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Leveraged ETF Arbitrage (LETFA) w/ Real Money



May 17, 2009 – Comments (13) | RELATED TICKERS: FAS , FAZ

First off I want to say that I'm a complete amateur and I have no idea if any of this stuff I am saying is actually valid or just totally wrong. I know this is risky for sure so be careful.

Some people have floated around the idea of shorting a pair of opposite ETFs. The idea is to offset their moves due to the direction of the market and profit from the volatility decay. (I'm going to call this trade LETFA, which stands for "Leveraged ETF Arbitrage", maybe it will catch on haha). This seemed to me like an interesting strategy but I haven't actually seen anyone implement it with real money. So I figured why not try it myself. At worst, I might lose some money but I would be doing the CAPS community a service :)

So yesterday, I shorted about $1500 of each FAS and FAZ. In order to control risk, I plan to hold until the ratio of FAS/FAZ is over 2 or less than 0.5, at which point I will rebalance them to have the same value again (let's call this the "rebalance limit ratio"). This way, the maximum amount I could lose on any given day won't be catastrophic and cause a margin call. In what I consider the worst case scenario, I will be shorting twice the amount of FAZ as FAS, and the market will plunge 33%. Here I will lose 33% of however much I am shorting (for example, if I am shorting $3000 total, $2000 of FAZ will go to $4000 and $1000 of FAS will go to $0, so I would lose $1000). Anyways, if you want to follow the portfolio, you can see it here. One hypothetical portfolio using these rules can be seen here.


It's common knowledge that leveraged ETFs like FAS and FAZ are terrible long-term holdings (though surprisingly, there are still many of uninformed users). Accounts like UltraSuck have racked up points by simply redthumbing these ETFs and nothing else. This strategy clearly has a lot of potential for profit, as you can see if you pull up the charts of FAS and FAZ - they are down 82% and 92% respectively since their inception about six months ago.

The reason everyone hasn't already jumped on this opportunity is because of the risks involved. This is because the two opposite ETFs don't fully offset each other after the first day, because when the position sizes change, one ETF will have more weight than the other, making the trade no longer market-neutral. Simply letting your positions run w/o rebalancing them will most likely make a lot of money in the long run, but you will be down a lot during prolonged rallies and corrections. The risk is that you will face a margin call and never get to the long-run.

I believe it is possible to largely mitigate that risk simply by rebalancing your portfolio whenever the proportions get out of whack. How often depends on your desired risk/reward level. This will mean you can miss the best days (when you have a large short position in FAS and the market plunges, for example), but it will also keep you out of the worst days (large short position in FAS and the market rallies). But you have to keep transaction costs in mind. So depending on your bankroll, the risk-to-return sweet spot changes.

My "Experiments"

I wrote a computer program to backtest different variations of this strategy. I plugged in the past price changes for FAZ and FAS and let the program run thousands of random sequences of these price changes. I played around with the starting funds and the ceiling and floor for possible FAZ and FAS prices.

I found that if you start out with $3000, the optimal rebalance limit ratio is around 1.7 to 2.1. The higher the starting funds, the lower the optimal limit ratio becomes. Very interestingly, if you start out with about $10,000 or more, you can actually just rebalance every few days if the prices change significantly, and make a decent profit with relatively low risk. I wonder if there are any hedge funds using this strategy! Surprisingly, you can actually rebalance every single day and make money, because on average, the funds have a negative tracking error, though this would not take advantage of the 3x daily returns math behind the strategy.

The problem with backtesting is that the results depend on the past market behavior, which can change in the future. The past few months have been very volatile, which is good for this strategy. So if volatility decreases, which has been happening recently, the optimal limit ratio actually goes up and the strategy becomes less profitable.

Has anyone else done some research into this strategy? And hopefully I didn't do something totally wrong or make a huge logical error. Let me know if you see something weird before my stupidity costs me a lot of money :)

13 Comments – Post Your Own

#1) On May 17, 2009 at 3:34 AM, walt373 (99.88) wrote:

By the way, I assumed a cost of $7 per transaction in my testing.

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#2) On May 17, 2009 at 4:12 AM, portefeuille (98.90) wrote:

It's common knowledge that leveraged ETFs like FAS and FAZ are terrible long-term holdings (though surprisingly, there are still many of uninformed users).

I think you are oversimplifying things a little here. Please have a look at these posts: 1,2 (see links in comment #22)

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#3) On May 17, 2009 at 4:36 AM, walt373 (99.88) wrote:

That's a lot of links. Thanks, I will look through them.

In what way do you mean I am oversimplifying? I know that if an index starts to follow a long-term trend with little volatility, the leveraged ETF can work as a long-term holding. This is the case for some commodity ETNs. But I don't see the financial sector or the stock market behaving this way anytime soon.

