How do Leveraged ETFs Work?

At one point I was hazy about the internal workings of leveraged and inverse ETFs, so I constructed models of hypothetical 2X and -1X Apple ETFs to clarify my understanding.  I ignored a whole host of issues (e.g., regulatory, cost-effective leverage), but even a simple model of a leveraged ETF can hurt your brain.  The basic inverse and leverage mechanisms shown below are essentially the same for …

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