**Summary**

- Leveraged S&P 500 ETFs are not intended for long-term investments. However, investors may be lured by the tremendous growth of these funds in recent years.
- Potential investors should consider historical growth and risk of these funds in various market scenarios, not just the recent bull market.
- Motivated by excellent tracking of SSO and UPRO, this article looks at hypothetical performance of zero-tracking error 2x and 3x S&P 500 ETFs going all the way back to 1950.
- 2x/3x ETFs would have had 13.2%/16.1% annualized growth and 87.3%/97.7% maximum drawdown since 1950. Monthly and annual gains would have been on average much higher, but also much more variable than the S&P 500.
- Buy UPRO and hold it for 5 years, and you might see 5x or even 10x growth. Then again, you might lose it all.

**Basic Background on Leveraged ETFs**

Investopedia.com defines a leveraged ETF as "an exchange-traded fund that uses financial derivatives and debt to amplify the returns of an underlying index." ProShares Ultra S&P 500 (NYSEARCA:SSO) and ProShares UltraPro S&P 500 (NYSEARCA:UPRO) are bullish leveraged ETFs that aim to multiply the daily returns of the S&P 500 by a factor of 2 and 3, respectively. The multiple works on daily gains only, so investors should not expect to realize the target multiple over any holding period longer than a day.

**Warnings and Technical Issues**

The focus of this article is on historical performance of long-term investments in leveraged S&P 500 ETFs. The overwhelming consensus among stock market analysists is that leveraged ETFs are best suited for intraday trading by very experienced traders. For a few cautionary articles, see for example: Bob Pisani at CNBC, Joe Light at The Wall Street Journal, or Justin Kuepper at Yahoo! Finance. There are numerous reasons to exercise caution with leveraged ETFs:

- Leveraged ETFs are designed to achieve a daily multiple of the underlying index. They will generally not achieve that multiple over any longer time period.
- They lose value in periods when the index fluctuates but has no net change. This is due to the somewhat unintuitive behavior of amplified percentages. For an illustrative example, see this SEC alert.
- They can experience massive drawdowns when the underlying index has significant losses. For example, S&P 500 declined 19.4% from April 29 to Oct. 3, 2011; UPRO declined 51.7%.
- If the S&P 500 ever reaches an intraday loss of 33.3%, you can lose your entire investment in UPRO. (Since 1950, the index's biggest percent loss from open to low was 20.5% on Black Monday, Oct. 19, 1987).
- There is no guarantee that daily gains for any leveraged ETF will achieve the target multiple ("tracking error").

There are even more technical issues associated with leveraged ETFs. Potential investors in SSO or UPRO should read the prospectuses to get a better understanding of these issues. The expense ratios are 0.89% for SSO and 0.95% for UPRO.

**Performance of SSO and UPRO in Their Relatively Short Lifetimes**

The figure below shows that SSO and UPRO have done an excellent job tracking 2x and 3x daily gains of the S&P 500. The ratio of mean daily gains for SSO to S&P 500 was 2.12 (0.070% vs. 0.033%) and for UPRO to S&P 500 was 3.26 (0.205% vs. 0.063%). These plots are from each fund's inception (SSO: June 21, 2006; UPRO: June 25, 2009) through Feb. 27, 2015.

Let's look at each fund's growth since inception (below). We see that the market took a big hit during the first 2.5 years of SSO's lifetime, resulting in SSO falling all the way to $2,258 while the index fell to $5,403. It took about 4.5 years, but SSO eventually made up for its losses and ended with $21,686, while the index ended at $16,806. Total growth favored SSO, but its 84.7% maximum drawdown wasn't pretty.

UPRO has performed extremely well in its lifespan, which has mostly covered a bull market. We can see UPRO and SSO tended to separate from the S&P 500, then take a big hits and retreat back towards the index, and so forth. All said, $10k would have grown to $98.3k in UPRO, $52.9k in SSO, and $22.9k in S&P 500 over the course of UPRO's existence. Maximum drawdowns over this period were 51.7% for UPRO, 36.2% for SSO, and 19.4% for the index.

Sharpe ratios (calculated as mean of daily gains divided by standard deviation of daily gains) for the S&P 500 and SSO over SSO's lifetime were 0.024 and 0.027, respectively; Sortino ratios (calculated as mean of daily gains divided by standard deviation of negative daily gains) were 0.030 and 0.033. Sharpe ratios for the S&P 500, SSO, and UPRO over UPRO's lifetime were 0.062, 0.068, and 0.069; Sortino ratios were 0.081, 0.088, and 0.088.

**10x Growth in 5.7 Years**

UPRO would have turned $10k into a shade under $100k in 5.7 years. Can you blame investors for considering buy-and-hold positions in leveraged ETFs?

**Zero-Tracking Error 2x and 3x S&P 500 ETFs Since 1950**

A bull market obviously favors leveraged ETFs, and the S&P 500 has had 15.6% annualized growth over UPRO's short lifetime. Let's see how hypothetical 2x and 3x S&P 500 ETFs would have performed over the past 65 years. This is a make-believe example, but I don't think it's too far-fetched since SSO and UPRO have proven that they can achieve excellent tracking.

First let's look at a few measures of overall performance from Jan. 3, 1950, to Feb. 27, 2015.

