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Quarterly Returns
Expanding out to look at quarterly returns, the results grew more extreme. DXD in particular exhibited a number of large errors, particularly on the downside, with negative tracking error extending as far as -30 percent. DOG also showed a sharp downward tail of negative tracking error, while DDM performed much better, as shown in Figure 8.
Large errors remained when tightening to a 95 percent return band, as shown in Figure 9. DDM remained relatively tightly confined to its index, staying within 3 percent of the index in 95 percent of all cases. DOG did slightly worse, with a range that extended to -5.17 percent on the downside. But on DXD, the misses were huge, stretching all the way from 4.74 percent to -20.80 percent.
Again, these returns must be understood in the context of the larger returns of the index itself. Quarterly returns on the Dow for the period ranged from 13.49 percent on the upside to -35.05 percent on the downside. Ninety-five percent intervals stretch from 10.68 percent on the upside to -25.51 percent on the downside.
At those levels, the returns of DDM and DOG are reasonable. But DXD remains an outlier, with large potential misses threatening returns.
One-Year Returns
When the study is extended out to one year, an interesting shift occurs. Not only do the outlier tracking errors grow significantly, but the skew of results shifts. As Figure 10 shows, the fat tails in the one-year analysis are primarily on the positive side, particularly for DXD, which significantly beat its index in a number of different scenarios.
This is shown again in the 95 percent confidence intervals, where the DOG ETF in particular shows no positive error at all in the 95 percent view, and both DXD and DDM skew sharply higher. In all instances, however, the bounds for error are large.
Of course, the Dow showed great variability of returns during the time studied. On a one-year basis, the Dow delivered returns as high as 30 percent and as low as -41.82 percent. The confidence interval stretches from 22.13 percent to -37.12 percent.
Even measured against the larger returns of the index, the tracking error shown by the funds is quite large. DXD in particular shows a wide variation in tracking error.
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