## Leveraged ETFs and Compounding

There has been plenty of coverage in the past few months regarding leveraged ETFs and the concept of decay when these ETFs are held longer than a day. Besides increased risk, decay is certainly one of the downsides of leveraged ETFs. However, there is an equal upside to leveraged ETFs that has not had much coverage which is the topic of compounding during trends. Before compounding is explained, it can be helpful to revisit some fundamentals in order to have a better understanding of how leveraged ETFs may behave in various scenarios.

**Volatility vs Trend**

When a stock or ETF is moving in the same direction day after day, it is said to be in a trend.

Conversely, when a stock or ETF is moving in opposite directions, it is said to be volatile.

Since in the real world stocks and ETFs have elements of both, they can look like the following.

And since some have a low volatility to trend ratio, their chart may look smoother.

While others have a high volatility to trend ratio (like the financials during the 2008-2009 credit crisis).

**Magnification of Characteristics**

Leveraged ETFs track an underlying instrument (typically a stock index). When the underlying index is trending, the leveraged ETF will amplify the trend. When the underlying index is volatile the leveraged ETF will amplify this volatility. The problem of decay arises from this amplification of volatility. Decay occurs due to very simple math and has nothing to do with how leveraged ETFs are run or managed. On the other hand when an index is trending, a leveraged ETF amplifies the trend by a multiple (such as 3x) and also by compounding.

- Leveraged ETF + Volatility = Decay
- Leveraged ETF + Trend = Increased Compounding

**Compounding Explained**

Compounding affects both non leveraged and leveraged stocks and ETFs. Consider this simple example.

When the ETF is at $10 a 10% gain results in an increase of $1. Each time the ETF goes up, a 10% gain results in a larger and larger dollar increase. By the time the ETF reaches $20, a 10% increase ends up being $2 which is double the $1 from the start of the trend.

The following is a chart that shows a trend of daily 3% gains.

A chart of the dollar amount gained each day shows days at the end of the trend to have higher dollar increases than days at the beginning of the trend. This is essentially the concept compounding.

**Leveraged Compounding**

Since leveraged ETFs multiply daily % increases by a factor such as 3, the effects of compounding are significantly increased. Rather than an ETF increasing by 3% each day, the 3x leveraged ETF increases by 9%. This alone causes a significant increase, but during a trend, each percentage gain becomes increasingly more significant as the trend continues.

Here is a chart showing an index increasing 3% each day and a 3x ETF increasing 9% each day.

Not only does a leveraged ETF increase faster than the index, but a chart of the daily dollar increases shows the leveraged ETF’s rate of daily gains *increasing*, which is from the amplified compounding.

If the previous descriptions and charts are not sufficient for understanding leverage ETFs and compounding, another way to visualize the increased compounding is to view a comparison between the underlying index, 3:1 leverage using a margin account, and a 3x ETF.

The 3:1 margin account starts and ends at 3 times the value of the underlying index. Here is a chart showing the profit.

The 3:1 margin will grow at exactly 3 times the rate of the underlying index since its compounding increases at the same rate as the index. However, the 3x leveraged ETF will grow at a much faster rate due to the amplified compounding. This is a huge advantage of leveraged ETFs. If you can guess the trend correctly, there is potential for significant profits.

**Bulls, Bears, and Trends**

Bull and Bear leveraged ETFs have the same compounding characteristics, but since not all trends are the same, these two opposite ETFs have some interesting behavioral differences during trends. Two types of trends will be considered for demonstration purposes.

- +50% trend (1% increments)
- -50% trend (-1% increments)

Guessing the trend correctly means choosing a bull in the positive trend and choosing a bear in the negative trend.

**Correct Guess**- o Bull 3x ETF with +50% trend
- o Bear 3x ETF with -50% trend
**Incorrect Guess**- o Bull 3x ETF with -50% trend
- o Bear 3x ETF with +50% trend

It is important to realize is that it takes fewer days to move 50% in the positive direction at 1% per day than it does to go 50% down in a negative trend. This is because compounding occurs in the positive direction making each +1% gain bigger and bigger, and the opposite occurs on the way down. There is ‘reduced exposure’ in a negative trend therefore each -1% change has less effect. All in all, it takes 69 days to go -50% versus only 41 days to go +50%, when +/- 1% daily increments are used.

This has very important implications because it seems bears will have a huge advantage during downward trends than bulls during a positive trend. Charts and data will indicate whether this holds true.

**Bulls in a Bull Trend**

In the 50% positive trend, the index gains 50% as expected, the 3:1 margin account gains 150%, and the 3x ETF gains almost 250% due to compounding.

**Bears in a Bear Trend**

Shorting an index that drops 50% results in a 100% profit (the index was sold at twice the price it was bought). Using 3:1 margin to short the index results in a 300% profit, and the 3x bear ETF has a massive 668% profit.

Even if the trend is over a shorter time period (such as -3% daily changes) the 3x bear profits over 620%. It is not the number of negative days that makes the bear so profitable; it is the ‘opposite of compounding’ effect.

**Bulls in a Bear Trend**

If the trend is guessed incorrectly, obviously significant losses will occur.

The 3:1 margin account gets crushed by losing 150%, which is more than the value of the index. Even though leveraged ETFs can move significantly in either direction, one advantage they have over margin accounts is that the most they can lose is 100% (the index goes to 0). With a 3:1 margin account, an index or stock that drops to 0 results in a 300% loss. In the chart above, the bull lost 88%.

**Bears in a Bull Trend**

The bear 3x ETF loses 71% which is less than the bull’s loss of 88%.

**Comparing Gains and Losses**

The final numbers are as follows.

**Correct Guess**- o Bull 3x ETF with +50% trend
**[+236%]** - o Bear 3x ETF with -50% trend
**[+668%]** **Incorrect Guess**- o Bull 3x ETF with -50% trend
**[-88%]** - o Bear 3x ETF with +50% trend
**[-71%]**

**Conclusion**

When it comes to profitability during trends the bears win hands down. Not only do the bears gain more during correctly guess trends, they lose less during incorrectly guessed trends. From the numbers presented it seems like there is little reason to use the bull 3x ETFs. In reality this is not the case. Even though leveraged bear ETFs have the upper hand when it comes to trends, they are severely affected by decay, much worse than the bulls. Future articles will cover the advantages and disadvantages of the bull and bear leveraged ETFs.