Double and Triple ETFs Decay Their Value Faster, By Design

Over time the inherent inequality between the same percent up, and then down, relentlessly erodes the value of a given starting investment. Every retailer knows this lesson.

On a $1000-ticket item a 40% mark-up moves the price to $1400, yet when later put on sale a 40% discount moves the price to $840. An equal percent up and down yet the retailer is at a $160 loss on his original $1000. Many a small business has folded because of not attending to this mathematical truth in their financial planning.

Over and over, this, in principle, is what is happening. With doubled and tripled percent moves, this disparity is greatly magnified. So we, in my amateur’s opinion, must treat all double and triple ETFs as if we are paying a premium on a wasting asset, because for all practical purposes they are decaying, somewhat like an option would decay. This happens regardless of whether it is a double up ETF or double down ETF, because the effect comes from the function of mathematics, not what market item is being measured. However, the frequency of computing the new value does matter.

Want proof? Below is 20%, oscillating, to demonstrate what would happen to a small investor. The same thing is happening, yet less obviously, when the up and down percents are lesser and inconsistent.

By back checking your date of purchase with the underlying price of the market item/package being tracked, and comparing to your dollar value now -when it touches that same price point, you can witness the erosion in value of the ETF. A huge up day can of course show a good gain, yet the erosion sets in again.

The bigger the percent swing, the faster the dollar-value erodes. A triple erodes even faster than a double, a double faster than a single. So in a sense the triple exacts a higher premium. Notice that at 20% - $1000 up and down was a $40 loss, where at 40% - $1000 up and down was a $160 loss. 20% doubled is 40%, $40 doubled is $80, yet the loss on 40% up and down is $160, or 4 times the loss ($40 x 4). That gives a rough sense of the mathematical impact on triple versus double ETFs.

(my example is rounded for reporting convenience)

$1000 invested goes 20% up ($1000 base times 1.2 [120%])

then goes 20% down (new base times .8 [80%])

$1000 to start:

• up $120 0, down $960
• up 1152, down 922
• up 1106, down 885
• up 1062, down 849
• up 1019, down 815
• up 978, down 783
• up 939, down 751
• up 902, down 721
• up 866, down 693
• up 831, down 665
• up 798, down 638
• up 766, down 613
• up735, down 588
• up 706, dow n 565, etc.

Just 14 up and down cycles, ending on $565/$1000 = 56.5 % remaining or a 43.5% loss. Of course an even 20% up and 20% down, repeating, will never happen. But, this proves that Down is the Prevailing Trend of every double and triple ETF.

Sometimes the underlying market item goes up more than one day, or down more than one day, yet any chart can let you count the number of zigs and zags up and down. Please notice that with this the volume is also irrelevant. A small volume day moves the percent up or down as easily as a large volume day. Multiple days up, then multiple days down does slow this trend down some, yet over two or three months it does happen.

Sometimes if the item goes up 20% and down 10% and up 20% and down 10% of course you do gain, but it is like bucking the tide. Like in Las Vegas, the odds are relentlessly with the house. The designers of these instruments, in my opinion, in all likelihood knew this going in.

My investments in DXD and SKF that never did as well as I expected, caused me to start thinking about an old maxim of mine. Do the math. It can disprove an obvious conclusion. I finally did.

I have been late in applying this to my own tiny holdings in UYG, EEV, ERY, and FAZ so I am looking for even a near break-even exit point ASAP. I made the mistake of thinking I could hold them long term. Because I now understand that the longer I wait, the further in the distance my break-even point is likely to move. I will start fresh, with a clearer understanding of how these products move.

If everyone who woke up to this pulled out of double and triple ETFs at once, the underlying market item components might get hammered with selling. Ouch. For example: at close February 5, 2009, SKF had traded a volume of 33,798,785, and FAZ 24,250,289. The same way short seller covering can move a market, I would bet ETFs, exited by too many investors at once, would move a market as well. Or would they?

I wonder how many hedge funds are hanging onto ETFs as investments?