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#4) On May 17, 2009 at 4:39 AM, portefeuille (98.90) wrote:

The problem with backtesting is that the results depend on the past market behavior, which can change in the future.

Are you sure what you are doing? Of course the results of backtesting depend on "the past market behavior". That is not a bug but a feature!

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#5) On May 17, 2009 at 4:55 AM, portefeuille (98.90) wrote:

Please have a look at this paper (pdf) as well.

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#6) On May 17, 2009 at 5:33 AM, walt373 (99.88) wrote:

Awesome, that pdf looks really useful. I'll check it out.

And by "the problem with backtesting", I meant "the problem with trying to predict the future by backtesting". If only we could "forwardtest"!

What is your take on this strategy? Since you haven't really voiced your opinion. I've read a lot of your other posts and you seem very mathematically inclined, which is an area I'll readily admit I am lacking in. If you think it's dumb, please don't hold back for my feeling's sake - I care more about my money :)

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#7) On May 17, 2009 at 11:23 AM, biggestfool88 (< 20) wrote:

I have thought of strategies like this and you are missing a logical point or two. 1. If it is an almost sure-fire way to make money with very low risk, don't you think you would have heard about it? 2. If you have to constantly rebalance trading fees will erode all of your profits.

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#8) On May 17, 2009 at 3:10 PM, MatJosher (< 20) wrote:

I back-tested this, setting my fas/faz ratio to 2/1 and never rebalancing, starting when the funds were launched. This resulted in 85% gains with relatively smooth curve.

But the curve has now gone flat as a pancake, meaning this play is probably only viable once in a while, when we have a massive crash.

I've played with idea in the past, but never thought to play a sector against itself. That's a neat idea, thanks.


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#9) On May 17, 2009 at 4:39 PM, walt373 (99.88) wrote:


1. There is a significant chance it won't make money so it's not "sure-fire". In my backtesting, starting with $3000, something like 20% of the 6-month scenarios lost money. Also, I have heard about this strategy before, but not seen anyone actually try it. The leveraged ETFs are losing a lot of money for the majority of retail investors, so you can't assume people always gravitate toward the smartest strategies.

2. I took transaction costs into account in my backtesting. That is why I said you need at least $10,000 to rebalance frequently and still make a decent profit. The more money you start out with, the less impact transaction costs will have on your profit.


If you set your FAS/FAZ ratio to 2/1, you're making a bet that the market will be headed down. It doesn't work in an uptrending market.

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#10) On May 20, 2009 at 4:05 PM, anchak (99.91) wrote:

Walt....have you thought about the fact what a low VIX would do to this trade in the short term....shorting both sides with VIX at 90 would turn out to be extremely profitable ( you would see that Ultrasuck is actually delta positive)......

Hans....outstanding paper as usual.

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#11) On May 20, 2009 at 5:12 PM, anchak (99.91) wrote:

Hans...time for a friendly ribbing....the article does attribute tje decay to gamma ( doesn't it).....and also found that it was correlated to the VIX movement ...which is what I tried to cover as part of my Leverged ETF blog.

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#12) On May 22, 2009 at 10:55 AM, walt373 (99.88) wrote:

Yes, a low VIX would make this trade less profitable. But since high VIX is usually associated with markets going down, this trade has some negative correlation and can act as a diversifier.

But one thing I noticed is that the ETFs themselves have a tracking error of something like -0.1% to -0.2% per day, which is pretty huge when you add it up over the course of a year. I am guessing it's a combination of the management fee, transaction costs of underlying holdings, and some stuff going on with their derivatives that I don't understand. There seems to be an opportunity in profiting from this as well.

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#13) On May 30, 2009 at 9:06 PM, alexxlea (61.65) wrote:

There are interesting plays day-trading and overnight trading these two etf's that, with margin, yield insane gains. I plan on using 2x margin and then 4x once I've built up enough of a profit buffer. Shorting them is simply not as profitable in my opinion, and I foresee June having a very ill effect on the effectiveness of this strategy. Also, I have not really been playing dota, maybe some games here and there when I am at home, but mostly I've replaced it with reading up and preparing myself for this strange future we're headed towards.

The government is beginning to realize that everyone has caught on to their ploy to keep the treasuries in line, and they're going to have to make bigger and bigger purchases until eventually no one buys the other hundreds of billions that remain to be sold this year. So this is definitely going to be a tumultuous summer of trading, but that's ok because volatility is perfectly suited for my trading system. Just don't get caught with any huge swings on this, and I assume you have enough of a buffer to not get called.

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