Welcome to the first of several articles exploring the ups and downs, ins and outs, of leveraged ETFs. These articles will attempt to visually explain the dynamics of leverage as well as go deep into exploring the benefits and pitfalls of extreme volatility that accompany 2x and 3x ETFs. As a software engineer by day, I lack the investment and trading experience of many who do it for a living or on a daily basis. However, the articles and comments that I read online make it clear there are only a rare few that really understand how leveraged ETFs work for periods longer than a day. All that is required is an understanding of some very simple math. To explore long term leveraging effects, custom software was written measure leverage in a variety of scenarios. Questions such as the following will be addressed on this blog:
- What is leveraged decay?
- How much do leveraged ETFs lose due to decay?
- Are leveraged ETFs going to 0?
- What are the compounding effects of leverage?
- If I hold on to my leveraged bull ETF, will it eventually ride out the volatility in a bull market?
- What are the differences between using margin and a leveraged vehicle?
Many investors put money into leveraged ETFs without understanding the risks involved. Aside from the risk of potentially losing money at 2 or 3 times an underlying index, there is also a risk of losing money due to volatility if these ETFs are held for longer than a day. This loss is often called “Leveraged Decay” or “Volatility Decay.”
A Simple Explanation
Consider both a 1x and 3x ETF that have a starting price of $100 per share.
If the 1x ETF were to drop 10% on a particular day, the 3x would drop 30%. That puts the 1x ETF at $90 and the 3x at $70. Then on the next day the 1x ETF increases $10 back to its original value of $100, which is an 11.11% gain (10/90 is 11.11%). The 3x ETF will gain 33.33% of its $70 which is an increase of roughly $23. This puts the 3x ETF at a value of $93, for a loss of $7! Repeat this process again and again and over time the 3x ETF will continue to lose value while the underlying index always returns to $100. Here is a chart that shows this process happening 15 times (30 days).
As you can see, the 1x ETF is still at $100 while the 3x ETF has decayed 65% to end up at $35. A 10% move on a daily basis is not typical market activity, but it does help illustrate how significant decay can be. To demonstrate something more realistic, we can use the average SPY daily percent change from 1993 to 2008 which is 0.8%.
At such low volatility of 0.8%, decay has much less effect than when daily volatility is 10%. The 3x ETF above lost only 0.59% over 30 trading days. Here is a chart showing a full year of 0.8% volatility.
For 250 trading days with 0.8% volatility, the 3x ETF would lose around 5%. This doesn’t seem like the doom and gloom many blogs and articles have predicted for leveraged ETFs. The reason is because 0.8% daily volatility is far from the current average in 2009. A 30-day SMA of daily volatility for various 1x indexes will give us an idea of the volatility we have seen in the past year:
Back in November the indexes were at extremely high volatility levels, averaging between 4% and 6% daily moves. There were several days that reached higher than 10% resulting in +/-30% for the 3x ETFs. Such large daily moves can cause significant decay over time. An important point is that the amount of decay that occurs is not linearly proportional to the daily percent changes. In other words, 2% daily percent changes of an index does not result in twice the decay of 1% daily moves. Instead, it is significantly more. The following chart demonstrates the amount of leveraged decay for a hypothetical 3x ETF over 30 days for various underlying index daily move percentages (the ‘down’ day is not shown in order to make a smooth plot).
|1x ETF Daily Change %||3x ETF Loss % due to Decay|
It is evident from the table that the loss from decay grows significantly as the daily percent change increases. You will not see 6 times the decay comparing 6% daily moves to 1% daily moves; you will see over 29 times the decay. The bottom line: expect more much more decay from higher daily percent moves. This is a large part of why FAS and FAZ have dropped so much since their inception.
A Closer Look at Decay
Some key points to understand are:
- Leveraged ETFs move at a multiple of their underlying index on a daily timeframe.
- It is volatility on a daily timeframe (not intraday volatility) that causes decay.
- There is no absolute measure for loss due to volatility; a trend significantly affects the loss or gain.
- Decay is the result of simple percentage math and is not specific to leveraged ETFs.
- Between any two equal points, there is more positive percent gain than negative percent loss.
- As a drop % increases, its difference between the gain % needed to reach the original price increases.
