Why a Four-Leg Option Position May Not Replicate Long Index Exposure

Summary

The document examines an ETF prospectus describing a four-leg European option position intended to provide long exposure to an equity index. The structure combines a long call and short put at a strike below the current index level with a long put and short call at a higher strike. It is compared with the conventional synthetic stock position, which pairs a call and a put at the same strike.

The response questions whether the described structure achieves the stated exposure. If the lower-strike synthetic is bought and the higher-strike synthetic is sold in equal size, the asserted net result is a bond representing 60% of notional rather than index exposure. However, the prospectus excerpt does not specify the relative quantities of the four legs, and the response itself says that something may be wrong with the reported description. Thus, the conclusion is conditional on equal sizing and does not fully resolve the ETF’s actual construction.

Key ideas

• A conventional synthetic stock position pairs a long call with a short put at the same strike.
• The described ETF position combines synthetic exposures at two different strikes.
• Buying the lower-strike synthetic and selling an equal-sized higher-strike synthetic is said to leave a bond exposure.
• The source does not state the relative sizes of the option legs, limiting the conclusion about the ETF’s actual exposure.

Tags

# 4 Leg Synthetic Stock Options Strategy


# 4 Leg Synthetic Stock Options Strategy












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?

## Answer by Ivan (score 1)

https://quant.stackexchange.com/a/41491

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.