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### Get an email when henry copeland finds good

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Let's say you make a $100 investment in each of three funds. One is a simple investment in an index. Then you have two leveraged funds that compound daily; one is double-long and the other is double-short (returning twice the inverse of the index). After one day, the index returns 10%. The index value would then be $110. The double-long would add 20% and end at $120, and the double-inverse would lose 20% and end at $80.
On day two, let's say the index loses 10%. That means that the average return [(10% -10%)/2] would be zero. However, the index itself would end at $99 because 10% of $110 is $11, and $110 minus $11 is $99. The fund that promises double the return of the index but compounds daily would end at $96. Remember, this fund started the day at $120. Its return for day two is -20% (double the index's loss), and leaves it with a $24 loss for the day. So, $120 minus $24 is $96. The double-short fund would also end at $96 because 20% of $80 is $16, and $80 plus $16 is $96.
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. 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. Talk about tracking error.
That's why compounding of daily returns is the dead horse that apparently needs a little more beating. Leveraged and inverse ETFs are NOT meant to be held as long-term investments. Let me repeat myself: Very bad things not only can happen whenever you hold these ETFs longer than their indicated compounding period (typically one day for stock-based ETFs, sometimes monthly for commodities), you are almost mathematically guaranteed to get a return that is not double that of the index. In fact, the longer you hold one of these funds, the probability that you will get nothing close to double the returns increases.

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