# 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!