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It says that leveraged ETF are constructed using options/swaps, but I didn't see any example of how you can replicated a leveraged index using options and swaps.

For example taking the S&P500 index how one will create a 3x leveraged ETF on the S&P500 using options and swaps?

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    $\begingroup$ Welcome. They are generally constructed with Futures or TRS (Total Return Swaps) on an Index. Have you looked at how these work? (The futures could be replicated by buying calls and selling puts, but that seems an awkward way to do it. Generally options are not used for this kind of thing). $\endgroup$
    – nbbo2
    Commented Apr 12 at 7:13

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In the paper by Cheng and Madhavan (2010) you will find an explicit example how to construct leveraged ETFs using TRS and what are the issues with it:

https://jplinvest.dk/wp-content/uploads/2020/12/The-Dynamics-of-Leveraged-and-Inverse-Exchange-Traded-Funds.pdf

Hope it helps

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