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I've thought about investing in UPRO, the ProShares UltraPro S&P500 3x leveraged ETF. But, of course, I don't want to invest in it until I have a good understanding of it, including its historical returns, the math behind its leverage, and the assets that it holds.

If I look at the list of daily holdings, I find that by far, the fund's largest holdings by "exposure value" are

  • S&P 500 INDEX SWAP CREDIT SUISSE INTERNATIONAL,
  • S&P 500 INDEX SWAP SOCIETE GENERALE,
  • S&P 500 INDEX SWAP UBS AG,

and so on and so forth. Of course, these swaps don't have a ticker symbol or anything, and if I do a Google search for "S&P 500 index swap", all that comes up is lists of ProShares holdings.

The prospectus for UPRO does contain a little more information:

Swap Agreements — Contracts entered into primarily with major global financial institutions for a specified period ranging from a day to more than one year. In a standard “swap” transaction, two parties agree to exchange the return (or differentials in rates of return) earned or realized on particular predetermined investments or instruments. The gross return to be exchanged or “swapped” between the parties is calculated with respect to a “notional amount,” e.g., the return on or change in value of a particular dollar amount invested in a “basket” of securities or an ETF representing a particular index.

So this makes it sound like an S&P 500 index swap is similar to a stock future. Perhaps UPRO has agreed with these financial institutions that at some future point in time, UPRO will pay the institution $300,000,000 and the institution will pay UPRO $100,000 times value of the S&P 500 index. Something like that.

Is there any way to find out what the details of these index swaps actually are?

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In short, there is no way to find out exactly the language of these contracts, but they're total return swaps. Although, in this particular case they may be a little non-standard given the 3x leverage.

Possible high-level structure of the total return swap:

  • UPRO agrees to swap some multiple (typically 1x but in this case it could be 3x) of S&P 500 return with the bank, on some notional amount.
  • UPRO pays some implied financing rate on the notional amount.
  • UPRO posts some initial margin amount to the bank, and the parties exchange daily variation margin plus maybe some adjustment to the initial margin amount.
  • There might be language in the contract for when the deal can be broken under extreme market conditions etc. Due to the leverage being employed here this language may(should) be different than a typical 1x total return swap.

To hedge their risk the bank could then buy futures (and trade dividend swaps because futures don't include divs) or they could find someone that wants to be short the market and write swaps in the other direction, or other things. The financing rates they include on their swaps will be such that they take something out of the middle and make money by essentially acting as a broker.

From this point I'd focus more on the other areas you mentioned: there's been a lot written over the years online generally, and here specifically, about leveraged ETFs, how they rebalance, the math involved etc.

Checkout @BobBaerker's answer to a related question here: Do the rebalancing costs of leveraged ETFs really outweigh the leverage?

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Perhaps UPRO has agreed with these financial institutions that at some future point in time, UPRO will pay the institution $300,000,000 and the institution will pay UPRO $100,000 times value of the S&P 500 index.

It's similar, but the cash flows will be more periodic, even daily. In a swap, one side pays a fixed amount while the other side pays a variable ("floating") amount. In these cases, the other side is paying amounts based on the returns (not level) of the S&P 500.

Since this is a 3X levered fund, it's likely that these swaps pay some amount scaled by 3 times the periodic return of the S&P 500. But it works both ways - so if the index earns less than the rate set in the swap, then the fund will have to pay the other side more money than it gets.

Is there any way to find out what the details of these index swaps actually are?

Probably not - these are over the counter contracts, so if they do not disclose that in their filings, there's no way to know the specific details.

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