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Judging by trading volume, the ProShares leveraged ETFs have attracted a large following, and so too have rivals, the more noteworthy, thus far, being the triple leveraged ETFs just launched by Direxion. Judging from the financial media, however, these funds have also attracted much, and sometimes shrill, criticism. There are more issues here than can be addressed at one time. I’ve already addressed longer-than-a-day holding periods on several occasions, the most recent of which can be found here. Today, I want to tackle "tracking error," the extent to which an ETF misses the performance target it is supposed to hit.

What if an index fund doesn't match the index

Imagine jumping through all sorts of strategic hoops and ultimately concluding that it's best to track the S&P 500. You buy an ETF that says it will do just that. But after a short time, you notice that your ETF substantially underperformed the S&P 500. That would be a disaster. It's bad enough to underperform when you assume the risks inherent in trying to outperform. How much worse is it when you deliberately forgo the upside opportunity, but wind up underperforming anyway.

"Tracking error" is the phrase used to describe this nightmare scenario. (Strictly speaking, tracking error also results when you inadvertently outperform the benchmark, and theorists jump on this as well.)

Fortunately, in the real world, tracking error on S&P 500 funds tends to be trivial. Transaction costs, other fund expenses, rebalancing protocols, and sometimes a decision to invest only in a sample of an index, all result in some sort of friction. So we can't ever expect tracking error to be zero. But when we're talking about well-established benchmarks, the error tends to be so small, it can be comfortably ignored by the average investor.

Tracking error in leveraged ETFs

Leveraged ETFs, whether long or short, are different. They use derivatives to help them achieve their goals of magnifying the benchmark's gain or loss. This can be considerably less precise than simply purchasing index constituent stocks. Therefore, if you are going to invest in leveraged ETFs, accept the reality of meaningful tracking error.

Critics believe this should end the inquiry. Leveraged ETFs have tracking error: Gotcha!

It's not that simple. If a leveraged ETF, even with noticeable and persistent tracking error, can still deliver in a way that will allow an investor to execute a chosen strategy, and do so more effectively than any available alternative, it would seem that the leveraged ETF remains a valuable tool. That is what will be examined here; whether or not leveraged-ETF tracking error prevents them from delivering what investors can reasonably expect.

A quick tracking-error study

Daily price changes were evaluated for several leveraged ETFs from the start of 2009 through 3/12/09. This includes some seasoned trading patterns for the ProShares offerings, which were released earliest, some less mature trading activity for some slightly newer Rydex offerings, and some early trading patterns for the most-recently launched Direxion ETFs.

Table 1 shows tracking error for ETFs based on the S&P 500. SPY, the most traditional of S&P 500-ETFs is included as a point of reference.
Table 1 - Tracking Error In Leveraged ETFs Based On S&P 500
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
None
-0.01%
0.01%
0.18%
Double Long
0.00%
-0.02%
0.36%
Double Short
0.01%
0.04%
0.38%
Double Long
-0.08%
0.01%
0.47%
Double Short
0.05%
0.02%
0.54%
BGU
Triple Short
-0.08%
-0.05%
0.65%
BGZ
Triple Long
0.11%
0.10%
0.60%

As expected, tracking error for SPY is miniscule and the propensity for error seems to grow as we move from double leverage to triple leverage.

Tables 2 and 3 show that tracking error grows a bit when we look at leveraged ETFs based on the Russell 2000 and the NASDQ 100. (Actually, it grows even when we compare unleveraged Russell and NASDQ ETFs to SPY.)

Table 2 - Tracking Error In Leveraged ETFs Based On Russell 2000
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
None
0.12%
0.02%
0.37%
Double Long
0.01%
-0.02%
0.70%
Double Short
0.21%
0.07%
0.79%
RRY
Double Long
-0.06%
0.02%
1.03%
RRZ
Double Short
0.03%
0.00%
0.93%
Triple Short
-0.03%
-0.01%
1.22%
Triple Long
0.20%
0.09%
1.07%
Table 3 - Tracking Error In Leveraged ETFs Based On NASDQ 100
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
QQQQ
None
0.16%
0.13%
0.48%
Double Long
-0.21%
-0.24%
1.10%
Double Short
0.24%
0.27%
1.05%
The question in all cases is whether the tracking error we see should scare us away from leveraged ETFs.

