Shorting leveraged ETF sounds like a money-making scheme, as far as i infer it from the question. It seems that the idea behind shorting leveraged ETFs (let me abbreviate it LETF) is to earn the beta-slippage as described in the posts below.

I’ve taken a closer look: Shorting LETFs only works if the ETF price follows a mean-reversion process (check Ornstein-Uhlenbeck process) with a considerably high mean reversion parameter.

So: Shorting LETFs is a disguised mean-reversion trading strategy.

The idea: Lets say the ETF rises by 10% the first day and then subsequently drops by 10%, so your ETF lost a total of 1% : (1+0.10)*(1–0.10)-1=-0.01. (This is due to the daily settlement)

It turns out the LETF without leverage (L=-1) also lost 1%: (1–0.10)*(1+0.10)-1=-0.01. So shorting the (inverse) LETF would gain 1%, right? And we haven’t applied a leverage factor yet.

That is the usual way to explain the effect of shorting the LETF, and most theoretical arguments end here, but how likely is it to receive the profits?

Lets illustrate this by applying a spread strategy and a binomial tree (also works for continuous stochastic processes, but i’m afraid 99% of the readers will get lost in the math):

My strategy is: Long ETF, short LETF, L=-1

Down-Down: (1-R)(1-R)-1 long ETF, 1-(1+R)(1+R) Short LETF, Diff: -2R^2

Down-Up: (1-R)(1+R)-1 long ETF, 1-(1+R)(1-R) Short LETF; Diff: +2R^2

Up-Down: (1+R)(1-R)-1 long ETF, 1-(1-R)(1+R) short LETF; Diff. +2R^2

Up-Up: (1+R)(1+R)-1 long ETF, 1-(1-R)(1-R) short LETF; Diff: -2R^2

Under the binomial tree-setting, the probability for each scenario is 25%, so the expected return (sum of each Prob*Outcome) is 0%:

Lot of Beta-slippage, but no return.

We see that the only way we get positive returns is if the scenario Down-Up or Up-Down is more likely that Down-Down or Up-Up, which i would interpret as reversion to the mean setting such that the short LETF outperforms the long ETF. If L>|1| then these returns are amplified.

If we assume momentum is present in the ETF market (as found by Jegadeesh and Titman (1993) for stocks), then you can expect to lose money by shorting LETFs, if there’s mean-reversion in ETFs, then you can earn money by shorting LETFs.

As far as i know there’s not much evidence for Mean-reversion in the stock market, however, i need to check whether this also applies to ETFs

So, i guess its not a good idea to short LETFs :-)

what is your opinion ?

I would love to hear your feedback and follow the solutions you offer.

Lots of interesting stuff, but you are reinventing the wheel. What you describe first is volatility drag (read up on it).

There is no significant mean reversion for ETFs . If it would be there, then it would be free money. Equity index ETFs track the index very closely.

A long short ETF strategy is analyzed in Euan Sinclair's Volatility Trading (Second Edition, Chapter 13).

Notation is the same as in Black-Scholes GMB model (S, S0, sigma, and t), and this is the result:



Basically, it is similar to a long straddle strategy.

Regardless, if you have an idea, then backtest it. Then, paper trade it or trade it with a small amount of money.

Also, in this game, you cannot use reference material from the 1990s. Most of the stuff from here:

http://www.godotfinance.com/workingpapers.xhtml

is already eliminated or the performance is reduced (I have backtested the volatility strats). Some strats were not good to begin with due to data snooping. The above link is good tho if you want an idea where to start.


EDIT:

There are backtested starts here too:

http://epchan.blogspot.com/

interesting subject...

professor at University of Washington has done tons of work on this. published a book i believe.

a few questions/comments:

short leveraged ETF against what? against what strategy?....i have fooled around with some stuff alot. hard to find reasonable algorithms that do better than basic 2x daily leverage. any improvement is incremental. 18.3% return vs. 18.1% (and even then exact time re: credit crisis, matters alot)

mean reversion and stock market.. people love "buy the dip" which is mean reversion-based BUT i find 1) you have to sell first, 2) "buy the dip" strategies are little better than owning the stock market a random 10-15% of the time i.e. no real alpha.

where leveraged etfs (esp. short-selling ones) really have problems is late 2008 to early-mid 2009.....the 2x leverage fund will be selling the market whole way down. and then the market reverses.... but if the fund didn't sell the whole way down, it would end up with 5x leverage (or maybe have infinite leverage/zero equity i.e. game over)

what about shorting long and short leveraged funds? maybe not 1-to-1 ratio.. and again "short against what on other side"

UW professor = Tim Leung..

books on LETF and mean reversion

Thanks for the reference. Might try to read it later.


