Home > Research > Exploring Leveraged ETFs and Tracking

Exploring Leveraged ETFs and Tracking

September 1st, 2009 Kevin

There has been plenty of criticism of leveraged ETFs recently, mostly due to lack of understanding of how they work. By now it should be clear to most traders and investors that leveraged ETFs are affected by decay and compounding and that they track an underlying index on a daily basis. There have been plenty of articles that cover decay and a few that cover compounding, but so far there is little information regarding how well leveraged ETFs track their respective index. This article attempts to explore leveraged ETF end of day tracking in depth by observing charts of four types of data.

1. Leveraged ETF versus hypothetical perfect leveraged ETF tracking the index (HLETF)
2. Tracking deviation percent from first day of data
3. Tracking deviation percent (21-day moving window)
4. Difference in daily return percentages

Leveraged ETF vs Hypothetical

The goal of leveraged ETFs is very clear: daily leveraged tracking of an index. Since index data is often publicly available it is easy to generate a perfectly tracking leveraged ETF data set that can be used for comparison purposes. We will call this an HLETF (Hypothetical Leveraged ETF). This hypothetical ETF data is created by calculating the daily returns of the index, multiplying each return by the leverage amount, and then normalizing the HLETF data to the first day of the real leveraged ETF data. Normalizing is just the process of adjusting the start value, and then applying the daily return percentages for all of the remaining days. The only purpose of normalization is to make it easy to plot a chart of the leveraged ETF versus HLETF in order to visually see any tracking error.

The following is a chart that shows FAS versus the HLETF of its underlying index. Yellow is the HLETF, green is FAS 

A casual glance at the chart shows what appears to be excellent tracking of FAS against the index, even through significant volatility. A closer look at the chart shows that over time FAS tends to slightly deviate from the index. As it turns out, FAS is tracking above the index. Rather than ’slipping’ due to fees, expenses, or other factors, FAS is actually outperforming a hypothetical perfectly tracking 3x of the index by 3.3% since the beginning of January 2009. FAS is still being affected by decay and compounding, but since the HLETF is equally affected, the chart is an apples to apples comparison for the purpose of tracking visualization.

Tracking Deviation Percent from First Day of Data

In order to see how FAS deviates from the HLETF over extended periods, at the end of each day we can plot the deviation percent. A chart of these plots looks like the following.

Notice how FAS seems to oscillate between outperforming and underperforming the HLETF during the first few months of the year. Each time FAS was underperforming, there would eventually be a ’snap back’ that would put FAS back on proper tracking. The same effect occurred after days where it outperformed. The range of deviation for the first three months of 2009 was about +/-3.5%. Some savvy traders may have already noticed this phenomenon of leveraged ETFs underperforming one day and then outperforming another day. Once the volatility started to subside in April, FAS began to slowly outperform the HLETF and not snap back to neutral or ‘perfect tracking.’

Tracking Deviation Percent (21-day Moving Window)

Rather than observe the leveraged ETF deviation from the first day to the last day, we can look at the deviation of a 21-day moving window. Each data point on the chart corresponds to the amount of deviation from the HLETF from a point 21 trading days prior. While the chart is not incredibly useful, it does at least provide an indication of how the leveraged ETF tracks over month long periods. A chart of FAS versus the HLETF shows similar deviation that was seen in the previous chart. The same ’snap back’ scenario seems to occur as well. Basically FAS appears to never deviate from the HLETF for more than a few days. It seems any time there is a deviation of 2 to 4%, within the next day or two FAS reverts back to proper tracking (or over reverts in the opposite direction). The chart shows that over the course of monthly timeframes the leveraged ETF typically oscillates between outperforming and underperforming the index.

Difference in Daily Return Percentages

One of the most useful charts is a plot that shows the difference between the daily HLETF returns and the actual leveraged ETF. For example, if the HLETF were to increase 1% but the leveraged ETF decrease 1% that same day, the difference is measured as -2%. The difference would also be -2% if the HLETF gained 3% while the leveraged ETF gained 1%. The difference is positive when the leveraged ETF outperforms the HLETF and negative when it underperforms. This is a chart showing the return percent differences between FAS and its HLETF.

