Return Patterns

An important trend emerges for the inverse funds if you dig into when and where tracking error appears. For all the periods studied except one-year, tracking error grows larger … and more negative … as the expected return grows.

Figure 12 showcases this point. It compares the tracking error of DXD to the fund’s expected return. The tracking error stayed generally flat-to-positive for all but the most extreme positive expected returns. Once those expected returns went parabolic—above, say, 20 percent—the tracking error got much more volatile and was generally negative.

This held true for all time periods studied except for one-year. In the one-year returns, tracking errors tended to be positive overall, and did not have the negative skew during large expected returns.

Errors Skewed Toward Late-2008

It is important to note that this study took place over a period of historic volatility, particularly in the latter half of 2008. In fact, the vast majority of the large tracking errors recorded during this study took place in the latter half of 2008. Had the study only extended through mid-2008, tracking errors would have been much smaller overall.

Figure 13 shows quarterly tracking errors for all three funds as they occurred in time. As shown, the majority of large tracking errors occurred during the tail end of the study, when the chaos of 2008 started to impact returns. Unfortunately, when those large tracking errors appeared, they tended to appear on the negative side of the ledger. It is no surprise that this is when public concern about these products began to develop.


How Long Can You Hold ProShares ETFs?

The results of the study are clear. As you move further away from the targeted one-day time period, tracking error on these funds grows. The problem is substantially more acute for the leveraged-inverse fund (DXD) than it is for the straight leverage (DDM) or straight inverse (DOG) funds.

In most market conditions, the funds stuck close to the simple long-term leveraged or inverse return of their index. But in the most volatile of markets, significant negative tracking error developed in some of the cases studied.

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