Do treat these ETF’s like some pros are now counseling, as short term trading tools. Take your profits sooner rather than later. Then, at a better entry point, get back in and do it again. Mathematically, these are definitely NOT long term investment instruments. So Be Aware. And tell a friend.

Disclosure: Long FAZ, EEV, ERY.

Comments

[Vox Rationalis:]

This does not describe the mechanism by which an ETF underperforms an expected return.

If the price of any stock were to go through the gyrations you describe, its price would move as you expect in your table above. But as there is no ongoing cost to holding the stock, there is no additional decline in its value. However, in an ETF, one is also paying fund expenses, which further erodes the value as time goes by. In a multiple ETF, these expenses are magnified, and in many funds that rebalance daily, they are further exacerbated. Hence the underperformance of these funds.

I'm sure somebody can offer specifics related to UYG or SKF or another of the multipleX funds.

Feb 09 08:07 AM

[alivewweb:]

I think the real question is why the issuer created the securities in the first place.

Whose need are they addressing? Was it simply to roll over these holdings or churn them if you will to generate in-house commissions like a kid with his first margin account in the discount brokerage. Or did they issuers not see a real need?

I do not understand how these are created in the first place.I always assumed they were long and short the same basket of stocks. And a equal number of shares issued so that both side would inially have the same market caps.

And I was troubled by the simple fact the total market caps of both sides seemed to be contracting and perhaps for the reasons you suggest.

But the issuers have constructed these leverage finds incorrectly IMO. Take that basket long or short, double long or double short using margins, and triple long or short using options as the added kicker.

Pretty simple. Or perhaps just simple minded.

Nice article.

Feb 09 09:09 AM

[adelante:]

Yes, be warned!
Performance Flaws in Leveraged And Inverse ETFs

Trend: Leveraged and inverse ETFs do not perform as expected due to tax distributions and tracking error.

Simon Maierhofer at ETF Guide describes the illogical returns of leveraged and inverse ETFs.

Link: ETF Guide: Leveraged And Short ETFs - 3 Flaws You Should Know, www.etfguide.com/resea.../. (Also, Morningstar.com has an excellent video.)

...short ETFs are a great and powerfull tool but they have their quirks and limitations. Short and leveraged ETFs are "power tools" and will punish the ETF investor if used irresponsibly.

How to lose 70% in 30 days or less

To illustrate, the UltraShort Real Estate ProShares (SRS) dropped from $259 a share to $57 a share in less than a month. $10,000 invested in SRS would have been reduced to a mere $2,200. In less than 30 days, SRS dropped twice as hard as the S&P 500 (SPY) and Dow Jones (DIA) in the entire year.

If used responsibly, there is no reason to shy away from short ETFs. You can thrive with short ETFs as long as you are aware of certain quirks.

Short ETFs and taxes
The two most established short ETF providers, Rydex and ProShares paid out capital gains tax distributions earlier in December (read related article here). The distributions were huge, affected nearly all short ETFs (also called inverse ETF or bear ETFs) and ranged from 4% to 86%.

In essence, SIJ and any other short ETFs affected by tax distributions, maintained their value. However, part of the ETFs share price is paid directly to investors to account for a different tax treatment. If you own short ETFs within a tax-deferred account, this is a moot point.

Not all short ETFs distributed short term gains. Some distributed long term gains or a combination of long term and short term gains. Long term gains are taxed at a more favorable 15%.
Short ETFs and tracking error

Short ETFs are designed to provide 100%, 200% or 300% the inverse (opposite) DAILY performance of the underlying index. It is a common misconception that inverse ETFs are made to attain 100%, 200% or 300% the inverse performance over longer periods, such as weeks, months or years.

Several factors contribute to this effect. According to ProShares, the most significant one is index volatility and its effect on fund compounding. In general, periods of high index volatility will cause the effect of compounding to be more pronounced, while the lower index volatility will produce a more muted effect.