It is clear that during volatile times, FAS either outperformed or underperformed the HLETF by a few percent. Again it is important to note that almost every time FAS underperformed, it appeared to outperform the next day (and vice versa). There is never a period where the daily return differences were consistent in one direction for more than a few days. The chart also includes a plot (red line) of a 21 day SMA of the absolute values of the differences. This smooth line is effectively an estimation of the amount of deviations that were seen over the course of 21 days. During the most volatile times in March and April of 2009 FAS was deviating daily around 2% on average from the HLETF. As volatility decreased by the beginning of August, FAS was only deviating daily around 0.23%. An example would be if the underlying index increased by 1% (and thus the HLETF +3%) and FAS increased by 3.23% (or 2.77%), making for the 0.23% difference.


The same charts can be generated for FAZ as well. The HLETF is generated by multiplying the index returns by -3 (instead of 3 for FAS). The chart shows FAZ tracking quite well.


However, a chart of the deviation from the first day shows a very interesting result.

According to the data it appears FAZ is decaying or ’slipping’ relative to the HLETF. However, this decay is not due to the math behind leveraged ETFs because the HLETF is affected by the mathematical decay by the same amount. FAZ appears to just flat out underperform the HLETF over long periods. Days of underperformance are unable to be recovered during the outperformance days. Critics of leveraged ETFs could use this kind of information to point out leveraged ETF flaws rather than claim the decay from the math is a flaw. Further research may indicate that the slippage is due to the leveraged ETF possibly being slightly more volatile than the HLETF, which would in fact cause the slipping.


Since SSO has been around for several years there is plenty of data to see how it has tracked a perfect 2x the S&P 500. A chart of the tracking deviation percent since the beginning of 2007 shows yet another interesting result.

From the beginning of 2007 to the middle of 2008, SSO tended to underperform a HLETF of the S&P 500. But towards the end of 2008 SSO started to recover the slippage until it was fully recovered by May 2009.


A chart comparing SDS to the HLETF gives a look into how well this popular inverse ETF tracks.

The SDS vs HLETF chart seems to show SDS significantly outperforming the HLETF (-2x of S&P 500). A chart of the tracking deviation will give a better look.

It appears SDS has incredibly outperformed the HLETF. According to data since the beginning of 2007, if SDS had tracked perfectly it would have a value of 40.48 like the HLETF. Instead, it has outperformed by 7.5% to end up at 43.64 at the end of August 2009. Regardless, notice the downward trend in 2009.

Comparison of Bull Leveraged ETFs

To compare how well the various bull leveraged ETF track on a daily basis, we can compare their 21 day moving average of the absolute value of percent differences. This chart does not include long term deviation. It merely shows the average amount of deviation on a daily basis.

Click here for a large version

Except for UYG and URE, the 3x ETFs tend to have the most stray from their respective index on a daily basis, probably due to their extra volatility. The daily tracking error appears to be directly correlated with the amount of volatility in the index.

Comparison of Bear Leveraged ETFs

Click here for a large version

The leveraged bear ETFs show a similar picture. The more volatile the index, the more the leveraged ETF tends to deviate on a daily basis.

Leveraged ETF Tracking Research Charts

FAS [Medium] [Large]
FAZ [Medium] [Large]
ERX [Medium] [Large]
ERY [Medium] [Large]
TNA [Medium] [Large]
TZA [Medium] [Large]
UPRO [Medium] [Large]
SPXU [Medium] [Large]
UYG [Medium] [Large]
SKF [Medium] [Large]
URE [Medium] [Large]
SRS [Medium] [Large]
QLD [Medium] [Large]
QID [Medium] [Large]
SSO [Medium] [Large]
SDS [Medium] [Large]


The investigation into leveraged ETF tracking behavior has yielded interesting results. The majority of leveraged ETFs appear to ’snap back’ to proper tracking soon after they deviate. But we have also seen scenarios where the leveraged ETF significantly outperforms or underperforms the HLETF over long periods. With the exception of SDS, it seems leveraged bear ETFs have significant amounts of ’slippage.’ Combine this slippage with the decay due to the leveraged ETF math, and it makes these bear ETFs risky long-term hedges. Alternatively, almost all bull leveraged ETFs tend to outperform their respective index. It is unknown how long the positive deviation can continue, but such gains combined with positive compounding make bull leveraged ETFs seem better suited for long term investing than bears.

Data is obtained from Yahoo and Google  

Categories: Research Tags: ,
Comments are closed.