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Page 4 of 6
One-Month Returns
The trend of increased tracking error continued in the one-month analysis. The average error grew significantly, and the fat tails got fatter, particularly for DXD, which missed by as much as 16 percent on both the positive and negative side of the equation, as shown in Figure 6.
The majority of tracking error was still positive, but the problems of large negative tracking error became more apparent. DXD, for instance, saw 37 cases (nearly 5 percent of results) where it trailed its benchmark by more than 5 percent.
Figure 7 shows how far the margin of error grew at the one-month interval. Even for DDM, the double-leverage ETF, the 95 percent interval has expanded to show tracking errors as large as -2.83 percent. And for DXD, the tracking error has become truly significant: The 95 percent intervals stretched as low as -11.82 percent.
These larger tracking errors must be compared with the larger moves in the Dow, of course. The largest absolute one-month return for the Dow during the studied period was 7.90 percent, with the largest one-month drop hitting -26.63 percent. The 95 percent interval extends from a 5.86 percent return on the upside to a -15.37 percent return on the downside.
Measured against moves of that size, the returns of DDM look quite good. DOG’s performance has wider errors, but they are still relatively contained given the broader movements in the Dow. DXD’s tracking error grows substantially, however. While we might have expected DXD’s tracking error to be 2X as large as DOG’s error (after all, it’s tracking -200 percent of the returns of the Dow), the downside error bands were nearly 3X as large on DXD as they were on DOG. While DXD tracked its linear return well in many, many scenarios, there were clearly a significant number of instances where the tracking error was wider.
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