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The Compounding Error of ETFs and Leveraged ETFs

When you buy a leveraged ETF, you would expect to get that profit if the index moves the right direction. Because of the compounding error of ETFs, you might not get the return you expected.

Inverse and Leveraged ETFs can be a great trading tool for profits. But ETFs and especially leveraged ETFs can return less of a profit than you expected or a loss you weren’t expecting.

The Basics of Leveraged and Inverse ETFs

An inverse ETF is an ETF that goes up when the underlying index goes down, it is like shorting the market or index without actually having to have a margin account to short.

There are the 1:1 ratio ETFs and inverse ETFs and there are the leveraged ETFs and leveraged inverse ETFs. These leveraged ETFs can be 2x (200%) or 3x (300%). This means that they are leveraged at 2:1 or 3: 1 ratios. They usually have 2x, 3x, double long, double short and ultra in their names.

When you read the disclaimer of a leveraged inverse ETF, it is clear and simple, yet not always fully understood. These leveraged inverse ETFs will state they seek daily results which corresponds to 2 or 3 times (200% or 300%) the inverse (opposite) of the daily performance of the underlying index. A long ETF will state the same without the word opposite or inverse.

The Compounding Error of ETFs and Leveraged ETFs

The key word in the disclaimer is the word daily and this is important. Not weekly, monthly or yearly, but daily. The reason this is so important is what is called the volatility drag or compounding error of ETFs.

If you owned an inverse ETF for a week and the stock market or underlying index went down every day, you would profit nicely. But the market usually has down days and up days and this is where the risks of the compounding error confuse the expected returns of ETFs and especially the leveraged ETFs.

Compounding is wonderful on the upside, but when you are losing money, compounding can be a problem.

Since the stock market and underlying indexes go up and down, you cannot be sure your inverse ETF will continue to compound in your favor. When the underlying index of an inverse ETF goes the opposite direction for more than one day, the compounding or volatility drag is what can give you a loss when you expected a gain or at least to break even.

Let’s look at an example of buying a 1:1 inverse ETF and a 2:1 inverse leveraged ETF. These two positions will gain when the underlying index goes down. You are in a way shorting the underlying index.

You invest $1,000 in a 1:1 inverse ETF and $1,000 in a 2x (-200%) inverse leveraged ETF for a total of $2,000.

Day 1: The underlying index goes down 5%. The 1:1 inverse ETF gains 5% and this gives you $1,050. The 2x inverse leveraged ETF gained 10% giving you $1,100 for this position.

Day 2: The underlying index goes up 5%. The 1:1 inverse ETF looses 5% and that trade is now at $997.50 since $1,050 – 5% = $997.50. The 2x inverse ETF looses 10% and this position looses you $110 since $1,100 – 10% is $110. Your position in the 2x inverse leveraged ETF is now at $990

After just two trading days with the underlying index breaking even, you would have actually lost money due to volatility drag or the compounding error of ETFs. You started with $2,000 and would have ended up with $1,987.50 and a loss of $12.50. Not a huge loss, but a loss when you might have believed you would break even. Take this trade out for weeks or months, and the volatility drag or compounding error could really add up.

This also affects long, 2x (double long) and 3x leveraged long ETFs the same way. The more leverage, the worse the compounding error can be.

The longer you hold the inverse ETF, the worse this compounding error can affect your returns as the market goes up and down. Obviously, the only way this would not affect you, would be if the market went your way every day you held the ETF or leveraged ETF. Not many of us get lucky like that in the market for long time frames.

We can see the compounding error in a real example that compares the S&P 500 over a three-month period to the ProShares UltraShort 2x S&P 500 inverse ETF. The S&P 500 lost 14% and the inverse ETF gained 12%, not the 2 times or 28% gain someone might have expected. 

Conclusion of ETF and Leveraged ETF Compounding Error

Leveraged ETFs and inverse ETFs can be a great trading tool for a one day trade. What you need to understand is when you buy an ETF and especially a leveraged ETF; the expected returns are not what you might have expected if you hold them longer than a day because of the volatility drag or compounding error.

Copyright © August 2011 Sam Montana


Charles Schwab

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Comments (6)

Informative and well written article.thanks...voted up

These are great eye-opener for those who wants to deal with Stocks and Trade.

I should have had this information a while ago. Thank you for sharing your wisdom so well.Promoted.

informative share :).. vote up

Returning with a well deserved vote up.

If you're not a financial advisor... you've done a marvellous write up... if you are, you've explained the process brilliantly!