If you look anecdotally at a smaller number of days, you will undoubtedly see instances of tracking error that are much larger than anything presented in the above tables, which reflect aggregate figures based on about ten weeks. Individual days will be larger, but there seems to be no systematic bias as to whether the error is positive or negative. As a result, the positive and negative errors largely cancel one another out in less than a quarter.

We'll also consider the absolute extent of tracking error, i.e. without allowing the ups and downs to offset one another. But before doing that, let's see how average tracking error looks for single-sector leveraged ETFs.

In the latter case, measuring tracking error may not always be so straightforward, since the ETFs are designed to track custom indexes often created specifically for use with that ETF. For this study, however, iShares offers some convenient sector benchmarks. For one thing, it's a major ETF brand and for many, the search for sector ETFs begins and ends with iShares. Better still, proprietary sector indexes tracked by the iShares ETFs (produced by Dow Jones) are the same ones used by ProShares. Rydex and Direxion use sector indexes created by other vendors (S&P and Russell respectively). Nevertheless, I benchmarked to iShares ETFs across the board.

Tables 4 through 8 show aggregate early-2009 tracking error for a sampling of sectors.
Table 4 - Tracking Error In Leveraged Real Estate ETFs (unofficial benchmark = IYR)
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
Double Long
-0.01%
0.09%
1.11%
Double Short
0.01%
0.12%
0.92%
Table 5 - Tracking Error In Leveraged Energy ETFs (unofficial benchmark = IYE)
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
Double Long
0.16%
0.03%
0.58%
Double Short
0.03%
0.01%
0.58%
Triple Short
0.24%
0.07%
0.79%
Triple Long
0.05%
-0.02%
0.91%

Table 6 - Tracking Error In Leveraged Financial ETFs (unofficial benchmark = IYF)
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
Double Long
-0.04%
0.00%
1.05%
Double Short
0.01%
0.08%
0.76%
Triple Short
0.11%
0.05%
1.64%
Triple Long
0.33%
0.35%
1.35%
Table 7 - Tracking Error In Leveraged Healthcare ETFs (unofficial benchmark = IYH)
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
Double Long
0.14%
0.00%
0.50%
Double Short
0.04%
0.01%
1.00%
Table 8 - Tracking Error In Leveraged Technology ETFs (unofficial benchmark = IYW)
ETF Ticker
Type of Leverage
Daily % Tracking Error
Median
Mean
Standard Dev.
Double Long
-0.02%
0.02%
0.52%
Double Short
0.10%
0.04%
0.46%
TYH
Triple Short
-0.04%
0.07%
0.66%
TYP
Triple Long
0.15%
0.03%
0.81%

We see above that the sector ETFs were imperfect. Deviations exceeded what we saw for leveraged ETFs based on major indexes. As to whether the imperfection is excessive, that's a matter of individual opinion. Speaking for myself, though, I do not believe these levels of tracking error will interfere with the sort of strategic goals that would cause one to invest in leveraged ETFs.

Tables 9 through 16 look at all the foregoing leveraged ETFs but this time, the focus is on "absolute value." In other words if the market moves 2%, and the ETF moves 2.5%, we would say tracking error is 0.5%, We'd say the same if the ETF moves 1.5%. This way, we can test how effective leveraged ETFs are at magnifying the daily moves without giving them an opportunity to offset positive and negative errors.

The first data column in each of the following tables looks at what happened in the market, the absolute size of the average daily benchmark move. The second data column applies the doubling or tripling, depending on what the ETF is supposed to offer. This is what a zero-tracking-error ETF would deliver. The final column shows what the real world ETF actually wound up delivering.

In other words, if the absolute value of a benchmark's average daily price change is 1.5% (first numeric column), investors would expect a two-times leveraged ETF to produce an absolute daily average change (second column) of 3%. An ETF that actually achieves an absolute daily average (third column) of 1.8% would not be considered a success. Its use of derivatives did not properly deliver on the 3% target. But if the ETF's daily average absolute price change (third column) is 2.9%, we'd acknowledge the presence of tracking error, but most observers would still say the ETF did a magnificent job in executing on its goals.

(Methodology note: There is a potential trap in using absolute value: the crossing zero issue. Consider the situation with SDS, the S&P 500 ultra short ETF, on 1/5/09. The index dropped 0.47 percent, thus making for a plus 0.93% ultra short target. SDS, nevertheless, dropped 0.09%. If I were to apply absolute value to 0.93% and -0.09%, we'd wind up with 0.93% and 0.09%, and, hence, a tracking error of 0.84%. That's not correct. I compute the tracking error first, which in this case is -1.02%, and then apply absolute value to get 1.02%.)

