I am going toÂ put to rest these issues surrounding whetherÂ double inverse ETFs accurately track the underlying indexes.

Editor’s Note: Thanks to Ottnot, I have found that I have erred. I will strike through the errors, explain them, and re-post the corrected spreadsheet.

Here are the facts:

1. If the underlying index has a daily percentage gain, the double inverse ETF (diETF) will lose twice as much as the underlying index gained.

2. If the diETF experiences aÂ one-day percentage loss, then the diETF can never ever recover to break even, relative to the underlying index it tracks. Not true. However, if the diETF experiences multiple days of losses or stays in a downtrend for a length of time, it can be very hard for it to recover to breakeven, relative to the index it is tracking.

Before I show why this is true, there are other issues to clear up. If we are talking aboutÂ [[SRS]], the diETF for the Dow Jones USÂ Real Estate Index,Â then we must compareÂ SRS historical data to the historical data of the index it tracks, *not to the historical data for another ETF, even though it may be tracking the same index. *To compare ETFs to ETFs, instead of an ETF to the actual underlying it is tracking, will compound errors.

This experiment will compare SRS, a diETF, to the index it tracks, the Dow Jones US Real Estate Index, symbol DJUSRE.

Historical data for DJUSRE is available from Dow Jones here: DJUSRE Historical Data. Also, if anyone wants to perform more research on this subject, here is the Dow Jones Indexes website: Dow Jones Indexes.

I have pasted the spreadsheet below. I will do my best to explain what it all means.

*Note* Click on the spreadsheet once, and it will open in a new window. In the new window, click it again, and it will open full size.

Column C has the daily percentage changes for SRS since inception. The sum of all daily percentageÂ changes is 51.77

Column I has the daily percentageÂ changes for DJUSRE during the same period. The sum of all daily percentage changes is -26.82

Ideally, 2(-26.82) would equal 51.77. Obviously it does not. We can see already, by summing the daily percentage changes, that SRS did not track the daily percentage changes of DJUSRE exactly, but this is a small error and is likely due toÂ irregularities in maintainging the swaps and futures. This may also be due to management fees.

Next, look at the last cell in column E and K. This number is the percentage gain or loss since inception. We can see that SRS gained 25.39% over the period, while DJUSRE lost 39.04%Â Note to self, never ever build a spreadsheet after midnight. I copied the wrong formula over and therefore the sheet calculated an erroneous gain/loss since inception. The corrected numbers are 34.046% for SRS and -28.080% for the DJUSRE

Yes, that is correct. **It is erroneous to assume that SRS would be +39.04%**. It does not track the annualized percentage change of the DJUSRE, only the daily percentage change. *Annualized, SRS has 13.65% less than twice the loss of DJUSRE.** ***It is erroneous to assume that SRS would be +28.080%**. It does not track the annualized percentage change of the DJUSRE, only the daily percentage change. *Annualized, SRS has gained 5.97 percentage points more than double the inverse of the DJUSRE.*

Finally, look at rows 15 and 18 in columns F and L. I have highlighted the cells. *These calculations show that even over the short term, if the diETF goes down EVEN ONE DAY, IT WILL NEVER EVER BE ABLE TO GET BACK TO BREAK EVEN.* The one known as “Ottnott” is right. Due to the 2x leverage, it will get back to breakeven, although if the losses are built during a sustained downtrend for the diETF, it may be very difficult for it to recover.

Let me explain. Look at the price changes from February 1 to February 23. During this time period, the DJUSRE valueÂ hasÂ moved up and down. On February 23, the DJUSREÂ index is almost back to breakeven. Cell L18 shows that the index hasÂ lost 0.71668% from Februrary 1 to February 23.

Now look at SRS during the same period. The closing price of theÂ SRS is actually higher than the inception price, as it should be, since DJUSRE is showing a small loss, right? **Be very careful here**. WhileÂ DJUSRE has lost 0.71668%, *SRS has only gained 1.3246%,* relative to its inception value.Â If weÂ calculate twice the loss of DJUSRE on that date, we would get 1.43336% *Observe that the gain of SRS is less than twice the loss of the underlying index.*

From February 1 to February 23, SRS has actually lost 0.10876%, *and it will never ever be able to make up that loss. In fact, these losses will compound over time.Â * Had I not been in a hurry making the spreadsheet, I would have went ahead and completed the calculations for the entire row, instead of just a few cells. I would have then realized my error. What the spreadsheet nowÂ shows is that when there is no trend, or the diETF trend is down, the leverage tends to work against it. However, once a strong uptrend emerges for the diETF, the leverage really kicks in and it begins to outperform (more than 2x, annualized) the index it is tracking.

The key point to learn here is that it will take a while for the leverage in the diETF to catch it back up to the underlying. Even when the point value of the diETF is showing a gain, in percentage terms, the diETF may still be less than 2x the underlying.

These diETF are certainly great to trade on short time frames, but buying and holding them will guarantee losses. I still maintain that buying and holding the diETFs is a bad idea, due to the fact that any series of losses will compound and make it very hard for the diETF to recover. Furthermore, since most markets have an upside bias, over time, it is reasonable to assume that these diETFs can compound lossesÂ due to their 2x leverage to the extent that they may never be able to fully recover.

Please, if you have any questions about how this all works, do not hesitate to ask. I hope that now we can put this issue to rest, once and for all. Now that we understand how diETFs are born to lose, I suggest we begin to figure out how to profit from this anomaly.

I would also ask humbly that you link to this post, and pass it around, if you find it helpful. In my estimation, there is no other resource available on the internet that explains this diETF phenonmenon as well as this article.