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Traditionally, a synthetic stock option involves buying a call and writing a put at the same strike price. I recently encountered an ETF prospectus that claims to achieve this exposure with a four leg trade which I do not understand.

Background: The prospectus for the PJUL ETF (pages 13-14) indicates that the ETF invests its funds in three separate "layers" of options trades. My interest is in the first layer. The prospectus says this first layer is a 4 leg trade that they claim achieves, when considered in isolation, 100% long exposure to the S&P 500. They indicate that the the layer/trade involves (a) buying a European style call and (b) writing a European style put both with a strike at 60% of the current S&P 500 price; while also (c) buying a put and (d) writing a call both at 120% the current S&P 500 price. As pointed out in a comment below, they do not appear to state the relative sizes of these legs (a) - (d), so they might not hold the same number of options for each leg.

Why would they do this trade instead of the traditional 2 leg synthetic stock strategy?

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    $\begingroup$ Well, clearly it works. But why use two synthetic stock positions (one above the market, one below) when one of them alone would be sufficient is a very interesting question... $\endgroup$ – Alex C Aug 26 '18 at 21:29
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    $\begingroup$ If the (a) and (b) legs have the same strike price then that is a traditional long synthetic stock. If the (c) and (d) legs have the same strike price as one another, then that is a traditional short synthetic stock. That seems strange since it would seem to imply that they are simultaneously holding positions which are morally inverses of each other. However, the prospectus does not say whether it is actually the case that (eg.) the (a) and (b) legs have at the same strike, just that both their strikes are below market. $\endgroup$ – John Aug 26 '18 at 22:08
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    $\begingroup$ This sheet innovatoretfs.com/pdf/PJUL_Factsheet.pdf seems to confirm that there is a long call and a short put with 60% strike, and a long put and short call with strike level of 120%. It does not give the amounts, though. $\endgroup$ – Alex C Aug 26 '18 at 23:24
  • $\begingroup$ Good catch. I've updated the question to mention that. $\endgroup$ – John Aug 27 '18 at 3:29
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I don't see how this 4-leg trade can provide exposure to the Index. The net result of buying the 60% synthetic and selling the 120% synthetic (in the same amount) is to end up with a bond for 60% of the notional. Clearly that does not provide exposure to the Index. Something isn't quite right with the ETF or its prospectus.

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    $\begingroup$ The prospectus does not explain the amounts, but it is pretty easy to construct the exposure to the index by buying 2 units of (a) & (b) for every 1 unit of (c) & (d). That gives you a synthetic stock without any worries about the discounted strike price. I still don't understand why you'd do it that way - it seems needlessly complicated. Perhaps the ETF provider has a good relationship with their broker and like to throw business their way! $\endgroup$ – Tim Wilding Aug 29 '18 at 6:25

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