Table 9 - Impact Of Leverage, ETFs Based On S&P 500
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
SSO
Double Long
1.55%
3.09%
2.89%
SDS
Double Short
1.55%
3.09%
2.86%
RSU
Double Long
1.55%
3.09%
2.80%
RSW
Double Short
1.55%
3.09%
2.73%
BGU
Triple Short
1.55%
4.64%
4.21%
BGZ
Triple Long
1.55%
4.64%
4.22%
Table 10 - Impact Of Leverage, ETFs Based On Russell 2000
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
UWM
Double Long
2.00%
4.00%
3.41%
TWM
Double Short
2.00%
4.00%
3.44%
RRY
Double Long
2.00%
4.00%
3.40%
RRZ
Double Short
2.00%
4.00%
3.31%
TNA
Triple Short
2.00%
6.00%
5.14%
TZA
Triple Long
2.00%
6.00%
5.17%
Table 11 - Impact Of Leverage, ETFs Based On NASDQ 100
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
QLD
Double Long
1.83%
3.66%
2.97%
QID
Double Short
1.83%
3.66%
2.88%

Table 12 - Impact Of Leverage, Real Estate ETFs
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
URE
Double Long
3.28%
6.56%
5.81%
SRS
Double Short
3.28%
6.56%
5.96%
Table 13 - Impact Of Leverage, Energy ETFs
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
DIG
Double Long
1.98%
3.97%
3.56%
DUG
Double Short
1.98%
3.97%
3.56%
ERX
Triple Short
1.98%
5.95%
5.49%
ERY
Triple Long
1.98%
5.95%
5.15%

Table 14 - Impact Of Leverage, Financial ETFs
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
UYG
Double Long
3.02%
6.04%
5.42%
SKF
Double Short
3.02%
6.04%
5.75%
FAS
Triple Short
3.02%
9.05%
8.13%
FAZ
Triple Long
3.02%
9.05%
8.37%
Table 15 - Impact Of Leverage, Healthcare ETFs
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
RXL
Double Long
1.14%
2.28%
3.32%
RXD
Double Short
1.14%
2.28%
1.92%

Table 16 - Impact Of Leverage, Technology ETFs
ETF Ticker
Type of
Leverage
Absolute Values of daily % changes
What happened in the market
The result one had hoped to achieve using leverage
What the leveraged ETF actually delivered
ROM
Double Long
2.03%
4.06%
3.79%
REW
Double Short
2.03%
4.06%
3.74%
TYH
Triple Short
2.03%
6.09%
5.68%
TYP
Triple Long
2.03%
6.09%
5.63%

As with Tables 1 through 8, reasonableness is in the eye of the beholder. But in my opinion, all the tracking error we see here is acceptable. Take, for example, SKF, the ProShares Ultra Short Financial ETF. Had I owned it in early 2009, I'd have hoped to see absolute average daily price movements of 6.04%, double that of the relevant Dow Jones sector index. But I only got 5.75%.

From the vantage point of a theorist, that gap is big enough to mention when discussing whether or not leveraged ETFs have meaningful tracking error. But from the standpoint of an investor, should that make me abandon an intent to double short the financials? In assessing whether or not magnifying 3.02% into 5.75% is a reasonable outcome for one who had hoped to magnify 3.02% into 6.04%, consider that alternatives. What sort of risks or impracticalities are associated with other methods of implementing an aggressive-bear strategy in finance?

I find it particularly noteworthy that tracking error on the triple leverage funds seems in line. Remember, those funds work with Russell benchmarks. Apparently, the differences between those and the Dow Jones indexes are not great, a separate topic that should be of interest when one is considering sector ETFs in general.

Conclusion

Yes, leveraged ETFs feature significantly more tracking error than ETF traditionalists are accustomed to accepting, and if we're playing "Gotcha," the traditionalists win big. But were not playing "Gotcha." We're looking to implement a variety of interesting investment strategies. In this regard, the ETFs examined here delivered quite nicely during the course of this early-2009 sample period.

It would not be appropriate for me to generalize from this to the point of saying we can disregard all tracking error for all leveraged ETFs. But I think the data is sufficient to say that if one is concerned about tracking error, it would be best to specifically study, case-by-case, the ETFs one is considering. To use tracking error as a basis for dismissing leveraged ETFs in general seems incorrect.

Source: Leveraged ETFs: Is Tracking Error Really So Troublesome?