Okay, first things first – I think I’ve officially lost my mind or made a simple formula error, but it’s late enough that my brain has turned to mush. I was toying again with the idea of the equal short paired leveraged ETF strategy (e.g. holding an equal short position on HXU/HXD for example). Reader Jordan Clark suggested I should back-test it and one thing led to another. Instead of dissecting it (because it will take some time), I’m going to throw out the results tonight and then discuss later…
I started by downloading the daily data for the TSX Composite index. Pictured here:
Next, I created a fictitious 2x Bull index, pictured here:
As you can see it was a wild ride, but since over the long term the index was mostly up, the 2x Bull was net positive (but definitely not 200% of the annualized return, and heck it was less than the regular index!). But let’s next add the 2x BEAR index:
The 2x Bear was decimated. You lost about 80% of your money over this time if you tracked this index. Now, Michael James on Money did an interesting experiment in which he looked at equal weighted positions in the bull and corresponding bear (although he simulated daily rebalancing). Let’s take that idea and show the hypothetical investment in a 50% 2x Bull and 50% 2x Bear index (although note, I did not simulate daily rebalancing, just fire and forget):
Okay, as expected it is between the pure 2x Bull and 2x Bear. It happened to have lost money over this time. I had tossed around the idea that you could short each index in equal amounts and perhaps you could capture some of the decay in these leveraged ETFs (not to mention their management fee). So let’s throw that into the mix:
It would seem that we are cooking with gas now… Or are we? The graph is getting pretty noisy, so let’s get rid of some lines and just look at the TSX and the equal short 2x Bull and 2x Bear…
Okay we see that the strategy of holding an equal short position (to start) of the corresponding Bull and Bear indexes gave us some outperformance versus anything else so far. The TSX was up 19.68% during this time (Jan 2000 to May 2009), but the equal short Bull Bear (without rebalancing) was up 42.00%. That might sound compelling, but take a closer look at where the outperformance came from. There is still a certain path dependency in the return. Note that when the pure index has a severe correction is when the equal short bull bear experiences significant upside.
Ultimately what I think is going to be significant is the sequence of returns (hmmm, same old story eh?). For example in a constant rising market, the bull’s leverage compounds. It starts at 200% daily exposure (to your initial capital) but increases if the index keeps going up. The bull gains steam in an upmarket. Vice versa, the bear decompounds its leverage in the same up market. It starts at 200% daily exposure (of your initial capital) but then decreases so long as the market keeps going up. But if a market is in a long bull run, the bear still gets killed and you are making gains there on the short.
I think the reason that the equal short bull bear looks so good in this case is because the compounding/decompounding can work in your favour in the more volatile down markets and in the less volatile up markets it doesn’t work against you as much.
In short (pardon the pun) it might seem that an equal short bull bear strategy might work over long periods of time if the market tends to go up more than it goes down (historically the market goes up 70% of the time and down 30% of the time – if the US market is a proxy). If corrections are severe it could be even better because the decay from volatility of leveraged ETFs are a killer (and you are shorting them). If markets went down more often than up, and if the up markets were more volatile than the down markets, then I think that the equal long bull bear would be better to own. More backtesting and different sequences of returns may confirm this.
But here’s the kicker. If the markets do tend to go up more than down, and the equal short bull bear provides it’s biggest bang for the buck in a correction, then it may have a place in portfolios as a long term negative correlator. Witness the following graph showing a comparison of the TSX versus a portfolio of 50% TSX and 50% equal short bull bear:
Very interesting. Not only did you outperform the TSX (+30.84% versus the TSX’s 19.68%), you did it with WAY LESS volatility. The risk adjusted return on this strategy would’ve been phenomenal. The standard deviation on the portfolio was 67% LESS than the regular index, with a 50% relative increase in return.
Like I said, I must’ve made an error on my formulas in my excel spreadsheets… I’ll go over it in more detail later and try looking at different return sequences to see if my shoot-from-the-hip conjectures are just crap or what. It could also just be a product of data-mining with no future validity.
If it isn’t, then you could short the bull/bear pair and use the proceeds to buy the plain index. But something tells me it isn’t that easy. Stay tuned…
Honestly, the last graph doesn’t look all that impressive to me. The market outperformed your combined fund about half the time, and looks like it would have outperformed it permanently if not for the recent once-in-a-lifetime crash.
Also, beware charts that normalize at “1” at a certain point in time and then compare two different investment options. The results change radically if you change the starting point. Your chart would look very different if you started during 2003.
Thanks for the link. Your analysis is interesting. One observation is that as the 2X bull and 2X bear diverged in price dramatically (roughly from 2006 to mid-2008), the bull-bear short became more like a big bull short plus a small bear short. The 50% TSX plus 50% bull-bear short went flat through this period because the bull-bear short was mostly a bull short that offset the 50% TSX.
I can understand not rebalancing daily, but perhaps the bull-bear short should be rebalanced whenever it gets too far out of sync. Otherwise, this short is very likely to eventually become just a bull short (because stocks tend to go up).
In the end it looks like shorting the leveraged ETFs is a way to profit from volatility. That does sound like it could be reasonably effective downside protection, although a long and slow decline (or no returns for a decade) might not have the same result.
Patrick: If you lag a bubble, then that’s perfect protection – you just need to wait a few years to come out ahead. If the higher returns and lower volatility hold in different situations that really says it all. The higher you go the farther you can fall.
Is there a supply of these ETFs available to be borrowed for shorting? Has anyone actually done this?
Could you explain what the term “decay” means when you say “capture some of the decay in these leveraged ETFs”?
Maybe it would be a quick topic for another post
@ Jordan – will do, but to satisfy your curiosity in the meantime: decay refers to how the NAV deteriorates in a sideways market because of the constant leverage. So index up 10%, then down 10% means a net -1% return, but the bull (or bear) would be down 4%. Wash, rinse and repeat and the NAV decays.
Ahhhh I think I finally get it now. Are there any other type of investments that decay in a similar way to these leveraged ETFs?
Also what software do you use to back test the results, have you tried metastock?
@Jordan, well there is time decay with options but that’s a bit different. Perhaps anything with constant leverage would be subject to decay, but I’m not sure on that.
I used Excel, never heard of metastock will check it out! Thanks!
Metastock looks totally awesome, and I bet would be an amazing tool in your hands since you know what you’re doing.
Part of it allows you create programs that make decisions based on any kind of fundamental analysis / indicator and see how well a strategy will back test for any available time period.
It’s owned by Reuters and apparently has a bunch of addons so you can download historical stock ticks and even pump in live feeds and unique indicators.
I’ve played with it a bit but it’s pretty expensive for a hobbyist who doesn’t really know what he’s doing to buy.
I found an interesting post along the same lines on another blog, they bring up more technical details which I can hardly grasp but some how still find interesting:
http://thesnowjob.wordpress.com/2009/01/20/a-risk-free-trade-shorting-leveraged-etfs/