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?

  • $\begingroup$ 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. $\endgroup$
    – T123
    Apr 18 at 7:17

1 Answer 1


A 3x leveraged fund that experiences a drop of more than 33% will lose all its money and close down when the value hits 0. Most funds, however, set a lower loss limit, usually around 5%, 10% or 20%, and will try to exit the market if those values are triggered. Of course, it is not that easy to exit efficiently in a day where the market drops that much.

So, usually you will not end up with a liability, but most likely lose your investment or retain a small part of it.

  • $\begingroup$ 33% drop in a day can certainly happen. But the famous Black Monday crash of 1987 was only 23%. So we are talking about rare events. $\endgroup$
    – nbbo2
    Jan 19, 2016 at 15:18
  • $\begingroup$ I'm not saying anything about the probability of such a loss, just that it can happen, and what will happen in the given case. $\endgroup$ Jan 19, 2016 at 17:03
  • 1
    $\begingroup$ I agree with you 100% $\endgroup$
    – nbbo2
    Jan 19, 2016 at 17:07

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