Performance of S&P 500 and 2x and 3x S&P 500 ETFs from Jan. 3, 1950, to Feb. 27, 2015: average annualized growth, maximum drawdown, and mean (standard deviation) percent gains over various time periods. | ||||||||

Fund |
Growth |
MDD |
1-M |
3-M |
6-M |
1-Y |
3-Y |
5-Y |

S&P 500 |
7.7 |
56.8 |
0.6 (4.1) |
2.0 (7.8) |
4.1 (11.0) |
8.8 (16.6) |
29.0 (30.2) |
60 (68) |

2x ETF |
13.2 |
87.3 |
1.1 (8.2) |
4.1 (15.7) |
8.5 (22.9) |
18.7 (35.1) |
64.0 (83.5) |
167 (234) |

3x ETF |
16.1 |
97.7 |
1.7 (12.3) |
6.3 (23.6) |
13.2 (35.7) |
29.5 (56.0) |
108.2 (173.9) |
349 (606) |

Annualized growth was substantially higher for the leveraged ETFs, but so were maximum drawdowns. Gains over one-month periods up to five-year periods were all much higher for the leveraged ETFs compared to the index, but were also much more variable.

It isn't very instructive to graph hypothetical growth of $10k over the entire 65 years, because the S&P 500 balance ends up being almost imperceptible compared to the 3x ETF (reflecting the 16.1% vs. 7.7% annualized growth). So let's take a look instead at growth of $10k over non-overlapping 5-year periods since 1950. Note that each graph has a different y-axis scale to provide a reasonable visual comparison of the funds during each period.

A simple takeaway here is that the leveraged ETFs make good markets better and bad markets worse. No surprise there. It is noteworthy that median 5-year gains were 55.9% for the S&P 500, 121.8% for the 2x ETF, and 187.9% for the 3x ETF. This tells us that historically an investment in a 3x S&P 500 has had a 50/50 chance of growing at least 2.8 times over a 5-year period.

But don't forget what an expert would tell you about a 5-year investment in UPRO. From the aforementioned CNBC article:

*As my friends at ETF.com have told me over and over, no one should hold leveraged and inverse funds for 5 months let alone 5 years. It's all about short term use unless you are crazy.*

**A Note on Sharpe/Sortino Ratios**

I reported Sharpe and Sortino ratios for SSO and UPRO, but not for the hypothetical 2x and 3x ETFs. The reason is that for a perfect leveraged ETF, these metrics (as defined in this article) are exactly the same as for the underlying index. For any set of observations, the ratio of mean to standard deviation is not changed by multiplying each data point by a constant. This is also true for any theoretical probability distribution, so the result also holds if you view the Sharpe ratio as the expected gain divided by the theoretical standard deviation, as opposed to the historical mean gain divided by the historical standard deviation of gains.

Technically, the Sharpe and Sortino ratios actually subtract off the best risk-free return available to the investor prior to dividing by the standard deviation. Using that definition, leveraged ETFs will always have greater Sharpe and Sortino ratios than the underlying index, because you essentially subtract off a constant divided by the standard deviation. The standard deviation is larger for the leveraged ETF, so you subtract off a smaller number, resulting in a higher Sharpe or Sortino ratio.

I'm not sure how relevant this is - it probably depends on how much importance you place on these metrics. In a sense, equivalence of these metrics means that, outside of tracking error, the risk-adjusted growth of leveraged ETFs and their underlying index are equivalent. Leveraged ETFs are capable of tremendous growth, but with an exactly proportionate amount of extra risk. At least according to these metrics.

I guess that begs the question: If two funds achieve the same amount of growth per unit risk, do you choose the one with greater growth, or the one with less risk (e.g. drawdown)? It probably depends on your investment goals and time frame. I guess I'd rather take a bumpy ride to the top than a smooth ride to the middle. But that is an oversimplification.

A disclaimer: various definitions of Sharpe and Sortino ratio are available and commonly used. The ones I use may not be the same as the ones you are familiar with or prefer. Also, these metrics are traditionally used to evaluate portfolios rather than individual funds.

**Conclusions**

As I said at the beginning of the article, very, very few stock market analysts would recommend long-term investments in leveraged ETFs. Such investments risk massive drawdowns and total loss of investment. I am not out to convince you to invest in UPRO.

I will say that I am personally very intrigued by these funds. UPRO just doubled three times (and then some) in less than 6 years. If the market does as well in the next 6 years as it has in the last, it could very well double another three times. How likely is it that the market keeps up this pace? Maybe not very likely. But more likely than me picking a stock that grows 900%.

I do want to address a frequently discussed downside of leveraged ETFs: the fact that they deteriorate when the underlying index bounces around, but has no net change. It's a bit scary, but practically speaking the effect hasn't been nearly as harmful as you might think. In a recent article, I found that about 99.4% of the variability in monthly gains for UPRO could be explained by net growth of the index. I also found that 98.5% of variability in annual gains for a perfect 3x S&P 500 ETF could be explained by annual growth of the S&P 500. Volatility, defined as standard deviation of daily index gains, could only explain an additional 1.3% of the variability. For all practical purposes, net growth of the index dictates monthly and annual growth of leveraged ETFs.

There are a number of things that could go wrong with long-term investments in leveraged ETFs, but in my view drawdown is the most concerning. Looking at the figure of 5-year gains since 1950, there were many instances where the 2x and 3x ETF got hammered, with drawdowns of 80% or even as high as 97.7% for the 3x ETF. I don't think I would handle 97.7% drawdown very well.

That's all for now. For those of us "crazy" enough to bet on these risky funds, let's hope for 900% growth rather than 98% drawdown.

**Disclosure:** The author is long UPRO.

**Additional disclosure:** The author used Yahoo! Finance to obtain historical prices for SSO, UPRO, and S&P 500, and used R to analyze the data and generate figures. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.