# Option Butterfly

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We have learned about both the similarities and differences between a straddle and strangle. Now we will look at a commonly traded strategy, referred to as a butterfly. Going long a butterfly, the trader buys a call of a low strike, sells two calls of a middle strike, and buys a call of a high strike. The three strikes are equidistant. The options have the same expiration and the same underlying product.

For example, if we bought a 2395 call, sold two of the 2420 calls and bought a 2445 call, this would be referred to as the 95, 20, 45 fly. The cost of the butterfly in this example would be 1.75. The 2395 and 2445 strikes are referred to as the wings, while the 2420 is known as the body of the butterfly.

Traders will buy the butterfly if they expect the market to stagnate. In our example, we are expecting the market to be around 2420.

You might be asking, if I expect the market to stagnate – why wouldn’t I just sell the 2420 straddle? As we learned, selling the straddle is a possible way to profit from a stagnating market, but the straddle’s loss potential is unlimited. That could be very costly for a trader.

The wings of the butterfly protect the trader from the unlimited risk of the straddle. Buying a butterfly limits the risk of being wrong to the cost of the butterfly.

If we sold the straddle by selling the 2420 call and put, we receive 105 from the buyer. Therefore, the maximum profit is 105 if the market is at 2420 at expiration.

The cost breakdown of the butterfly is:

• Buy 2395 call at 69.75
• Sell 2420 call twice for 53.25 each
• Buy 2445 call at 38.50
• For a cost of 1.75

In that same scenario, we can calculate the maximum profit from our butterfly.

The 2395 expires 25 points in-the-money. The short 2420 calls expire worthless. The long 2445 call also expires worthless. Less our initial cost of 1.75, we will make a profit of 23.25.

Compare the breakeven points between a straddle and a butterfly. The breakeven points are where the payoff equals the original premium for each strategy. For the straddle, they are the strike plus or minus the premium received. For the butterfly, the breakeven points are the lower strike plus the premium paid and the upper strike minus the premium paid.

In our example, we bought the butterfly for 1.75. The low strike of the fly is 2395. Adding 1.75 to that strike gives us our first breakeven point of 2396.75. Our high strike of the fly is 2445. If we subtract the butterfly’s premium of 1.75 from that  our high breakeven point is 2443.25. Recall that the maximum profit for the butterfly is 23.25 and the maximum profit for the straddle is 105.

Time Decay

The time decay of a butterfly is greatly dependent upon the current level of the market. Near the short strikes, time decay is in your favor. Near the wings, time decay works against you.

Looking at our chart, we can see the butterfly has a lower cost, lower maximum profit potential but a much lower loss potential.

Maximum Loss Infinite Cost of butterfly

1.75

Maximum Profit 105 23.25
Breakeven – Upside 2525 2445
Breakeven –Downside 2313 2443.25

In our example, the straddle’s breakeven range is much greater than the butterfly. Although that range for the underlying market to land is greater than the butterfly’s, if the market does not land there, the potential loss could be detrimental.

Utilizing the butterfly allows traders to profit on their view that the market will be at a certain point at expiration; and the wings limit the loss if they are incorrect.

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Regards,