A few weeks ago I evaluated the Proshares Ultrashort S&P500 ETF, (NYSEARCA:SDS). That ETF was designed to perform *twice the* *inverse* of the popular Standard and Poor's 500: if the latter gained 10%, you would expect the Ultrashort to fall 20%. The overall conclusion was the SDS performed as expected, with little tracking error and not much evidence of *volatility drag.* The latter arises from the daily rebalancing of "Ultra" ETF holdings. I shall give an example in a moment.

This time we shall examine the performance of the ProShares Ultra S&P500 ETF (NYSEARCA:SSO). The fund is designed, according to Yahoo Finance*, *"to invest in securities and derivatives that ProShare Advisors believes, in combination, should have similar daily return characteristics as two times (2x) the daily return of the index." In simpler words this ETF tries to "double" the market return. If the S&P500 rose 1.3% yesterday, you would expect SSO to gain 2.6%, or twice as much. A nice way to rebuild your wealth on short notice, if you can time the market correctly.

Of course, the opposite also is true: If the market dropped 1% yesterday, you would expect SSO to drop 2%.

Let me turn to an illustration of volatility drag first, using an extreme example to make the discussion and mathematics brief. Suppose you bought a stock for $20 a share. The first day it rises to $25; the second, it falls to $15, and the third day it went back up to $20. A buy-and-hold investor has broken even. What happens to an ETF designed to "track" this one stock?

OOPS! Not so good, especially a double index. On the first day the stock gained 25%, doubled this is 50%. On the second day it fell 40%; doubled, this is an 80% loss; and on the third day it rose about 33%, for a 66% doubled gain. What is your overall result if you rebalance each of the three days? Turning the percentages into decimals, and multiplying we have

- (1.00 + .50) for day 1;
- (1.00 - .80) for day 2; and
- (1.00 + .66) for day 3. The final result is

(1.5)x(.2)x(1.66) or approximately .50.

Returning to percentages (isn't math fun!) you have 50% of your investment remaining. You have lost half your money!

This example is extreme, but the point is that *over a long period of time market volatility acts as a drag (thus the name) on the performance of ETFs which rebalance their portfolios daily.*

How does this affect SSO? Let's see how SSO performs under various market conditions and draw our own conclusions.

Start with advancing markets. Traders would be looking for this when they buy SSO. From March 2009 to May 2010 the S&P500, as measured by the S&P500 Trust Series ETF (NYSEARCA:SPY), gained over 70%. And SSO?

source: www.bigcharts.com

The double ETF gained nearly 180%, **more than double** than the index it was designed to track: twice 70% would be 140%. While you may be tempted to say "bully for you, SSO!," remember this technically does mean the fund is not performing as advertised.

This "overperformance" occurs in other bull market periods as well. Look at the second leg of the current bull market:

Double the 30% gain of the SPY and you get 60%, whereas the SSO shot up nearly 70%.

And in the third leg up, which may have ended last month?

Double the 35% gain in the SPY and you get 70%, whereas SSO gained nearly 78%. The Holy Grail of finance: a consistent overperformer!

Of course, perhaps the SSO is simply more than twice as volatile as the index it is designed to track. A finance professor would say the **BETA** of this ETF is greater than 2. If that is the case we would expect results to suffer more than we expect, in declining markets. No shortage of examples of those in the last few years. Let see how the SSO performed in the 3 down waves of the great recession.

The first wave, in late 2007...

With a 10% decline in the market, we'd expect a 20% decline in SSO, but the actual fall was 25%. But look at the second wave, a big down move in the market:

The market fell by 37%; a simple 2x analysis would suggest a fall of 74%. The SSO fell less than this. "Overperformance?" No. Tricky mathematics, though we need not get into the details here. (I will in the comment section for those who wish). In a nutshell, since SSO is an equity holding, it cannot fall more than 100% in value. For example, suppose the market fell 70%...a nasty day! Could you expect SSO to drop twice that, or 140%? Impossible. It can decline only 100%; after that it has gone to zero. The bigger the drop in the index the ETF is designed to track, the greater this percentage "overperformance" becomes.

We see this with the final leg of the bear as well. The market dropped 27% in the first three months of 2009. The SSO did not fall 54%, but somewhat less:

about 47%, not the 54% we expected.

Finally, as I discussed in my first article, the real opportunity for tracking error and volatility drag to show themselves are in sideways markets. From February to August of 2010 stocks traded flat. So did the SSO:

Same for a similar period in 2011:

Thus, first we can conclude the Proshares Ultra S&P500 exhibits no significant volatility drag over a periods up to several months. While my extreme example showed such drag, the daily percentage fluctuations typical of broad market indexes such as the S&P500 are much smaller---less than 1% on most days---so the drag is very minor.

Second, SSO appears to more volatile, especially to the upside, than its "2x" moniker suggests. Thus for traders confident they can identify periods of rising stock prices, SSO provides opportunity for eye-popping total returns.

**Disclosure: **I am long SPY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.