ProShares Ultra and UltraShort Sector ETFs: Does 2 = 2?

ProShares has offered a variety of "Ultra" and "UltraShort" sector ETFs for more than a year now. These funds are designed to track twice the return of the underlying index, and each corresponding long fund is created to match its corresponding short.

There is no doubt that these ProShares offerings have been the subject of a great deal of interest. They promise the rewards of leveraged sector returns without the headache of margin or portfolio construction, allowing profitable bets with less capital and less risk. This might not come for free, however, and many have investigated how closely these funds track their double-return target in terms of price. For more on that topic, I suggest this article directly from ProShares.

Instead of asking whether these funds track twice their underlying index, however, I've decided to investigate whether each pair of funds behaves as expected. That is, given two well-constructed index portfolios, the sum of the long fund's return and the short fund's return should equal zero. Though the behavior of the underlying derivatives might be expected to introduce some tracking error, we should expect to see only relatively small differences relating to the difference between price and NAV.

The following chart demonstrates the cumulative return difference between the long and short funds.

click to enlarge

The chart demonstrates that this is far from the case. In fact, nearly half of the sectors have seen over 20% deficits in this balance since June of last year.

Looking for explanations outside of portfolio construction leads to a believable alternative. Charting dollar volume differences shows that almost every single sector had greater dollar volumes on the short side. In some sectors like Materials and Real Estate, the difference in dollar flow over the past year has hit tens of billions. It seems likely that these funds are much more valuable as insurance for the down-side than as single-sector long bets. In other words, if investor are much more likely to bid on and bid up an UltraShort Sector insurance contract, imbalances such as these might be expected.

Comments

[SJC]

Nice article. Interesting take on ETF and the short side insurance uses. Its hard to draw specific conclusions though since the opposite funds have huge differences in market cap and the qualities of swaps they may hold. Very rarely are you going to have the exact perfect swap between a long a short position on these ETF's. In regard to insurance popularity, you saw this during the Bear Stearns collapse, volume interest in ultra short financial SKF, was became the most actively traded instrument for a brief period of time.

[SHB]

Does this mean shorting each would have resulted in a net gain (net of interest for all except last two)?

[GKM]

SHB, I think there is an arb play in there. If you pick a very volatile day, then short the ultrashort and short the ultra you should be able to make a spread over time. However, entry points would be critical. I almost did this once with a double long natural gas ETF because someone had a stupid bid out on it and I could have hedged the other side with the double short. I couldn't get it done though as the broker couldn't find the shares to short.

[RogerNusbaum]

Unless I missed it in your article you did not mention that the funds' objective is to capture whatever it is supposed to capture on daily basis. Given that fact doing a study like the one charted from 8 or 9 months ago tells us nothing about the future. The outcome looking forward depends on how the various underlyings zig and zig.

Example; for all of 2007 the double long SPX ETF lagged SPY.

[2TallTurk]

I have traded the +/-2 beta funds at Profunds and Rydex since 1998. Yes, there is tracking error. It is difficult to do what these companies are trying to do and they do a very good job. You are still better off using these products than using +1/-1 beta products on 50% margin. Also if you trade for very short periods 1-10 days, the cumulative tracking error for your long and short moves is a fraction of staying on one side for several months at a time.

[User 170913]

These funds also issue dividends. Have you taken those into account?

[MichaelBommarito]

Roger & 2TallTurk, note that I'm not talking about whether these funds return twice their underlying index's price return. I point readers to the ProShares article on the difference between daily NAV tracking and cumulative price return...

What I *am* investigating is why the daily NAV return for these fund pairs do not match. That is, the daily NAV return of UYG should be the negative of the daily NAV return of SKF.

2TallTurk, note that I readily accept tracking error from portfolio construction. These ProShares funds have done well considering that the difficulty of matching the magnitude of returns lately. I was merely investigating alternative reasons for the imbalance.

[BenDavenport]

I think your fundamental premise that the cumulative returns must be the negatives of one another is wrong. Take the following example of an ultra-long etf ULX and and ultra-short etf USX. Assume both start at 100.

On day 1, let's say the index moves up 25%. ULX should move up 50% to 150, while USX loses 50% to close at 50. Now, on the second day let the underlying index lose 15%. That means that ULX loses 30% (45) to close at 105, and USX gains 30% to end at 65.

So, at the end of 2 days, ULX now has a return of +5%, while USX has a whopping -35% loss. So, even with perfect tracking, you do NOT get what you expect.

In other words, it makes a difference whether you lose x% and then gain y% than to gain y% and then lose x%. Therefore, your chart is not really telling us much of anything useful.

[cato]

Bingo Ben! People get confused and think these funds will attempt to track 2X (or -2X) over the course of a year. In fact, their goal is to do it _every day_.

Whether you realize it or not, a 2X fund is an implicit momentum play, since it reloads every day. It will always force you to buy a little more at higher prices and a little less at lower prices. If the market goes up and down a lot over a year and then ends the year unchanged, you will lose a lot of money!

[sammyg123]

Yeah. These are good vehicles for short term plays for sure.

[MichaelBommarito]

All numbers I use in calculations are cumulative log-returns, so Ben and Cato's comments are not relevant. The bar charts are endpoint cumulative log-return comparisons converted to standard %-return.

[MichaelBommarito]

Also, in response to User 170913, I've used adjusted close values for these calculations, so the dividends are already incorporated.

[Kunst]

(1 + x) * (1 - x) = 1 - x^2

(1 + 2x) * (1 - 2x) = 1 - 4x^2

Still, if you get the direction right, the 2x should still put you ahead more than the 1x, but not twice as much. If you get the direction wrong, you are in a world of hurt. In a trading range, the above formulas show that the ultra bleeds you much faster than the straight.

This is true of both ultra and ultrashort.

[johnthebear]

IYR was down today -0.36% while SRS was up +2.76%. How do you explain that relationship if they try to balance on a daily basis?

I am not complaining that SRS was up more than 2 x .36, that is not the point. The real problem here is that the -.36 does not look correct for the index when compared to the average of the top 9 funds that make up the index were down -12.24% or an average of -1.36%. I don't have the average percentage gains of all of the funds that make up IYR and I realize an average of percentage numbers is not accurate, but it makes me wonder what happened.

But if you take 1.36 x 2 = 2.72% which is very close to actual amount that SRS increased at 2.76%! So did they lose the 1.0 factor or was the index flawed?

Does anyone know exactly how the manage to keep the two indexes as close as they do? Thanks, John

[james22]

As has been already said in earlier comments - it's the constant 200% leverage at work, dumdum. Twice the daily return (which are these funds mandates) will exceed twice the overall return over an extended period when markets are trending, and underperform in markets that see many trend reversals, even in a perfect world of zero management fees and zero tracking error. In essence holders of 2X ETF's are short daliy realized volatility of the index.

If you plot the long-minus-short portfolio 'shortfalls' against the realized volatilities of each index over the corresponding periods, you should see that sectors with the highest volatilities would have the largest shortfalls.