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# Dissecting Synthetics: Don't Be Baffled by Iron Butterfly Spreads

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February 23, 2016

What do a call option butterfly, a put option butterfly, and an iron butterfly have in common? Well, surprisingly, they all share a similar risk profile. That’s right, these three trades are similar, thanks to something called synthetics.

The term synthetic is a fancy way of saying that we’re recreating a risk profile of a strategy by using a combination of other options strategies. Understanding the differences in the risk and reward relationships between the strategies can help when trading these flighty creatures in the real world.

Let’s break it down with an example.

## Pinning the Butterfly Down

Call and put butterflies use three strikes that are the same distance apart. We’ll use 45, 50, and 55 strikes as an example to show how each trade is created.

Some experienced options traders might buy the 45 and 55 calls and sell the 50 calls twice, which creates a long call butterfly. Another approach is to use puts to form a long put butterfly.

Looking at things another way, these trades are also just combinations of two vertical spreads. They use a long vertical spread and a short vertical spread, with the short option of each vertical sitting at the middle strike.

Now for the synthetic part. A long call vertical spread is mathematically the same thing as the short put spread using the same strike prices. So for this example, buying the 45/50 call spread for \$3 (long call spread) is the same as selling the 50/45 put spread for \$2 (short put spread). Take a look at this table:

 Stock = \$50 Call Put 45 \$6 \$1 50 \$3 \$3 55 \$1 \$6

Both spreads are bullish trades that aim to make their maximum profit with the stock at \$50 or higher come expiration day. Both risk \$3 for the chance to make \$2. And both even have the same greeks profiles.

To come at the butterfly from the other direction, the short 50/55 call spread for \$2 is the mirror image of the long 55/50 put spread for \$3. Here, both trades are bearish and are designed to make their maximum profit with the stock at \$50 or lower. Both also risk \$3 to make a possible \$2. And, yes, both verticals share the same greeks profile.

If you put it all together, the call butterfly costs \$1, with a chance to make a \$4 profit, which would happen if the stock sits at \$50 on expiration. And guess what? That’s true for the put butterfly, too. All you need to do is swap out “put” for “call,” and you end up with a put butterfly that’s a similar trade.