Point number 5 says that no matter how many days it takes for an ETF to go down by a percentage, the total percentage to get back up to the original value will always be greater than the percentage down. As proof, from any two equal data points in a graph we can compute the sum of all percent gains and losses, and the gains will always be greater than the losses. Here is a chart of the SPY from the start of 2000 until May 2009 that includes such a calculation.
The light blue line (which is not important and just used as reference) is the % change since the start of 2000. The green data points represent the aforementioned calculation and show that between two equal price points in the SPY, the sum of the percent gains are more than the sum of the percent losses.
Point #6 can be confusing, and basically means that as the magnitude of a percent drop increases, in order to reach the original price, the difference between the drop percent and the gain percent increases. Better explained by an example, consider a 10% drop from $100, which results in $90. To get back to $100, an increase of 11.11% is needed. The difference between these percentages is 1.11%. Now consider a more significant drop of 30% from $100 which results in $70. To get back to $100 a gain of 42% is needed. The difference between 30% and 42% is a much larger 12%.
|Drop||Gain to Recover||Difference|
(3x the 1x ETF)
For a non-leveraged ETF, this does not mean much. But for a leveraged ETF, the fundamental problem of leveraged decay arises from the fact that as daily percent changes are increased due to leverage, the gain percentages are not enough to make up from the increased loss percentages. The example above proves this point since a 3x ETF drops 30% for an index that drops 10%. When the underlying index gains 11.111% to reach its original value the 3x ETF will increase 33.333% which is not enough for the 3x ETF to reach its original price point.
Doom and Gloom: Bearish ETFs
While there are some positive aspects of bearish ETFs which will be covered in future posts, the math is unfortunately set up against them. As we have seen previously, a repeated pattern of a 1x ETF of -10% and +11.11% results in the 3x bull ETF moving -30% and +33.33%. The bear does the opposite which is +30% and -33.33%.
Bull 3x: -30%, +33.33% (+3.33 extra percentage points)
Bear 3x: +30%, -33.33% (-3.33 extra percentage points)
Leveraged bear ETFs not only suffer from decay, but they also suffer from point #5 which means in a horizontal market the bear ETFs are always moving down by greater percentages than the percentages they move up. If the market turns into a bull market, or even moves sideways, bear ETFs are a one way ticket to zero. Only a market that continually moves downwards can sustain leveraged bear ETFs. This has significant implications for long term holders. Anyone that has a long term hedge position in a leveraged bear ETF has both decay and loss percentages working against them. A chart of 6% daily moves for a 1x index over 30 days (15 oscillations of -6% then +6.4% for the 1x ETF, resulting in -18% then +19.2% for the 3x bull ETF and +18% then -19.2% for the 3x bear ETF) shows the bear ETF getting destroyed compared to the bull:
Hypothetical Long Term 3x ETF performance
To get an idea of how 3x bull and bear ETF might perform (excluding fees and other costs), this is a chart showing IWM (Russell 2000) during the bear market of 2000 to 2003:
|IWM 3x Bull||-84%|
|IWM 3x Bear||+44%|
For the bull market of 2003 to 2007:
|IWM 3x Bull||941%|
|IWM 3x Bear||-97%|
This is a good example that demonstrates that 3x bull ETFs are not going to 0, provided there is enough upward trend in the underlying index to offset loss due to decay.
Trend, Volatility, and Returns – A must read study that goes more in depth on leveraged decay, but also covers other aspects such as compounding. Written by Connors Research, (the research division of The Connors Group) which is part of a network of sites such as TradingMarkets.com.
Direxion Literature – A fantastic set of 5 articles describing the ins and outs and risks of leveraged ETFs.
Understanding ProShares’ Long Term Performance – A 2-page document that has a simple explanation of the relationship between compounding and volatility in leveraged ETFs.
On-Demand Webinar: Getting Leverage, Going Short – A must watch webinar that covers the history of Leveraged ETFs, an overview of how they work, and information on their tracking properties. Written by Matt Hougan, editor of IndexUniverse.com. The link includes a PDF of the slides if you do not want to watch the video.
This post covered the reasons for leveraged decay and the factors that influence the amount of loss due to decay. However, there are many other aspects to decay and leveraged ETFs that will be covered in future posts. Here is a peek at some topics that will be covered: