Assuming the underlying can only go to zero, how could one go about calculating the maximum NAV of a double short etf?

could you kindly explain how you came up with this number? According to logic, if an index falls to zero, the inverse fund on said index cannot appreciate anymore in value..

I guess you can get an approximation by looking at the long unleveraged ETF from the same fund family. Look at the ratio between the two in thjis case one point igain in the long means 2 point loss in the short (see if it's consistent over time not sure how exactly they get their leverage). Calculate how many points the short will go up if the long ETF goes to 0 (which will never happen) .

it's related to procentual change. If the index goes down 10% the inverse ETF should go up 10%. If it goes from from 1 to 0.8, the inverse ETF goes up another 20%, if it goes from 0.8 tot 0.64 it goes up another 20%. 0 is the limit move, just like infinity of the reverse ETF. Of course in reality it will never reach infinity, just like an ETF in reality will never reach 0. Bankrupt firms would be replaced in the index of the ETF.

according to logic, if an inverse fund reaches infinity it cannot appreciate more in value ... You might think I am fooling around here, but I am not, it's just (theoretical) math and logic.

no. actually i don't think you are fooling around. its makes perfect sense. i had not approached my previous reasoning with percentage terms.

And I wouldn't have passed the interview obviously. Oh well good thing you don't have to be any good at math to have a clue of what the market is gonna do next.