Trading leveraged funds
Since the fund's value is related to its NAV, when it returns to the same NAV, then your initial investment will be completely restored.
This is correct.
To put it another way, and ignoring any minor adjustments, if the index is at 1000 and goes to any value, then when it returns to 1000, so will the NAV
This is false. When the index returns to its original value, the NAV of the fund will not necessarily do so. In fact, given these funds charter, it is essentially guaranteed that it won't.
If your math was correct, then all the index would have to do would be to oscillate between 1000 and 1010 for n-trading days and your funds would eventually go to 0. That simply is not the case.
It is the case and my math is correct - I challenge you to find any mistake (other than rounding error) in the computation. If the index returns to its original value after oscillating around it, you will lose money held in one of the leveraged funds (no matter which one). You won't lose money if the index doesn't move at all (as opposed to moving but eventually returning to its starting value) - but that never happens.
Regards,
Vesselin
News 
Market Data 
Discover 
