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Some ETFS like NUGT,DUST say that they replicate the performance of the underlying index on a daily basis.

My first question is, do all ETFS do this, or only some? Also, why does it say that "not designed to track the underlying index over periods longer than one trading day".

I mean,the ETF is just buying a basket of underlying stocks that represent the corresponding index. If at the start of day1, the ETF purchased the basket of stocks, then it just needs to hold on to the udnerlying stocks to make sure that they are in sync with the index. How can they be in sync on a day to day basis but not on a long term basis?

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    They replicate a multiple of the index and not the index. Do you understand the leverage used here? – JB King Feb 6 '15 at 19:26
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    This answer addresses this too. Does this help you? – JoeTaxpayer Feb 6 '15 at 19:29
  • See also this question. – BrenBarn Feb 6 '15 at 20:27
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From the link in the question:

These leveraged ETFs seek a return that is +300% or -300% of the return of their benchmark index for a single day. The funds should not be expected to provide three times or negative three times the return of the benchmark’s cumulative return for periods greater than a day.

(Emphasis added be me)

A leverage ETF will produce a return that is a multiple of the index which in the case of 2 or 3 times the return is worth doing some simple examples:

Consider the case of an index that goes up 10% and down 10% on back to back days. At the end, the index is down 1% as if the index was at 100 at the start, it went up to 110 and then came down to 99.

Now, let's add the leverage and see what happens. A 3x tracks would go up 30% and come down 30% which in the end is down 9% which is much more than 3 times the 1% on the index after 2 days. Again, if we start with 100, then go up to 130, coming down we take off 39 points and are left at 91. Thus, we got 3 x 3 which is way more than what we wanted here.

This is just taking a couple of days. If we keep adding more time then the differences will be magnified which is why the statement is made about the deviations existing. While my example is a bit contrived in taking an up and down, one could also take an up and up to consider how that deviates as well. The index would be at 121 after 2 days while the leveraged ETF would be at 169 which is up 69% which compared to 21% for the index is a bit more than 3 times and thus this deviates as well as compounding happens here.

If you want another example, consider an index that goes down 20% each day for 5 days straight and starts at 100: 100, 80, 64, 51.2, and 40.96 for the end. Thus, it ends down 59% in the end rounded off.

Now, let's take 3 times that return and take off 60% each day for 5 days straight and start at 100: 100, 40, 16, 6.4, 2.56. In this case, we ended up down 97% which isn't 3 times the return which would be over 100%.

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    Thanks. So leveraged etf tracks the index on a daily basis but an unleveraged etf tracks the index on a long term basis(as well as daily basis). Ah, the magic of geometric progression – Victor123 Feb 6 '15 at 19:45
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    Right. The math of the leveraging makes a long term leverage impossible. – JoeTaxpayer Feb 6 '15 at 20:17

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