TWM: An ETF Arbitrage Opportunity

Don't ever say Running of the Bulls won't admit our mistakes.  That's one good thing about authoring a blog, you can learn from others.

My post below is wrong.  This was pointed out to me by Quarrel, who posted in the comments section.  This is what Quarrel wrote

The ETF provides twice the inverse daily movement.

This is very different to twice the inverse monthly movement.

Run some basic numbers using percentage movements each day - if you take twice the daily movement, you get a very different end month result.

In particular if you take twice a large down day, then twice a large up day (the order matters!) as we got for the last two days, then you are very different to what the month to month index would be.

This is basic maths, and not a hole in the ETF.--Q

Posted by: Quarrel | September 30, 2008 at 07:56 PM

 

I knew that it tracked the daily inverse.  I was surprised at the monthly differential.  It was so wide, I thought it had to be wrong.  

Quarrel said I should do the math, so I did.  Here is a screenshot of the math.  Hit the table to expand and view.

The confirmation of what Quarrel is saying is at the bottom of the last column.  Col A is the daily return of the index.  Col B is the inverse of the daily return of the ETF, divided by two.  The third column from the right is the difference between the two.  The second column from the right is the difference plus one.  The last column is the sum product of all the daily differences plus one.  The very bottom cell on the right is the cumulative difference over the month.  The variability between the index and what we would expect the ETF to return was 0.75% in September, not 8.9% as I originally thought.

Obviously, I'm surprised by this.  On a down 8.1% month, I would have thought the double inverse ETF would have been much higher.  I did not think the difference would be that wide.  But Quarrel was right. 

I learned something tonight.

The post below is wrong; I decided not to delete it as an example of my fallibility.  (We already knew about your fallibility. - ed.) This is the original post:

ORIGINAL UNCORRECTED POST:

I’m pimping my book here.  (That means I own the security I will discuss.)

There is a disconnect between the value of the Russell 2000 and the value of the The ProShares Russell 2000 UltraShort ETF, ticker TWM.

The TWM began the month at $66.12 and closed today at $71.90 for an 8.7% gain.  The Russell 2000 was at 739.50 at the start of the month and closed September at 679.58, a loss of 8.1%.

The UltraShort ETFs are supposed to provide a double inverse return relative to the index.  Clearly, that did not even come close to happening with the TWM.  An 8.1% loss would imply a 17.6% gain, not an 8.7% gain.

Now, the ETFs do not track the double inverse of the index exactly.  There are several reasons for this, including fees paid to the fund management company, carrying costs for the derivatives used to replicate the index, and liquidity flows. 

However, a 9% difference?  This seems too wide to me.

There you go, arbs.  Do your thing!

Comments

[Gross Bill:]

< A common misconception is that ProShares should also provide 200%, -200% or -100% of index performance over longer periods, such as a week, month or year. However, ProShares' returns may be greater than—or less than—what you’d expect over longer periods. >

Apparently you have never read any of Proshares material regarding their ETFs. Shocker...

2008 Sep 30 08:24 PM

[Vladimir Se...:]

Oh man, oh man, where do I begin . . . Ok, let's try to be constructive here.
If I recall correctly, these type of funds are trying to mirror DAILY returns. So even if it tracks perfectly you will experience different results over longer term. And why would you expect it to track perfectly to begin with?
Yeah, spreads (even if they actually exist once you calculate everything correctly) may narrow eventually, but who knows when? Have you heard of LTCM?
How many years did it take for those spreads to narrow? Can you sit it out? What is your WACC? Will it be worth it? Of course not.

2008 Sep 30 08:47 PM

[Toro:]

I have amended this post. My original assumptions were wrong. It was suggested I go back and do the math for the daily fluctuations, so I did. The difference over the month is not 8.9% like I thought but 0.75%, which is perfectly within the expected tracking error.

I was aware that the ETF is constructed with daily fluctuations, had read the prospectus and had sat in on presentations by ETF companies. However, the dispersion seemed exceedingly wide. It is not.

2008 Sep 30 09:03 PM

[cuts:]

The difference has to do with the chaining of individual days. During each individual day, the double short is set up to track the inverse of a single day’s move in the index times two. However, chaining out the moves of the ultra short over several days does not equal the chained performance of the underlying index over several days (times two). See their web site for a complete explanation.


1 " 1
0.9 down 10 " 1.2 up 20
1.1 up 10 " 0.8 down 20
0.9 down 10 " 1.2 up 20
1.1 up 10 " 0.8 down 20
0.9 down 10 " 1.2 up 20
1.1 up 10 " 0.8 down 20
"
0.970 " 0.885
-3.0% " -11.5%


0.970 chained 0.885 chained
-3.0% -11.5%

Arb that.?

2008 Sep 30 10:59 PM

[Alan Brochs...:]

Toro, if you ever have a question about the NAV, here is a link: www.proshares.com/fund....

With that said, there have been several occasions this month when pro-shares has put up bad info (including Friday's info which was later amended). Also, note that the NAV is calculated at 4PM, while the market price is as of 4:15.

2008 Oct 01 08:06 AM

[User 194469:]

in other words -8.7+17.4=8.7%. 0 is not the pivot, the actual return is...

2008 Oct 01 09:13 AM

[Hedged In:]

TWM performs badly if the Russell 2000 index meanders around but stays flat over the long run. But if the index plummets in a sustained fashion over time, it performs even better than double the inverse of the index, because each 1% down move in the index is less and less on a dollar basis, while TWM gains 2% compounded each day.

Maybe that's what we'll see now.

Thoughts, anyone?

2008 Oct 04 05:02 PM

[Kirribilli ...:]

If you knew (or at least that was your bet) that an index (or stock) was going to "plummet in a sustained fashion over time", why would you even putz around with a 2X ETF, when there are options and futures out there that give you much more leverage.

Seems to me the only way to make money with these inverse ETFs over time is to short them. The negative compounding on price down days is going to eat away at them eventually, almost like theta on an option.

You would need a helluva run and then the prescience to get out, to make money on these day-trading tools. Look at some of the long-term performances.

Jan 26 05:43 PM