarding that is just them building a closed form formula to represent what I showed and what you can see in Excel. The rest of the more advanced stats math is related to the tracking error caused by the ETF manager having to internally rebalance daily, and how that has to happen more frequently in volatile times than in less volatile times. I stand by the simplicity of being able to completely understand what's going on by doing some examples, but if you see an error with a specific part of that methodology I'm happy to reconsider. Happy to do advanced stats (and calculus as well but it clearly has nothing to do with this or most anything in finance), just don't believe it's required here. BTW, the term "beta slippage" that seeking alpha trots out is just another attempt to obfuscate and confuse things. This has nothing to do with either beta or slippage, so tossing them together to explain this smacks of someone trying to sound important by pulling out important sounding words they don't actually understand themselves.
It's at $1.34 down from $1.85 when the thread started a week ago. That's a 28% drop in a week. These triple etfs seem to attract greedy people who lack the experience or education to understand what they are buying. The whole concept of buying because it went down a lot is absurd ( see S2007S and his UWTI "ownership"; he's lost 85% of his stake in a few months ).
The seekingalpha article does explain that shorting the pairs is not risk-free at all! PS, I still think UGAZ looks bottomy...low-bottomy
haha!! This is what I used to do decades ago: buy very cheap stocks / ETFs. Then it became even much more cheaper stocks / ETFs. What sort of company is that?!?!? Price dropped from 4 digits to 3 digits to 3 digits to 1 digit to ?!??! How did the UGAZ CEO do that ?