In Part 1 of this series, we showed how you could limit the risk of a short straddle by turning it into an iron butterfly, i.e. buying a put option with a strike below the shared strike of the short options, and buying a call option with a strike above the short options’ strike. But how do you know which strikes to use?
The most common setup for an iron butterfly is to use the nearest At-The-Money (ATM) strike for the short call and put. The long call and put strikes are typically equidistant from the short strike. For example, if the short strike is $60 and the strike increment is $5, then you might choose $55 and $65 for the long put and call strikes respectively, or for a wider butterfly you might use $50 and $70. Either of these would result in a “balanced” iron butterfly. For now, let’s not worry about the situations where it might make sense to set up an unbalanced position, sometimes called a broken wing butterfly.
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One way to select the long outer strikes is to simply determine the maximum loss you’re willing to occur on each butterfly. For example, if you’re willing to risk $400 per butterfly, then you could look at the strikes $4 above and below the short middle strike. Your maximum possible loss would then be $400 less the premium you received when opening the position.
Another approach is to use the probability of the trade being profitable as a guide to selecting the strikes. Let’s review the risk profile for short straddles and iron butterflies:
The blue lines show the butterfly where the outside strikes are relatively close to the middle strike. This butterfly has the least risk (smallest potential loss), but also the smallest maximum profit. In addition, it has the narrowest range of stock prices that will result in the trade being profitable, which is to say it has the smallest probability of success.
The purple lines show the butterfly which has outside strikes that are further away from the middle strike. Compared to the narrow blue butterfly, the purple butterfly has greater risk, greater maximum profit, and a higher probability of success.
So, how can we determine the probability of a successful trade? In the Straddle and Strangles article, we discussed two ways to determine the probability of a particular option expiring in the money. One is to use a field such as “Probability of ITM” if your broker supplies such a value. The other is to use the option Greek value delta, which closely approximates the probability of the option expiring in the money.
Both the short straddle and the iron butterflies will be profitable if the stock price is between the points where the risk profile line crosses the breakeven line. For the red short straddle, these prices are marked by A and F in the diagram above. For the wide purple butterfly the points are B and E, and for the narrow blue butterfly the points are C and D. If $P is the premium received for entering the trade, then the breakeven points will be $P above and below the middle strike. For example, if the middle strike is $55 and the premium received for entering the iron butterfly is $3, then the breakeven prices will be $52 and $58.
Now we can use the option data from your broker to determine the probability that the stock price will be between the breakeven points at expiration. Let’s say that the probability of the long $52 strike put expiring ITM is 21%, and the probability of the long $58 strike call expiring ITM is 23%. Keep in mind that for the put to be ITM at expiration requires the stock price to be below $52. Likewise, the call will be ITM if the stock price expires above $58.
These two events are mutually exclusive: the stock price cannot expire below $52 and above $58. When two events are mutually exclusive, the probability that one of them will occur is simply the sum of the two individual probabilities. Therefore, in our example, the probability of the stock expiring below $52 or above $58 is 21% + 23% = 44%. However, that condition marks failure, as the trade would not be profitable if the stock expires outside these limits. If the probability of failure is 44%, then the probability of success is 100% – 44% = 56%.
In similar fashion, you could also determine the probability that you will incur the maximum possible loss. Armed with either or both of these probabilities, you can now make a quantified determination of whether the trade seems attractive to you.