So you agree that you're making a -EV martingale bet, but you're okay with it because if you keep at it you'll eventually win (if you don't go broke first)

"no realized drift" would be a great backtest in a market where the underlying is guaranteed to return to the starting price in all instances. i don't think real markets work like that.

i'm pretty sure brianthemick is just trolling at this point. he can safely be ignored.

The thing is, these things do decay and some guy on the internet like 8 years ago decided to explain it by showing that daily leveraged ETFs underperform 2x/3x the underlying in certain instances, particularly when the underlying starts and ends around the same price with some price movement in the interim. That is "the math" people keep referring to. The idea went sort of viral in the "I think I'm a quant but really I'm a moron" community. Guys like BrianTheMick2 took this to mean that shorting them is brilliant because "the math" guarantees they'll always win. And of course they do win in the median case, giving them the confirmation bias they need, but get crushed in the tail end.

Leveraged ETF decay is real for other reasons (management fees, trading costs, slippage, leverage costs) especially when volatility is high and liquidity is limited. They were especially inefficient in their youth, particularly around the mortgage crisis when volatility/liquidity were nuts. And the "math" proponents have incorrectly taken this as confirmation that they're right.

I'M NOT TALKING ABOUT BEING SHORT

I'm talking about the original point which is that these decay due to the math of leverage and compounding over time.

They will decay over time because of this math (even ignoring slippage and any other costs associated with the actual product).

By you admitting that you will eventually win by being short you are proving my point that the compounding and leverage math eventually overpowers even sustained trends. The whole point is that it only takes as little as one outlier day to wipe out ANY multiple of capital you made prior to that. This has nothing to do with issues related to the product and their rebalancing as you were stating.

this is where it started

Look at my posts. They emphasize the long-term.

If you're in a 3x levered product and the underlying is down >33.33% in a day then you go to 0. It doesnt matter if you made 4927433254564135441349033841x your money previously and that underlying was up every single day for 432 years.

You always win even outside of median cases. You keep saying you get crushed in the tail end which is possible in practice based on your sizing, but you always win if your sizing is sufficiently small. As with all investing, the issue of sizing and timing if you're taking the short side. If you're taking the long side you can obviously make money in the short run, but if you leave it on in perpetuity it will always go to 0 even without drift, slippage, management fees, etc.

You're still wrong about the inevitability of these things going to zero in the absence of the drag from administration costs.

What will your returns be like over 100 years in a leveraged fund?

What if your leverage is 1.05x? Almost guaranteed to beat the underlying return over a long time frame. 1.2x? Same. 1.5x? Probably. 2x? You'll have periods of underperformance and overperformance. Overall return and volatility will determine whether your median result beats the underlying.

3x? Well that's a different animal. There's a reasonable chance you'll get wiped out, or close to it, over 100 years. Particularly in an ETF with a volatile underlying. Yeah, you'll lose most of the time. But "without drift, slippage, management fees, etc." there's still no inherent decay and taking any short position, even for 1-2% of your capital where it's "basically impossible to blow up" as you suggested would be crazy because it's a hugely -EV bet when the underlying has positive expected returns.

A 2x ETF with perfect daily tracking would still be a very very investable instrument. It would even be more prudent than just investing in the underlying for many people, because the daily EV would be exactly double. EV over 50 years would be orders of magnitude higher. The problem is there's management fees, leverage costs, rebalancing costs, slippage, etc. that drag these down at a much faster rate than makes sense for a long term investment.

Why in the world would you think 2x SPY is going to 0? (forget that that isn't a sufficient condition anyway)

Well, its less likely now that there are circuit breakers, but without circuit breakers you would eventually get a 50% loss which zeroes out your investment. I don't know if that loss would come this year, this decade, or this century, but it would come at some point before the end of time.

This depends on how you define "long time frame." If you define it as forever then they will lose. If you define it as a retirement horizon (so say 30-50 years) then I agree it is likely fine to invest in a moderately leveraged ETF if it tracks well. Like you say though, the volatility of the underlying matters. With enough leverage even indexes that have almost no volatility still go to 0. In cases of lighter leverage, sufficient volatility can push them there.

And there is inherent decay due to leverage. For simplicity and because the answer is very straightforward think about a 5x leveraged ETF on the DJIA. If you held this prior to Black Monday you would go to $0 no matter how much capital you have or how much profit you made. The math of the leverage causes inherent decay to 0.

It is inherent that this will happen over time to anything provided the timeline is long enough. Sure, the timeline required for certain volatility levels in the underlying and the leverage of specific instruments might still dictate that they are viable for investment over someone's specific timeframe, but they are certainly not suitable in perpetuity unlike unlevered instruments which are never in a position where they completely evaporate.

Ok, if you cap daily moves to +/-49%, why would you think 2x SPY is going to 0?

The problem is you can't use that logic to say that all leveraged ETFs must eventually go to zero. If you did you'd also have to claim that a 1.05x leveraged ETF also has to go to zero because eventually there's going to be a 96% drop. The logic is wrong.

You could make an argument based on expected underlying returns, volatility and assumptions about mean reversion that a leveraged ETF loses money the vast majority of time under the given conditions, but you're just making broad blanket claims that aren't congruent with reality.

For your assertions to be true, you have to accept that the probability of a daily move of x% (say 50% for a 2x fund) is 100% over a finite timeframe. That is a bad assumption.

why do we need a finite timeframe? Why can't we use a perpetual timeline?

Because then you're just talking about the inevitable heat death of the universe which is boring

Because infinity is an abstract that has no place in reality. You can't take something with a small finite probability every day and just say it occurs with 100% probability eventually and then use that certainty of failure in your EV calculations over finite timeframes.

SPY is going to zero in 4 billion years when the sun expands to consume the earth.

Nah, by that time most S&P500 companies will be established in other solar systems/galaxies. If it goes to zero it'll be much sooner than that because of a meteor or something.

I never was discussing finite timeframes. I was always discussing the long-run which in finance is not a concrete finite period. You can look back at my initial posts and you will see them reference the long-term or long run as opposed to finite timeframes. You brought those timeframes into the discussion.

I'm not talking about specific concrete defined timeframes. I'm talking about you using infinity in your math as if it somehow applies. "Long-term" and infinity are very different things mathematically.

One billion years is finite. If you base your math on that it won't break like it does when you use infinity. If you're interested in longer timeframes I recommend the Science, Math and Philosophy forum.

this became a math question when you asserted that these won't fail due to math but rather due to frictional costs.

I'm not saying it's not a math question, I'm saying you shouldn't use incorrect math.

what's incorrect about my math?

You can't just plug infinity into a formula, math doesn't work that way

Also you've been talking about several decade samples in some of your posts. You can't just claim now that you always meant infinity, this isn't WW.

interesting topics.

leveraged etf's have their issues but if the market does ok or well long term you should do well in a double leveraged etf.

you won't get double the return, that's for sure - for so many reasons..........

but other ways of getting leverage have their problems. if you started at almost any time in financial history with double leverage and then never adjusted anything you would have gone bankrupt - sometimes in under 10 years, sometimes in as long as maybe 80 years. basically if the market goes down 50% from peak you are bankrupt or near bankrupt.

the place where there were some HUGE HUGE issues were leveraged short etf's. imagine you shorted real estate or china before credit crisis in triple leverage and then found out YOU LOST MONEY WHEN IT WENT DOWN 50%...... hard to fathom.

anyway, basic leverage strategies in lieu of leveraged ETF have all kinds of issue too. for one, i believe only 1 major online broker has good margin the rates. the rest seem to charge 4%-6% or even more when market rates were/are basically zero.