# Multi-year Performance of Leveraged ETFs

November 13, 2013 • **Posted in** Volatility Effects

An array of leveraged exchange-traded funds (ETF) track short-term (daily) changes in popular indexes. Over longer holding periods, these ETFs tend to veer off track. The cumulative veer can be large. How do leveraged ETFs actually perform over a multi-year period? What factors contribute to their failure to achieve targeted leverage versus underlying indexes? To investigate, we consider:

- 46 ProShares 2X and -2X leveraged equity index ETFs (23 matched long-short pairs), with start date 4/23/07 (determined by the youngest of these funds), encompassing broad indexes, style indexes and sector indexes.
- 10 ProShares 3X and -3X leveraged equity index ETFs (five matched long-short pairs), with start date 2/11/10, encompassing broad indexes only.

We measure achieved average daily leverage by comparing the average daily return of each leveraged ETF to the average daily return of a 1X ETF designed to track the same index. We measure achieved long-term leverage by comparing the terminal return of each leveraged ETF to the terminal return of a 1X ETF designed to track the same index. Using daily adjusted prices for all these funds through 10/31/13, *we find that:*

The following table summarizes average daily and terminal leverages for the 23 2X and 23 -2X ETFs since 4/23/07. Results are:

- The 2X (-2X) ETFs modestly underachieve (achieve or slightly overchieve) targeted daily leverage on average, perhaps due to leveraged fund expenses and the contribution of dividends to the underlying 1X ETFs.
- The 2X ETFs generally do not deliver the targeted daily leverage over a long period. Terminal leverages range from -1.8 to 35.1, with the latter outlier (real estate sector) relating to a 1X underlying ETF with a small negative terminal return.
- The -2X ETFs are generally more consistent than the 2X ETFs over a long period, with all these funds losing most of their value. However, two of the -2X funds deliver positive leverage. The outlier with leverage 3.0 relates to an underlying 1X ETF with negative terminal return (financial sector). The outlier with leverage 46.6 relates to the same underlying ETF as the above 2X outlier (real estate sector).

Some of the leveraged ETFs are illiquid, with daily action distorted when there are no trades.

What causes leveraged ETFs to deviate from targeted leverage?

The following scatter plot relates average daily leverages of the 2X ETFs and -2X ETFs separately to their respective standard deviations of daily returns. The R-squared statistics are 0.27 and 0.28, respectively, with best-fit lines sloping down from left to right. In other words, a higher daily ETF volatility indicates lower achieved average daily leverage, with variation in volatility explaining about a quarter of the decrease. Excluding the notable outlier for each of the 2X and -2X funds (in both cases for the financial sector) flattens the slope and cuts the explanatory power of volatility about in half.

How does terminal leverage relate to fund volatility?

The next scatter plot relates terminal leverage of the 2X and -2X ETFs separately to their respective standard deviations of daily returns, excluding the financial and real estate sectors that produce the outliers above. The R-squared statistics are 0.48 and 0.12, respectively, with best-fit lines sloping down from left to right. In other words, a higher daily ETF volatility indicates lower achieved terminal leverage. Including the financial and real estate sector outliers disrupts these linear relationships.

What about the 3X and -3X ETFs?

The final table summarizes average daily and terminal leverages for the five 3X and five -3X ETFs since 2/11/10. Results are:

- As above, the 3X (-3X) ETFs slightly underachieve (overchieve) targeted daily leverage on average, perhaps due to leveraged fund expenses and the contribution of dividends to the underlying 1X ETFs.
- Over the generally bullish sample period, the 3X ETFs are generally effective at delivering terminal leverage.
- However, the -3X funds do not (cannot) deliver -3X leverage, which would require negative fund values. This result reflects the asymmetry of gains and losses based on simple returns (the largest possible loss is -100%).

The sample period here is much shorter than above and does not include any disruptive bear markets. Results are likely not representative of a sample including a major bear market.

In summary, *evidence from simple tests shows that the multi-year performances of leveraged ETFs may deviate dramatically from daily leverage targets.*

These funds are therefore very risky for implementing any lifetime equities leverage strategy.

Cautions regarding findings include:

- The sample period is not long in terms of number of market regimes relevant to outcomes, especially (as noted) for the 3X and -3X funds.
- Leverage may amplify return distribution wildness, such that “normal” statistical measures lose meaning.

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