Spotlight on the Butterfly Spread

Similar to the Iron Condor, that we talked about in our last option strategy write up, the Butterfly spread consists of two consecutive spread positions.  However, instead of combining a Call and Put spread, the Butterfly consists of two Call spreads or two Put spreads.  Regardless of whether one executes a Long or Short or Call or Put Butterfly, these strategies, like the Iron Condor, are considered “risk defined”, as max gain and loss is known at the time of execution.  

There are a couple of interesting characteristics of the Butterfly strategy:

The options P&L profile graph for a Long Call and Put Butterfly look the same and the P&L profile for a short Call and Put Butterfly look the same.  

Even though a Long Butterfly spread would involve a debit (a trader would be a net buyer of options), the position actually realizes its max profit, at expiration, when the futures price does not deviate significantly from the “middle” strike. 

Specifically, A long butterfly position involves Buying 1 Call/Put at one strike, selling 2 Calls/Puts at a higher strike and buying 1 Call/Put at an even higher strike.  Oftentimes, traders will refer to the single Calls/Puts as the wings and the 2 Calls/Puts as the body.  

For our example, we chose to use CME’s E-mini Nasdaq-100 options from late afternoon trading on 8/26/2024.  At the time we constructed our hypothetical Butterfly position, September E-mini Nasdaq-100 futures were trading at around 19,553 and we used the September options that had 25 days until expiration.  

Therefore, we chose the following strikes and premium levels for the trade example.  We chose to use Calls but, as we stated earlier, could have created a similar position using Puts.  In fact, one of the first lessons some traders learn is that Calls and Puts are the same; they simply have a different sign in front.  

Buy 1 19,400 Call for 485.25

Sell 2 19,600 Calls for 741.5

Buy 1 19,800 Calls for 273.75

As you can see, this position would result in a net debit of 17.5 points.  Because E-mini Nasdaq-100 options have a $20 multiplier, in dollar terms, this debit would amount to $350.00.  The maximum profit this position could realize, at expiration, occurs when the underlying price is equal to the strike of the short Calls.  When this occurs, the trader keeps the premium collected from the sale (741.5 points) because those Calls expire worthless, relinquishes the premium paid for the out of the money Call (273.75) and collects the 200 points from the in-the-money Call (19,600-19,400).  But remember, they paid 485.25 for the in-the-money Call, so the resultant P&L would be as follows:

741.5 minus 273.75 plus 200 minus 485.25 = 182.5 points ($3,650) 

So, essentially, the trader, in this hypothetical example, would risk $350.00 for a maximum profit potential of $3,650.  

As we stated earlier, another way to look at this spread is as follows:

Buy 1 19,400/19,600 Call Spread for 114.5 points ($2,290)

Sell 1 19,600/19,800 Call Spread for 97 points ($1,940)

As we know, the max profit on a Long Call spread occurs when the price of the underlying, at expiration, is equal to or above, the strike of the short Call.  In this case, 19,600.  

The max profit on a Short Call spread occurs when the price of the underlying, at expiration, is equal to or below, the strike of the short Call.  Again, 19,600 in this case. 

Therefore, it logically follows that the max profit for the combined spread position would be when the futures price expires at that 19,600 level.  

Long Call Spread Profit @ 19,600 = 200 points (difference between strikes) minus the premium (114.5) = 85.5

Short Call Spread Profit @ 19,600 = premium collected (97 points), as both Calls would expire worthless. 

Sure enough, the max profit = 182.5 points, as shown earlier.  

The top image below depicts the overall P&L of this hypothetical position at expiration and the lower image shows the two Call spreads that comprise the Butterfly strategy. 

Of course, options are multi-dimensional and several factors can impact the value of a position between the time the trade is executed and expiration.  We explain two such situations below:

Volatility 

Using an options calculator that is available on CME Group’s website that uses the “Black 76” options model, we changed the implied volatility of each option and kept all else constant:

Implied Volatility = +4% in each option

Results in the following new theoretical value:

19,400 Call:  ~565.75

19,600 Call:  ~457.25 (*2=914.5)

19,800 Call:  ~353.50

Therefore, the new overall theoretical value of the position would be 565.75-914.5+353.5=4.75.

Because the position had an overall negative Vega value, an upside shock to volatility results in a decline in the theoretical value of the position from 17.5 ($350.00) to 4.75 ($95.00)

Time to expiration

However, if we were to leave all else constant and reduce the number of days until expiration to 10 from 25, we get the following theoretical values:

19,400 Call:  ~339.5

19,600 Call:  ~229.5 (*2=459)

19,800 Call:  ~139.75

And the new overall theoretical value of the position is 339.5-459+139.75=20.25.  

The decrease in the number of days until expiration results in a positive impact to the overall value of the position.  

Conclusion

As you have seen, the Butterfly strategy can be an effective way for a trader to express a view that the price of a given futures contract will move more, or less, than the options market is currently pricing.