I’ve read many comments expressing confusion about the fact that the ultralong and ultrashort (leveraged) ETFs do not seem to be correlating 2:1 with the underlying indexes they are supposed to be tracking. While this should not be of a real concern to traders with short time horizons, this discrepancy can be extremely detrimental for long-term holders of leveraged ETFs. I think most traders will be very surprised to see how these leveraged ETFs really work.
As best as I can determine, there are 2 major reasons why the ETFs do not track the underlying indexes 2:1
The first and primary reason is that these ETFs seek to track the daily return. For short term traders, this is acceptable. However, for longer term holders, the ETF will not double the underlying index on an annualized basis. It is calculated only on a daily basis.
Lets look at some numbers.
We’ll use the $NDX, the Nasdaq 100 index, and assign it a value of $100.00Â
For the QLD, the double long ETF that tracks the $NDX, we’ll assign a price of 50.00, and we’ll assign the same price for the QID, the double inverse ETF of the $NDX.
| Gain/Loss | $NDX | Â QID | QLD |
| Â | $100.00 | Â Â $50.00 | Â $50.00 |
| 5.00% | $105.00 | Â $45.00 | Â $55.00 |
| -13.00% | $91.35 | Â $56.70 | Â $40.70 |
| 7.00% | $97.74 | Â $48.76 | Â $46.40 |
| -2.00% | $95.79 | Â $50.71 | Â $44.54 |
| 10.00% | $105.37 | Â $40.57 | Â $53.45 |
| -9.00% | $95.89 | Â $47.87 | Â $43.83 |
| -7.00% | $89.17 | Â $54.57 | Â $37.69 |
| 11.00% | $98.98 | Â $42.57 | Â $45.99 |
| 2.00% | $100.96 | Â $40.87 | Â $47.83 |
| -5.00% | $95.91 | Â $44.95 | Â $43.04 |
| Â | Â | Â | Â |
| Ratio after 10 days | Â | Â Â 2.13 | Â Â 2.23 |
| Total Loss | 4.10% | 10.1% | 14% |
In the chart above, we have the beginning amounts, and then 10 days of index results. Of course, I magnified the hypothetical daily moves to be much greater than would occur in real trading to show how easily the ETF gets off track with the underlying index. In this example, the QLD has now lost double the underlying index loss, plus 6%.Â
Even more interesting is that the QID has lost 10%, despite the fact that the underlying index it is supposed to be double short has lost 4.10%. A common misconception is that the QID would have gained 4%.
The real culprit here is that with percentages, once the ETF has a loss, it must increase more in percentage terms than it lost to get back to break-even.
The second source of any tracking error is also due to the returns being tallied on a daily basis. If the ETF value at the close is even a fraction of a percent off from the value of the underlying index (this seems to happen very often), that discrepancy is carried forward to the next trading day, where it becomes part of every calculation thereafter.
I hope these calculations will help put to rest the confusion concerning the 2x leveraged ETFs and the underlying indexes they track. These calculations should be of greatest concern to buy-and-hold type investors who believe erroneously that these ETFs will track 2x the underlying on an annualized basis.
Wood,
Have you made any additional studies on the RSI(2) and ETFs/ETNs.
Last I saw you were thinking about a 12% stop loss, exiting after crossing RSI(2) below 70 if it did not cross 80, and possibly a timed exit based upon x number of days after RSI(2) below 10 signaled a buy.
Tyler
Tyler, I am using a 12% stop loss and a percent-risk formula. However, a 12% stop may not be the optimum. For me, it works well with the testing and is acceptable for my level of risk aversion.
I was unable to find a time stop that improved results enough for me to implement one. However, I have not tested a stop that would take one out if RSI(2) spent x days below 10.
I have done initial testing on a stop that would take one out if RSI(2) crossed back below 70 before crossing 80. I think that it has merit but needs more testing.
Nice analysis, that makes a lot more sense now.
Good analysis, it’s very helpful to have an explanation for the way these inverse ETF’s trade. Right now, there are very few inverse ETF’s that I want to hold for longer than a couple of days. I still have positions in DUG and SMN that I’m willing to hold longer, but that’s it.
Boca, these leveraged ETFs make great short-term hedges. I would never hold them for more than a few weeks, for obvious reasons.
There are triple leveraged ETFs on the way too. I can’t wait for those!
Glad to help Gapping. I know its been pissing you off to watch FXP getting screwed despite FXI getting screwed as well.
nice post, wood. these leveraged ETFs remind me of styrofoam cups with a pin hole.
I think I’ll pass on the triple-leveraged ETF’s LOL. FXP and FXI have been frustrating enough.
I’ve been going in and out of DUG, so far so good. I’m on my second trade in SMN and as long as it continues to hold up ok, I doubt it will be a problem. But I’m not as enamored of them as I used to be.
