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Why Combining a Long Butterfly and Straddle Does Not Guarantee Profit

Article Quant Q&A · Author: user51413
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Summary

The document examines whether combining a long butterfly, which benefits from a price near its center at expiration, with a long straddle, which benefits from a large move, can produce a profit across all terminal prices. The accepted answer explains the payoff relationship: a long butterfly can be decomposed into a short straddle and a long strangle, so adding a matching long straddle leaves a long strangle exposure.

A strangle has no intrinsic payoff when the terminal price lies between its strikes and positive payoff outside them. Option premiums shift the break-even points, leaving a loss region between the adjusted thresholds; therefore, the combination does not guarantee profit. Another answer proposes a cross-market timing tactic, but gives no supporting evidence or risk analysis. The central payoff explanation concerns expiration values and does not establish profitability after transaction costs or under changing volatility.

Key ideas

  • A long butterfly can be represented as a short straddle combined with a long strangle.
  • Adding a matching long straddle to a long butterfly produces long strangle exposure.
  • The resulting position has a region of terminal prices where its payoff does not cover the premiums.
  • Combining the positions does not create a guaranteed-profit strategy.

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Full text
# Would it be possible to combine long butterfly with long straddle, achieving profit no matter the outcome?


# Would it be possible to combine long butterfly with long straddle, achieving profit no matter the outcome?












This has been bugging me for a while, I feel like I'm missing something.

Simply put, a long butterfly will make profit if the price at maturity does not change much, as shown below

A long straddle is the opposite of the above, making profit if the price goes considerably up or down, as shown below

Combining those two might seem like overlaying both graphs, achieving profit no matter what the price. What am I missing?

## Answer by Chris Taylor (score 11, accepted)

https://quant.stackexchange.com/a/60013

Your butterfly is short a straddle and long a strangle. If you add a long straddle with the same strike/notional you are now just long a strangle.

The payoff for a strangle is zero if the terminal price is between the two strikes and positive otherwise. Once you take the premium into account you will see that you make a loss if the terminal price is between (low strike minus premium) and (high strike plus premium) and otherwise you will make a profit. In particular there is no guaranteed profit.

## Answer by Artun (score 0)

https://quant.stackexchange.com/a/74211

It’s a professional strategy and needs to be bought at correct timing and at correct prices. The great way to do it is to go for a straddle at SPY and a butterfly at SPX. Make sure to center your butterfly exactly at the same spot of the straddle in 2 tickers. If market makers pin the price around your straddle, sell your butterfly 2-3 minutes before the closing bell and sell your straddle within the 15 mins after the closing bell.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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