Seems like some people made this exact strategy work. Then, enhanced it when volatility is in a high regime.

https://jot.pm-research.com/content/13/2/69

Paper can be downloaded from Sci Hub (just google it if you are not familiar) and enter the DOI of the paper (click the link above). Don't want to post a direct link cause of copyright.

Or send me a PM if you want a copy.

No, it has nothing to do with daily settlement. If you hold your investment while it rises by 10% then loses 10% then you have lost 1%, whether it happens in one hour, one day, or one year. The same is true if it drops first then rises by 10% (or any percent).

one thing about "obvious +EV shorts" (if they exist) is that shorting fees are high

at various (most) times in recent years, marijuana stocks have been obvious shorts.. BUT i believe borrow fees are/were in the 20-25% per annum range..

makes me wonder who in their right mind would own "freely trading" marijuana stocks

the daily up/down doesn't affect the leveraged ETF performance very much

where you really get hurt is if the market range trades a long time (i guess that means tons of up/down days)... and really bad if it pings between support/resistance for weeks/months.

and a huge one is when the market changes direction....... in 2008/09, LETF sells the whole way down to bottom and then market takes off quite quickly

There are inverse leveraged ETFs that are liquid and have reasonable management fees. For example, here are the funds used in the above study:

IIJ is a pretty solid publisher (they are also pretty trigger happy when it come to copyrighted material so this post might be removed). Most decent strategies/empirical work have to include the 2007-2008 crisis (they do that in the paper except for one index).

The authors' findings is pretty good. Not mind blowing, but those strats get eliminated pretty fast (if the large advantage was there to begin with).



My only minor problem is that they didn't measure the skewness risk and didn't include equity curves.

Might backtest some of these to see how the strats did in 2020.

Canuck.. thank you... I'm also a "Canuck"

I believe that inverse leveraged ETFs had some really wonky behaviour relative to the the credit crisis i.e. they went completely the wrong way.

the math and common sense understanding of "path dependence" of leveraged ETFs seems so simple but tricky at the same time

could not replicate this with SPY.... as I recall, it was either asian equities or REIT's. or maybe both (including asian real estate)

LOL picked the wrong pair (or one of the wrong pairs). They use volatility to try to forecast the returns for the next month. Should have mentioned that, according to the paper, this approach doesn't work for SPY and QQQ.

Also, they use monthly frequency and this is bad. Small sample size and all. They also use "median volatility" as a filter and don't mention how they obtain median (is itfor the whole sample or running?). So this might be data snooping.

Didn't have time to read it very carefully. Some of the above details might be off. But after implementing a lot of these published studies, I wouldn't be very optimistic. Worth a try to check tho cause it doesn't take a lot of time and effort.

Crazy canuck, I meant I couldn't replicate my own statement... Wasn't based on anything you posted

No, it's not free money

If you are betting on "mean-reversion" you can just short a straddle using options.

Why make it so complicated?

In any "bet" if you get to gain in one scenario, you have to be exposed to loss in some other scenario. In this case you want to bet on "mean reversion" then the risk would be a one sided market (up-up/down-down in your binomial tree)

In short there is no free money.

Hi guys . Thank you very much for your good ideas and tips. it was useful . I consider all comments and suggestions.

This strategy has a small edge (see the results from the paper above) and is not really worth it at the retail level. It wouldn't work with options cause of the transaction costs. And selling naked straddles without a huge edge is not worth it.

Either way, there is only way to find out whether the strategy has potential or not. Simply backtest it.

Backtesting tends not to give the most reliable results for strategies that pick up pennies in front of a steamroller.

Not sure what your point is with trying to dismiss a work with one sentence criticisms.

Backtest it and then test it out-of-sample. Standard approach for any strategist/quant fund. Tail risk can be easily noticed. Either from the equity curve or measuring the relevant stats.

Also, editors usually ask for much more work that is not included in the final work (reviewed for their sister journal and published in much better). Editors/reviewers are fully aware of the points you raised.

Standard rule still applies for any academic publication regardless. If there is a small edge, publish it. If there is a large edge, trade it. I did find stuff from other academic publications that significantly outperform the market (had to modify it tho).

I don't always think profit is guaranteed, but when I do play leveraged options.