PS I owe you an email Shed, haven’t forgotten, just busy. Hopefully tomorrow AM I’ll finish it up.
Boca,
Be careful with DUG if your goal is to short oil because DUG is not based on the price of oil, but rather the price of oil companies, coal companies, gas companies, etc., etc. Trader Mike digs into the details here.
thanks Dogwood, I bought it more as a general hedge against all oil, gas, coal, and energy companies that I might own. I tend to get a little paranoid if a sector is ripping higher and I don’t have any hedges against a sudden turn.
Boca, don’t worry about it. She’s sewing like crazy. Hopefully I’ll be able to soon send some pics of the dresses.
Shed your niceness pisses me off. Seriously. If someone owns a 2x etf and doesn’t know this, I’m pissed. I don’t know. You’re a scholar and a saint for taking it upon yourself to be the bigger man and educate with a truly nice example.
Am I the only dude in ‘merica who reads filings? I’m asking an honest question. They state it on page obvious of the prospectus
as a point in fact, it is on page 1. the very first line. emphasis added.
Each series of ProShares (“Fund(s)â€) is designed to corre-
spond to the performance of a daily benchmark, before
fees and expenses, such as the daily price performance,
the inverse of the daily price performance, a multiple of
the daily price performance, or a multiple of the inverse
of the daily price performance, of an index or security. convertible securities and rights and warrants.
Stocks represent an ownership interest in a corpo-
ration.
But, I guess I’m the asshole.
btw, I’m answering your question about a dgly secondary in a post up nigh.
Danny, I only read the prospectus/various filings if I’m buying something for a trend following hold. I would never read the prospectus for a stock/ETF that I planned on holding for a few days.
Anyway, even knowing they seek to match the daily price performance, it is important to see how percentages fuck you in the long run, assuming the ETF has some decent sized down days.
I thought this was the purpose of the site — to share knowledge and be able to ask each other questions, as no one person will ever know it all. Together we are all smarter and stronger by sharing knowledge.
Honestly I really didn’t ‘get’ why there was such a discrepancy between how fxp actually traded and my expectations of how it should trade, until I saw it visually laid out in Shed’s chart. So it was appreciated.
so it’d be better to short the leveraged ETF rather than buy the inverse a sell and hold investor rather than buy and hold?
Short both to be hedged and dollar cost average?
yeah but it’s obvious that it doesn’t correlate properly. it was a good post. I just am surprised that people didnt know that. Also, if you built a whole strategy of trading these ETFs you ought to read the filings.
boca – you’re right.
Great post, Professor Wood.
You should do more educational posts like this, since most of our readers are illeterate [sic] malcontents.
Danny:
Wood is a Southern Gentleman.
Thanks, Mr. Fly.
Hoo, I’m not trying to be a smart ass when I say those variables are too much for me to consider at 2 a.m.
In the above example, the inverse(short) ETF came out better, but only because the hypothetical had the underlying index falling over the course of 10 days. Had I made it instead rise, then the QLD should come out better.
In fact, as long as the ETF never loses, you are golden. It is just when it encounters a string of losses that everything gets out of whack.
Wood,
I’m suprised the arbs haven’t corrected this anomaly. If your figures are correct, that’s quite some spread.
jog on
duc
Duc, I’m sure there are possibilities for arb. However, the basic spread is created simply by the fact that for every loss experienced, the ETF has to have a slightly larger percentage gain to get back to where it started. This is an impossibility since the next day, the goal is simply to match the new day’s gains or losses of the underlying.
I checked and rechecked my calculations, but I’d be happy to email you spreadsheet if you want to fool around with it.
Wood,
No I’m sure your calculations are correct, and as you say the problem arises due to the construct using %’s
However, the underlying, have a consistent value. For example MSFT = $27 regardless of which structure holds it.
Thus, it should be possible to arbitrage the spread that opens up due to the highlighted problem.
I’ll have to have a think on it.
jog on
duc
Duc, if anyone can figure it out, you can.
Let me know what you discover. If there is an opportunity, in situations like FXI and FXP, it seems the profits could be substantial.
Wood,
If it’s doable…it’s a goldmine, spreads are tiny generally speaking, the market is EFFICIENT that way.
With potential spreads like that, leveraged, one good trade would make your year.
jog on
duc
Well, if it turns out to be doable, for God’s sake don’t post the solution here in the comments section! lol I need that type of good trade!
Wood,
Hell no son…I’ll e-mail you.
jog on
duc
Wood,
Just a quick look for QID;
UltraShort QQQ ProShares: Top holdings
Top holdings
Company name % Net assets
Nasdaq 100 E-Mini 20/3/08 12.39%
Nasdaq 100 Swaps 0.53%
Nasdaq 100 Swaps 0.29%
Nasdaq 100 Ubs Swaps 0.16%
Percentage of holdings 13.37%
Swaps…complicates matters somewhat, derivatives always do…which is why the banks have all their current woe’s.
jog on
duc
Good…
Although now that I think on it a bit, Hoo might be right.
