# What The Numbers Say About Long-Term Investments In Leveraged ETFs

## Summary

- The internet is filled with articles warning people not to invest in leveraged ETFs for longer than a day.
- This article looks at common claims made about leveraged ETFs, and shows why each claim is either untrue or greatly exaggerated as it relates to leveraged S&P 500 ETFs.
- Long-term investments in 2x/3x S&P 500 ETFs can generate tremendous gains, grow with the index in a very predictable manner, and do not deteriorate to nothing due to volatility.
- You can gain big or lose big with long-term investments in leveraged ETFs. But it’s not a sucker bet, and you aren't crazy if you do it.

## What Are Leveraged ETFs?

Leveraged ETFs are exchange-traded funds that use debt and options to amplify daily gains of some underlying index. The main focus of this article is leveraged S&P 500 ETFs, which aim to achieve some daily multiple of S&P 500 gains. Two of the more popular such funds are the ProShares Ultra S&P 500 ETF (NYSEARCA:SSO ) and the ProShares UltraPro S&P 500 ETF (NYSEARCA:UPRO ), which are 2x and 3x S&P 500 ETFs.

## "Leveraged ETFs are the Worst Investment Ever"

Here are a few of the more damning things I've read about leveraged ETFs:

*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. -* Bob Pisani, CNBC

*It is my fiduciary duty to inform you as to why [leveraged and inverse ETFs] do not work exactly like their names imply, and I urge everyone in the ETF industry to embark on a similar public awareness campaign.* -Paul Justice, Morningstar

*Retail investors looking for long term performance should stay as far away from these instruments as possible.* -Jacob Ross, Capital Cube

*Leveraged ETFs are the worst investment ever. the single worst product for individual investors I've seen in two decades of covering markets.* -Howard Gold, Market Watch

*Over time, with the ups and downs in the market, these products are designed to underperform.* -Steve Claussen, Options House

## If The Index Swings 10% on 180 Consecutive Days.

I think the most common argument against holding leveraged ETFs for longer than a day is also the least convincing. The argument is that if the index repeatedly gains a lot and then loses a lot (or vice versa) over a time period, ending at the same value it started with, the leveraged ETF will lose value. It's true, but the effect is way overblown.

Let me take an example from the aforementioned Morningstar article, entitled "Warning: Leveraged and Inverse ETFs Kill Portfolios." The author compares $100 investments in an index vs. a 2x ETF and a 2x inverse ETF of the index:

*If you were to repeat 10 consecutive days of up 10% days followed by down 10% days, both of the leveraged funds would end up at $81.54, which is a sizable difference from the $95.10 the index would end at.*

Now that would be something. A 10% swing on 10 straight days. There have been exactly 3 days since Jan. 3, 1950, when the S&P 500 changed by at least 10%. Never two in a row, and certainly never 10 in a row.

Regardless, this example fails to isolate the effect of volatility during a period of no net growth. The index itself lost about 5%. Leveraged ETFs will always lose more than the index when the index declines.

Later in the same article:

*Repeat this process for only six months, and your 'investment' in either of these leveraged funds would stand at only $2.54. Yes, that's a 97.46% loss.*

By 6 months he really means 180 trading days (about 8.5 calendar months). Anyway, the index would lose 59.5% of its value in that scenario. Leveraged ETFs will always get killed in periods when the index loses 60%. Not because of volatility decay.

Let's consider a more realistic scenario for how 2x and 3x leveraged ETFs might deteriorate due to volatility. Since 1950, the S&P 500 has gained or lost at least 1% on 20.2% of trading days. What would happen if we had an extremely choppy period where the index lost 1%, then gained back 1.010101% (to get back to its starting value), and repeated this pattern over 20 trading days (about 1 calendar month)? A 2x ETF would finish at $99.80 and a 3x ETF at $99.40. In what would be a very volatile month with no net change in the index, 2x and 3x leveraged ETFs would deteriorate by 0.2% and 0.6%, respectively. Not negligible, but not crushing, and anyways you wouldn't expect this type of volatility very often.

The figure below illustrates this examples as well as 5 others, all of which have no net change in the underlying index.

In the upper-right panel, we see that if we had 2% daily swings rather than 1%, the leveraged ETFs would lose 0.8% and 2.4%. But daily swings of 2% or more historically only occur on about 4.3% of trading days, so you'd never expect to have an entire month of this pattern.

