Incidentally this also means that if you buy the etf on day 1 and the underlying is at 100, on day 2 the underlying falls to 99 then on day 3 goes back to 100 then you would be left with less than 100% of what you started with (assuming perfect tracking and no fees).

Volatility drag. Not trying to be a shill but I wrote a blog post about the mathematics of volatility drag if anyone is interested:

https://smabie.github.io/posts/2019/10/04/vol.html

It involves deriving “perfect” leverage ratios and talks about some other interesting (imho!) stuff.

Yes, this is called "decay", and it's why you don't want to hold a leveraged fund over any long period.

According to my models there are very few market environments in which you would make less money with a leverage ratio of 2.5x. In order maximize return your leverage should be:

Expected Return/Expected Variance

For example even if the expected return is 1% and the vol 5%, the ideal leverage ratio for maximizing return is 4x!

In short, a 2-3x leveraged ETF is an excellent investment and should outperform the index in almost all market conditions. It’s when your leverage ratio goes over 5x that you start to have major problems a lot of the time.

I can appreciate this, but the fund decay actually has nothing to do with leverage.

All "leveraged" ETFs (to the best of my knowledge) are synthetic - they achieve their "leverage" using derivatives, not by borrowing. These derivatives are not free, and like an option, can expire worthless. That's how the value in these ETFs evaporates over time, regardless of how the market performs.

Of course not “regardless” of how the market performs, take a look at UPRO over the last 2/3 yrs. But those are in theory reasonable concerns, however empirically most leveraged funds have performed as promised relative to their benchmarks (with a couple notable exceptions I admit). The entire point of derivatives (as suggested in the name) is that they inherantly bear an underlying relationship to their underlying security.

If you look at UPRO, its daily returns almost exactly track 3x of SPY. There’s no long-term “decay”, unless you are referring to volatility drag. VIX etfs are the notable exception, in that they do suffer from persistant negative carry.