Sunday, July 6, 2008

Horizon ETF Math

As I have mentioned before on this site, Horizon ETFs are a type of investment that allow traders to go long or short a particular market with 200% daily exposure. For example, this organization has two ETFs that track natural gas:

HNU-which stands for Horizon Natural gas Up
HND-which stands for Horizon Natural gas Down

This means that if in a given day, the price of natural gas rises by, say, 2%, then HNU should rise by about 4%, and HND should fall by about 4%.

Both of these ETFs were launched in mid-January 2008, with a price of $20.00 per share. What I was curious in finding out is what if you had purchased both of these ETF right from the start and held them to today. At first I thought that purchasing equal amounts of both ETFs would create a perfect hedge, with the gain of one fund offsetting the other. However, this was not the case.

Below is a chart showing HNU on the top panel, and HND on the bottom panel going back until the date these funds were launched:

If you click on the above image and read the annotations, you will see that if you had invested $10,000 into each fund on inception date, you would actually have produced a nice profit. The two funds, in other words, did not cancel each other out.

The reason for this is that as the price of natural gas rose, the balance of HNU was growing larger, and the balance of HND was becoming smaller. As this trend continued, the percentage change had a larger dollar value to work on with HNU and a smaller balance to work on with HND.

Put another way, the bull ETF has unlimited compounding potential upwards, but the bear ETF cannot reach zero, and its chart becomes what is know as asymptotic as it approaches the X axis of the chart.

Believe it or not, knowing this can be useful in the real world. Let's say you have $10,000 worth of energy stocks in your portfolio, and you feel that perhaps now you want to take out some insurance against a potential market correction. To do this you would buy $5,000 worth of HED, which will rise 2% for every 1% the Canadian energy sector falls.

At this moment your $10,000 position is hedged. But if energy stocks continue to rise, your insurance in HED will start eroding, which will mean that to remain hedged you will need to buy increasing amounts of HED to maintain the hedge. Conversely, if a correction in energy does in fact materialize, then you would become over hedged if you do not trim back your exposure to HED as the correction continues.

I still think these ETFs are an innovative product, and, luckily, a new set of these type of ETFs have just been released:

•S&P 500 Bull Plus ETF
•S&P 500 Bear Plus ETF
•NASDAQ-100 Bull Plus ETF
•NASDAQ-100 Bear Plus ETF
MSCI Emerging Markets Bull Plus ETF
MSCI Emerging Markets Bear Plus ETF
•U.S. Dollar Bull Plus ETF
•U.S. Dollar Bear Plus ETF
•U.S. 30-year Bond Bull Plus ETF
•U.S. 30-year Bond Bear Plus ETF


Gio said...

Hey that's neat stuff. You must be a math guy or something.

I've noticed the same thing in other ETFs. After trading ETFs for quite some time, I compute (aka, "guess") an implied amount I call the "hedge/spec factor." In other words, I treat ETFs a lot like an equity but also a little like an option contract. Here's a generic example, if people think financials will go down, they buy SKF... it does go down quite hard so SKF goes up like 10%, then the next day financials come in flat, but SKF ends down -2%... I conclude that people have "overshot" the SKF the previous day and/or people are thinking the bottom is in.

Danny Merkel said...


Thanks again for the comment- you make an excellent observation.

I have theorized that during a rapidly falling market, bear ETFs will start accumulating a "hedge/spec" factor due to the fact that it becomes more difficult to actually short stocks due the need for an uptick, so traders start pilling into bear ETFs instead, which will cause their price to start exceeding their NAV per share.

Similarly, option prices also get more expensive during a strong correction due to an increase in the implied volatility.

By the way, if these type of topics interest you, I would recommend reading Larry McMillan's 'McMillan on Options."

This book is filled with about 600 pages of almost pointless, but interesting, Wall street rocket science.

Aaron Fishbein said...

Hey Danny, keep in mind that the SEC got rid of the uptick rule for shorting stocks.

Anonymous said...

Hey there my frined Danny,
Interesting observations!
How about the Ultra Short EFT that bets the S&P500 is going down. Say the S&P500 goes down 75%, what do expect would happen to the opposite Ultra Short ETF that bets it goes up double?

Also, what affect does actual annual inflation of 15-18% like we have now (according to shadow stats & others) have on the price of the ultra oil/energy ETF's?
Glad to see you back Danny.

Danny Merkel said...


I was not aware of that fact, but I am pretty sure it applies up here in Canada. I remember trying to short XGD, the gold stocks ETF, last year and it took about 4 minutes to go through. Now I can just buy HGD in about 4 milliseconds.

Traders can also pile into these ETFs in the US during times of panic, and this can also cause the price of the ETF to deviate from the NAV per share, which is what gio was getting at.

Danny Merkel said...


IF you were to buy the ultra Long S&P 500 ETF, and the S&P 500 were to decline by 75%, then I think you would have a similar situation as the HND ETF I showed in my post.

Natural gas is up up 70% so far this year, yet the Ultra Short bear ETF is only down about 70%, not 140%.

There's no way it could double the exposure, for if it did, the ETF would have to have a negative unit price!

Anyway, I hope that makes sense. Thanks again for the comment.