A look at the ETFs and short ETFs tracking the financial sector illustrates the “tracking-error”. Over the past six months, the Financial Select Sector SPDR (XLF) lost 42%. The UltraShort Financial ProShares (SKF) lost 18% while the Short Financial ProShares (SEF) gained 15%. In a perfect world, SKF (200% inverse) would be up 84% followed by a 42% gain in SEF (100% inverse).

Even on a daily basis, short ETFs don’t always deliver on their promise. A few days ago, the Nasdaq (Nasdaq: QQQQ) was up 2.67% while the 200% inverse Nasdaq UltraShort ProShares (NYSEArca: QID) only lost 4.33%. Similarly, the S&P 500 (AMEX: SPY) shot up by 2.44% while the UltraShort S&P 500 ProShares (NYSEArca: SDS) fell by only 4.49%.

Short ETFs are a valuable tool to hedge your portfolio or speculate on market movements. Nonetheless, if you want a mirror image of the underlying index, consider shorting an ETF that tracks the index rather than buying a short ETF.

Feb 09 09:16 AM

[ETF King:]

Do any of you really do your due diligence? When calculating say your long term performance of your SKF short position, did you remember to add in your MASSIVE $33 per share dividend payment? HELLO!

Feb 09 11:17 AM

[donzelion:]

Way I see it, 2x and 3x up and down ETFs have shown an impressive capacity for overshooting their mark. How else could a 3x short ETF leap up into the hundreds after a few down days, even when the indices they track aren't nearly as far down as they were in Nov 20?

What I'd like to know if whether that's the design of the ETF, or the manner by which computers buy shares in an ETF.

Feb 09 12:40 PM

[mule65:]

There isn't any tricky math going on here. 20% of $1000 is $200 and 20% of $800 is $160. If you think they're all going to zero then why not short them?

The leveraged ETF's are detrimental to the market -- huge money that once found its way into stocks is now going here. Money in these ETF's never gets invested in shares of companies. I suspect the SEC would like to see these go away.

Feb 09 02:01 PM

[bsharvy:]

There's more to investing than looking at the volatility. Otherwise, the only relevant stock-picking criterion would be the lowest possible beta. Yet, it isn't. If you're on the right side of the trend, volatility is good. That's why volatile stocks are more speculative, and dangerous. The 2x ETFs are no different.

The problem with ETFs doesn't come from 2x volatility. That is a known quantity. The problem is that the short leveraged ETF's in particular simply don't perform as they mathemtically should. They often simply don't return the inverse of the corresponding 2x long ETF.

Feb 10 01:06 AM

[Augustus:]

Your analysis would somewhat imply that both QID and QLD should both be trading at near zero. They both have been in the market for some time but still have value.

Feb 12 03:26 PM

[squark62:]

holding leveraged etfs as they were equity securities is a mistake. buying and selling options is not buying and selling equity in the underlying. such is the case with leveraged etfs. these etfs are one of many different ways to hedge equity positions you have. if you own equities in the underlying etfs, it's makes sense to own the inverse. otherwise the leveraged position is 'naked' - you've heard the saying when the tied goes out you'll see got their shorts pulled off.

the other to own these etfs could be to hedge by arbitrage. this i the main reason i own leveraged etfs and i always own them in pairs. to maintain the hedge, the weight of each etf in the pair is periodically adjusted to achieve my hedge objective. i plan my work and work my plan.


On Feb 09 09:09 AM alivewweb wrote:

> I think the real question is why the issuer created the securities
> in the first place.
>
> Whose need are they addressing?

Feb 12 09:51 PM

[todehls:]

I've done some analysis and have in fact started shorting the leveraged ETFs in pairs. So far I'm shorting UYG & SKF, DIG & DUG, and TNA & TZA. I bought into positions 4 times at 9 days apart for some cost averaging. So far I've held positions for an average of 23 days and have gained 4.4%. DIG and DUG have BOTH gone down since I shorted them. UYG is down 18.4% while SKF is only up 3.3% netting me 15% on that pair. Since my brokerage requires a 75% margin for shorting these ETFs, I've used less buying power than holding positions would require. When you calculate the gains on buying power used the 4.4% becomes 6% gain in three weeks doing nothing other than shorting both sides.


