# Leveraged ETF calculation - dropping below zero?

I'm running some simulations with a leveraged ETF to investigate that notorious leveraged-ETF decay effect I keep hearing about. When I put in a typical Black-Scholes lognormal model of returns on the underlying, I run into the following issue:

It is theoretically possible for an ETF to lose half its value in a day. E.g. ITOT can go from a price of 100 dollar to a price of 50 dollars in the next day, for a -50 percent daily return. Now suppose I have a 3x leveraged ETF whose underlying is ITOT. In theory, my return should be 3*(-50)=-150 percent. But this would mean that a 100 dollar investment in the leveraged fund turns into a 50 dollar LIABILITY overnight!! I have not only lost all my money, I now owe 50 dollars!

Do any of you know what would actually happen in this scenario? Would the price just drop to zero? Or would it drop to negative 50 dollars? Do the leveraged-ETF prospectuses address this?

• Hi, just saw your question I think the flaw in your calculation is, that you are using arithmetic returns and add them up. If you use geometric returns they should converge to zero.
– T123
Apr 18 at 7:17