The middle-left and middle-right panels show that it doesn't matter if you alternate down

days and then up days, or you have 10 down days then 10 up days. You leveraged ETFs have the same losses as in the first scenarios.

In the lower-left, we see that a 5% loss in the index on day 1, followed by daily gains of 0.2703% so that the index returned to $100 on the 21st day, would result in 0.3% and 0.9% losses in the 2x and 3x ETFs.

In the lower-right, the index lost 5% on day 1, then gained it all back on day 2, and for the rest of the month alternated between 1% losses and 1.010101% gains, and the ETFs lost 0.7% and 2.1%. Not good, but it's hard to imagine the S&P 500 having this degree of volatility and no net change over a one-month period. In fact, there has been only one month out of 782 since January 1950 in which the S&P 500 had a net change less that 1% and volatility this high (standard deviation of daily gains at least 0.0193).

In the highly cited SEC Alert about leveraged and inverse ETFs, a similar hypothetical example is provided. They write that if an index loses 10% one day, then gains 10% the next, it will have lost 1%. A 2x leveraged ETF, however, would lose 4%. Again, this may be relevant for other indexes, but the S&P 500 very rarely loses 10% in a day. A 4% loss when the index loses 1% is not great, but it's not the end of the world if you happen to be holding a leveraged ETF when the market suffers its 3rd 10% loss day since 1950.

Let me summarize my point:

*If you're thinking about investing long-term in leveraged ETFs, you should be aware that some deterioration can occur when the index is volatile with no net change. But you shouldn't worry too much about extreme hypothetical examples, e.g. where the index gains and loses 10% for 180 consecutive days.*

## They Underperformed in 2008, So Don't Invest in Them

Another thing to watch out for is analysts writing about very specific historical periods where leveraged ETFs did not perform well. For example, this Bogleheads article points out that SSO, the 2x S&P 500 ETF previously mentioned, underperformed the S&P 500 from 2006 through 2013. The index grew 69.7%, and SSO grew 61.0%.

Of course this period includes the financial crisis of 2008, when the index had a 56.8% drawdown. There were 11 days in 2008 alone where the index lost at least 5%. To put that in perspective, there were a total of 24 trading days with 5% or greater losses from Jan. 3, 1950, to Feb. 27, 2015. The only other year with more than one -5% day was 1987, with 3.

My point:

*Just because leveraged ETFs performed poorly in 2008 does not mean they are bad investments in general.*

## All Bets Are Off on Long-Term Growth

Wrong again. In a recent article I showed that 99.7% of the variability in monthly gains for a 3x S&P 500 ETF can be explained by net growth of the index. Volatility explains an additional 0.2% of the variability.

Not only that, but it turns out that one month is a short enough time period that UPRO and S&P 500 gains actually do follow very closely to the Y = 3X line. In other words, UPRO basically multiplies S&P 500 monthly gains by 3.

Here's a figure from that article showing the tight relationship between monthly gains for UPRO and the S&P 500 over UPRO's lifetime.

For annual gains, 98.5% of variability in gains for a 3x S&P 500 ETF can be explained by net growth of the S&P 500. Volatility explains an additional 1.3%.

*There is an extremely predictable relationship between monthly/annual growth of a leveraged ETF and monthly/annual growth of the underlying index.*

## Leveraged ETFs are Not Built for Long-Term Investments

It doesn't matter what they're built for. It matters whether you can make money investing in them long-term.

And you can. Over the last 5 years:

It's not just the last 5 years. If you go back and simulate how zero-tracking error 2x and 3x S&P 500 ETFs would have performed since 1950, it turns out that while the index gained 7.7% annualized, the 2x ETF would have gained 13.2% annualized, and the 3x ETF 16.1% annualized.

## Conclusions

(**This is intended to be sarcastic** ) Don't even think about investing in leveraged ETFs for more than a day. They aren't built for it, and their long-term growth is completely random. You'd be crazy to do it - just look at what happened in 2008.

**Disclosure:** The author is long UPRO. **(More. )** The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure:** The author used Yahoo! Finance to obtain historical prices for the S&P 500 and UPRO, and used R to analyze the data and generate figures. Any opinion, 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.

Category: Forex

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