Understanding Returns Of Leveraged And Inverse Funds

August 25, 2009



Case Study Of Rebalancing For A -2x Oil & Gas Index Daily Target Strategy

To demonstrate the potential impact of rebalancing, we looked for a recent historical period with a significantly large difference between an inverse fund return and the daily target leverage ratio times the index for a longer holding period. The inverse -2x ETF based on the Dow Jones U.S. Oil & Gas Index has been cited as having large performance gaps for longer periods. For our rebalancing case study, we evaluated a hypothetical fund based on this index over the period December 2008 through April 2009, when volatility levels were exceptionally elevated and the index rose just 2.2 percent. (For this hypothetical fund, we used index total returns, excluding expenses and trading costs. The fund, therefore, does not represent an actual investment or actual ETF returns.)

A hypothetical fund with a one-day target of -2x based on this index without rebalancing would have returned -25.8 percent over this period without fees, expenses and transaction costs. This is a difference of 21 percent in return from the -4.4 percent for a -2x period return, given the 2.2 percent index return and excluding fund fees, expenses and transaction costs. How might percentage-trigger rebalancing strategies have fared in narrowing this gap? We analyzed a broad range of percentage-trigger strategies (from 0 percent to 25 percent) and found that any such strategy may have meaningfully reduced the gap in performance. Figure 14 compares the performance for the unrebalanced fund with three such sample percentage-trigger rebalancing strategies.

Given the high level of volatility during the case study period, we focused on the 10 percent gap trigger (that is, we rebalanced when the cumulative difference between index return and fund return was greater than 10 percent), and assume all rebalancing is done based on end-of-day index levels with no fees, expenses or transaction costs. Using this 10 percent rebalancing trigger, the return for a daily target -2x rebalanced strategy based on the Dow Jones U.S. Oil & Gas Index would have been -6.0 percent, just 1.6 percent below the -4.4 percent return that a -2x fund investor might set as a target for a five-month holding period. There was an average of 3.8 days between rebalances. It is worth noting that in a lower-volatility period, the 10 percent trigger likely would have prompted less frequent rebalancing.

Figure 15 shows the index cumulative return over the period for the Dow Jones U.S. Oil & Gas index (black line), during a very choppy return environment. This result is consistent with the type of periods in which a gap develops for a -2x inverse fund. The orange line shows a hypothetical daily target -2x strategy with no rebalancing, and the blue line shows a similar -2x strategy rebalancing with a 10 percent trigger. This case study is just one hypothetical example with a specific rebalancing rule employed on a particular index for a single time frame, but it illustrates how a perceived performance gap may be reduced significantly for investors focused on achieving longer-term target leverage returns using daily target fund ETFs.


Leveraged and inverse funds have been and can be used successfully for periods longer than one day. Our study shows that the impact of compounding on these funds over multiday periods for most broad indexes was virtually neutral. There is a high probability of approximating the one-day target for periods longer than a day; the shorter the period and the lower the index volatility, the higher the resulting probability of meeting the one-day target. Finally, rebalancing the size of fund positions, while resulting in some additional trading costs, may be an effective mechanism for investors whose goal is to approximate the daily leverage target over time. The process is straightforward and simply involves monitoring index returns versus fund returns and establishing a trigger percentage of deviation as a basis for the rebalancing strategy.

Solomon Teller contributed to this article. The authors would also like to thank Howard Rubin and Cynthia Truong.


Marco Avellaneda, Stanley Zhang, “Path-Dependence of Leveraged ETF Returns,” Working Paper. Courant Institute of Mathematical Sciences, New York University; Finance Concepts, 2009.

Richard Co, “Leveraged ETFs vs. Futures: Where Is the Missing Performance?” CME Group Research & Product Development, February 9, 2009.

Matthew Hougan, “How Long Can You Hold Leveraged ETFs?” Journal of Indexes, March/April 2009.

Lei Lu, Jun Wang, Ge Zhang, “Long Term Performance of Leveraged ETFs,” Working Paper. Shanghai University of Finance and Economics; 2009.

Jason Ruspini, “Making Leveraged ETFs Work,” Seeking Alpha, July 07, 2009.


1. Including exchange-traded notes, the total number of leveraged and inverse exchange-traded index products as of June 30, 2009, was 140, with total assets of $34.7 billion.

2. IndexUniverse.com, Matt Hougan, “Getting Leverage. Going Short.” webinar, May 14, 2009.

3. We use extreme examples +10 percent and -10 percent for daily returns for purposes of illustration. These levels of daily returns are highly unlikely for most indexes.

4. Over this 50-year daily return history, the annualized volatility of the S&P 500 Index was 15.5 percent.

5. Over the 50 years of S&P 500 return history, there were more than 18,000 rolling periods in our sample for each holding period out to six months. The analysis is based on the distribution of differences between the returns of a hypothetical daily target leverage fund for each holding period and the returns of the index for the same period multiplied by the leverage ratio (2x or -2x). Each holding period return has embedded (but different) compounding effects, allowing us to analyze the distribution of these differences in terms of the arithmetic mean, median and percentiles.

6. Some investors in leveraged and inverse funds have strategies based more on a trading view of an index and are primarily seeking to profit from this view. They may be looking to benefit from trending markets or lower levels of short-term volatility and are less concerned about precision in achieving the daily leverage target over a longer horizon.

7. One weakness of a calendar-based approach is that it does not allow for reaction to large and quick moves that are event-driven, such as was seen in October 1987 and on September 11, 2001, and the recent volatility associated with the global financial crisis.

8. The Financial Industry Regulatory Authority (FINRA), “Non-Traditional ETFs,” Regulatory Notice 09-31, June 2009.



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