Multi-year Performance of Leveraged ETFs

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 perform over a multi-year period? What factors contribute to their failure to track underlying indexes? To investigate, we consider a set of 46 ProShares 2X leveraged equity index ETFs (23 matched long-short pairs), with the start date of 4/23/07 determined by inception of the youngest of these funds (UltraShort Russell1000 Growth). Using daily dividend-adjusted prices for these funds over the period 4/23/07 through 10/13/11 (about 4.5 years), we find that:

The following chart summarizes cumulative returns for all 23 pairs of 2X ETFs, along with those of comparable 1X long ETFs, from 4/23/07 through 10/13/11. Over this period, all 2X long and all 2X short ETFs underperform their 1X long counterparts, often by large margins.

How do the 2X cumulative returns evolve over the sample period?

The next chart shows the average cumulative returns for the group of 23 2X long and the group of 23 2X short ETFs over the sample period. After about two years, both sets of funds experience cumulative losses.

What are the relationships between cumulative returns for the 2X ETFs and cumulative returns for the comparable 1X long ETFs at the end of the sample period?

The next chart relates the cumulative returns of the 2X long and 2X short ETFs to those of comparable 1X long ETFs at the end of the sample period. Results indicate that:

Cumulative returns of 2X long ETFs map to those of their 1X long counterparts systematically. However, the realized leverage (slope) as of 10/13/11 is only +1.25 instead of +2, and there is a performance penalty (y-intercept) of 37% across all 2X long funds.

Cumulative returns of 2X short ETFs are essentially unrelated to those of their 1X long counterparts. The realized leverage (slope) as of 10/13/11 is +0.04 instead of -2, and there is a performance penalty (y-intercept) of 67% across all 2X short funds.

In other words, over the 4.5-year sample period, targeting leverage on a daily basis tends to be costly. Cumulative effects essentially dissociate leveraged short ETFs from underlying indexes.

Note that these results and those above depend on the specific return path during the sample period. Results for another period of equal length could be substantially different.

Note also that ProShares states: “Due to the compounding of daily returns, ProShares’ returns over periods other than one day will likely differ in amount and possibly direction from the target return for the same period.”

How do cumulative returns of leveraged ETFs relate to their volatility?

The final chart relates the cumulative returns of the 2X long and 2X short ETFs to their individual volatilities (standard deviations of daily returns) over the sample period. For both groups of leveraged ETFs, higher daily volatility indicates lower cumulative return. Per the R-squared statistics, variation in volatility explains about 60% of the variation in cumulative returns. In other words, unsurprisingly, the grind of targeting daily leverage escalates with volatility.

For this sample period, the slopes of best-fit lines indicate that increasing the volatility by 1% knocks about 22% (13%) off the cumulative return for the 2X long (2X short) ETF group.

Results are generally in line with the “Volatility in Perspective” discussion offered by ProShares, which relates leveraged ETF performance to volatility of the underlying index.

In summary, evidence from simple tests confirms that the multi-year performances of 2X long and 2X short ETFs can deviate profoundly from daily leverage targets.

These funds are clearly inappropriate 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. Outcomes for this timescale clearly depend on starting point.
• Leverage may amplify return distribution wildness, such that “normal” statistical measures lose meaning.