On Feb 09 02:01 PM mule65 wrote:

> There isn't any tricky math going on here. 20% of $1000 is $200
> and 20% of $800 is $160. If you think they're all going to zero
> then why not short them?

On Feb 12 09:51 PM squark62 wrote:

> the other to own these etfs could be to hedge by arbitrage. this
> i the main reason i own leveraged etfs and i always own them in pairs.
> to maintain the hedge

Feb 16 04:22 PM

[yichen:]

holding both sides of leveraged etfs is not risk-free, in fact, there is a risk of infinite loss. basically, you are betting on the market to trend sideways. it’s a good bet right now, but if the market trends upwards OR downwards consistently, the “decay” becomes negative and you’ll lose money. the worst case scenario is that the market will trend upwards infinitely. you would double up on your bearish short (buy to cover at 0) but you wouldn’t be able to cover your bullish short at all.

here is what i mean by "negative decay":

imagine if the underlying index trends upwards like this
day 1: 100
day 2: 110 (10% gain)
day 3: 121 (10% gain)

a 2x etf would trend like this:
day 1: 100
day 2: 120 (20% gain)
day 3: 144 (20% gain)

the index is now up $21, but the etf is up $44--it would be $42 higher if it tracked the index instead of the daily change in the index. this is a "negative decay" of $2.

Feb 20 10:08 PM

[pantheistic...:]

found this via google, did some quick testing by modeling double ETFs with an excel file, and playing around with it.

I modeled a doubled and inverse double ETF by having the double ETF always have 2x the percentage change of the underlying between two discrete times, and the inverse double -2x the percentage change. Also, I put in a paired long column to make looking at the results of paired shorting or paired long strategy.

Here are some observations:

With the same starting and ending prices and varying intermediate prices, both the double and inverse double ETFs have the same (but lower) value.

Increasing the volatility decreases the ETF values.

Essentially, a double ETF is short random noise, but long a directional movement. Shorting ETFs in pairs is basically betting that the current price reflects some underlying fundamental which will cause the price to revert to that mean. If you want to interpret it graphically, think of a graph of a running average with noise bands superimposed on it. Paired ETF trading is betting on the slope of the running average relative to the size of the noise bands. Paired long is on the high slope side, paired short is on the high noise side.

Feb 25 04:26 AM

[Mascis:]

Here is a more graphical explaination:

www.stretchtarget.se/2.../

May 20 04:57 PM

[kkerr:]

Yet another explanation (with charts):

blog.quantumfading.com.../

Jun 02 11:45 PM

[Alok Swain:]

Pantheistic,

I sort of understand you concept about trending forces and volatility or noise as you call it. These are the two forces that influenc the long term behaviour of these leveraged ETFs.

I was wondering if you can share how did you model it, like in Excel, can you share the model or any other info that would help me/us do similar simulation.

Thanks for your insight.

Regards,

Alok


On Feb 25 04:26 AM pantheistic multiple-ego solipsist wrote:

> found this via google, did some quick testing by modeling double
> ETFs with an excel file, and playing around with it.
>
> I modeled a doubled and inverse double ETF by having the double ETF
> always have 2x the percentage change of the underlying between two
> discrete times, and the inverse double -2x the percentage change.
> Also, I put in a paired long column to make looking at the results
> of paired shorting or paired long strategy.
>
> Here are some observations:
>
> With the same starting and ending prices and varying intermediate
> prices, both the double and inverse double ETFs have the same (but
> lower) value.
>
> Increasing the volatility decreases the ETF values.
>
> Essentially, a double ETF is short random noise, but long a directional
> movement. Shorting ETFs in pairs is basically betting that the current
> price reflects some underlying fundamental which will cause the price
> to revert to that mean. If you want to interpret it graphically,
> think of a graph of a running average with noise bands superimposed
> on it. Paired ETF trading is betting on the slope of the running
> average relative to the size of the noise bands. Paired long is on
> the high slope side, paired short is on the high noise side.

Aug 06 02:48 PM