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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 long-butterfly - source Wikipedia

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

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

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    $\begingroup$ You can always guarantee some positive payoff no matter what. But in almost all cases, you should not be able to make a guaranteed profit. $\endgroup$ – Kermittfrog Dec 16 '20 at 16:23
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    $\begingroup$ Don’t forget about the premium you pay at inception. $\endgroup$ – Daneel Olivaw Dec 17 '20 at 1:09
  • $\begingroup$ Chris Taylor provided the correct answer. You can also figure out the answer to this type of question by combining the positions in a program that accepts multiple positions or you can utilize the Synthetic Triangle to solve it algebraically. $\endgroup$ – Bob Baerker Dec 17 '20 at 1:20
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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.

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