Of course, I know very little about arbitrage, but it seems like buying some sort of way out on the horizon index calls (Leaps?) and shorting the inverse ETF could work.
***Edit*** it seems like as I think more, that wouldn’t work. Maybe it would be to buy way out calls on the ETF, and then shorting the inverse.
Retards.
There are men like Hilibrand who dedicate their lives to this type of shit and you think you just hit a gold mine?
Back to my charts.
el-midge,
A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty.
It may well not be possible, but in looking, you may discover something totally unexpected.
jog on
duc
Wood,
QLD
Ultra QQQ ProShares: Top holdings
Top holdings
Company name % Net assets
Nasdaq 100 Ubs Swaps 11.00%
Nasdaq 100 E-Mini 20/3/08 8.86%
Apple, Inc. 8.45%
Microsoft Corporation 4.85%
Qualcomm, Inc. 4.63%
Google, Inc. 3.73%
Research in Motion, Ltd. 3.22%
Cisco Systems, Inc. 2.92%
Gilead Sciences, Inc. 2.40%
Intel Corporation 2.26%
Percentage of holdings 52.32%
Already there are significant differences in the construction
QQQQ
PowerShares Exchange-Traded Fund Trust – PowerShares QQQ Trust, Series 1: Top holdings
Top holdings
Company name % Net assets
Apple, Inc. 10.37%
Microsoft Corporation 5.95%
Qualcomm, Inc. 5.68%
Google, Inc. 4.58%
Research in Motion, Ltd. 3.95%
Cisco Systems, Inc. 3.59%
Gilead Sciences, Inc. 2.95%
Intel Corporation 2.77%
Oracle Corporation 2.73%
Teva Pharmaceutical Industries, Ltd. ADR 2.06%
Percentage of holdings 44.63%
The differences reside in the SWAPs and FUTURES, both derivatives of the underlying, but with EXPIRY DATES.
Hmmm.
jog on
duc
thx SHed .. exactly as I thought: these products are designed to take money out of pockets of unsuspecting and suspecting investors alike, due to egregious factors like time and slippage.
The money they make is the price we pay for laziness and ease of use.
^yes
Huh. Apparently surly pills were handed out last night along with the drinks and chips.
Juice,
Trade them, don’t buy and hold them forever.
Good post. You were right on.
Tracking error on leveraged ETFs increases the choppier the market is, for the reasons you illustrated in your calculations.
I think of it simplistically. If you start out with $100 and the market is down 10%, you now have $90. If recovers 10%, you only recover back to $99. If you magnify this over an extended period of time during a volatile market environment, you can see how the tracking error will increase.
This is true for both long and short leveraged ETFs.
Wood, do you have any advice on establishign stop losses on day trades. somehow, i am the most skillful person at setting the exact price a security will drop to — it always seems to be my stop loss price and 90% of the time, i get filled then the mkt rips higher.
Bearshitter, I suggest establishing the pivot points from the last couple of days and setting your stops below those.
I guess a good question might be why are you using hard stops for day trading?
Another consideration is what is it about your stops that causes them to get hit at the bottom? Maybe you should consider setting a buy limit instead of a stop.
Why can’t they design a 2x inverse ETF using the underlying points instead of using %? (shown in table below)
Underlying % Change 2x Inverse (Using Underlying) % Change
100 100
105 5.0% 90 -10.0%
100 -4.8% 100 11.1%
105 5.0% 90 -10.0%
100 -4.8% 100 11.1%
105 5.0% 90 -10.0%
100 -4.8% 100 11.1%
105 5.0% 90 -10.0%
Total Loss/Gain 5.0% -10.0%
Tim, I’m guessing that it would some how not be as profitable for the fund managers.
That’s alright though. I’m working out a system to profit from the spread.
Wood,
I’ve been looking at this over the last couple of days.
No pure arbitrage will be available for I believe the following two reasons;
*Swaps…not available to retail market [no position available to close any potential spread]
*Futures.
The Futures would have been the way to set-up a pure arbitrage had it been available.
What I *believe* happens is this.
The Futures represent X% of each ETF The Futures provide the leverage necessary to multiply the %gain/%loss/day.
Each day, the Futures position is closed out, and reopened the following trading day. This then prevents any arbitrage on the futures and explains why the SPREAD on a day-to-day basis blows out to such proportions.
Thus any SPREAD based trades will need to overcome this problem. Doesn’t look too promising.
jog on
duc
Why arbitrage?
You short the double long and you short the double inverse and you hope for high volatility.
Ottnott, I will look at this exact strategy in a future post.