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I was reading on the pros and cons of shorting an ETF vs buying an inverse ETF on yahoo

I do not understnad this explanation why over hte logner term, shorting is not equivalent to buying an inverse ETF, but over shorter term they are equivalent. Can someone explain the below in lay terms:

From the link:

Inverse ETFs are generally only intended to provide the inverse return on a daily basis. If the Dow Jones Industrial Average ETF (DIA, A-) moves down 5% over a week or a month, the Short Dow 30 ETF (DOG, A) won’t likely be up 5%. Due to compounding returns and losses on an increasing or decreasing ETF price, over the longer-term you can expect some disconnect between gains/losses on a tradition ETF and the losses/gains on the corresponding inverse ETF.

I got confused on this line:Due to compounding returns and losses ....

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Suppose that the ETF is currently at a price of $100. Suppose that the next day it moves up 10% (to a price of $110) and the following day it moves down 5% (to a price of $104.5). Over these two days the ETF has had a net gain of 4.5% from its original price.

The inverse ETF reverses the daily gains/losses of the base ETF. Suppose for simplicity that the inverse ETF also starts out at a price of $100. So on the first day it goes down 10% (to $90) and on the second day it goes up 5% (to $94.5). Thus over the two days the inverse ETF has had a net loss of 5.5%.

The specific dollar amounts do not matter here. The result is that the ETF winds up at 110%*95% = 104.5% of its original price and the inverse ETF is at 90%*105% = 94.5% of its original price. A similar example is given here.

As suggested by your quote, this is due to compounding. A gain of X% followed by a loss of Y% (compounded on the gain) is not in general the same as a loss of X% followed by a gain of Y% (compounded on the loss). Or, more simply put, if something loses 10% of its value and then gains 10% of its new value, it will not return to its original value, because the 10% it gained was 10% of its decreased value, so it's not enough to bring it all the way back up. Likewise if it gains 10% and then loses 10%, it will go slightly below its original value (since it lost 10% of its newly increased value).

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The most fundamental answer is that when you short a stock (or an ETF), you short a specific number of shares on a specific day, and you probably don't adjust this much as the price wobbles goes up and down.

But an inverse fund is not tied to a specific start date, like your own transaction is. It adjusts on an ongoing basis to maintain its full specified leverage at all times. If the underlying index goes up, it has to effectively "buy in" because its collateral is no longer sufficient to support its open position. On the other hand, if the underlying index goes down, that frees up collateral which is used to effectively short-sell more of the underlying. So by design it will buy high and sell low, and so any volatility will pump money out of the fund.

I say "effectively" because inverse funds use derivatives and contracts, rather than actually shorting the underlying security.

Which brings up the less fundamental issue. These derivatives and contracts are relatively opaque; the counter-parties are in it for their own benefit, not yours; and the people who run the fund get their expenses regardless of how you do, and they are hard for you to monitor. This is a hazardous combination.

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