Martin Noël

July 18, 2017

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A butterfly spread is appropriate when you expect that the price of the underlying asset will remain relatively unchanged and reach a specific target price upon expiration of the options used in the strategy. The following graph illustrates such a situation with shares in BCE Inc., when their price fluctuated within a range of \$57 to \$59 from November 15, 2016 to March 17, 2017.

There are three ways to build a butterfly spread: solely with call options, solely with put options, and combining call and put options (called the mixed butterfly spread). We will now compare these three butterfly spreads using our example, in which the markets closed on November 15, 2016 with BCE trading at \$57.88. Building a butterfly spread generally involves buying an option with strike price X1, selling two options with strike price X2, and buying one option with strike price X3, where X3 > X2 > X1. Furthermore, the spread between X3 and X2 must be equal to the spread between X2 and X1. This procedure is valid for each of the three cases analyzed below. Note that we will use options expiring on February 17, 2017, since the March 17, 2017 expiration was not available on November 15, 2016.

Profit and Loss Diagram of the Butterfly Spread Using Call Options

Profit and Loss Diagram of the Butterfly Spread Using Put Options

November 15, 2016 (February 17, 2017)
BCE = \$57.88 (\$58.76)
Purchase one BCE 170217 C 60.00 at \$0.49 (\$0.00), for a debit of \$49
Sell one BCE 170217 C 58.00 at \$1.21 (\$0.76), for a credit of \$121
Sell one BCE 170217 P 58.00 at \$1.89 (\$0.00), for a credit of \$189
Purchase one BCE 170217 P 56.00 at \$1.07 (\$0.00), for a debit of \$107
Total credit = \$154 (total debit = \$76)

Profit and Loss Diagram of the Mixed Butterfly Spread

Based on the above evidence, we can confirm that the three strategies have almost the same profit and loss diagrams, even though each is built from a different combination of instruments. As we can see, the butterfly spread takes advantage of the relative price stability of BCE, since profits are realized when the price of BCE falls within a range bound by the two breakeven prices and losses are incurred when its price falls outside of this range, either above or below. On expiration on February 17, 2017, BCE closed at \$58.76, so the results of each strategy are as follows.

Results as at February 17, 2017

BCE = \$58.76
Initial debit = \$50, credit on expiration = \$124, net profit = \$74
Initial debit = \$50, credit on expiration = \$124, net profit = \$74
Initial credit = \$154, debit on expiration = \$76, net profit = \$78

As we can see, implementing a butterfly spread for the period from November 15, 2016 to February 17, 2017, a period when the price of BCE stayed within a range bound by \$57 and \$59, generated profits of \$74 or \$78. All three of these strategies offer similar profitability potentials, so we can use them interchangeably. However, it is worth noting that when using options, particular attention needs to be paid to any dividends that may be paid on the underlying asset. The preceding examples do not take this into account.