Broken Butterflies

So far we've examined symmetrical butterflies exclusively. These were all made up of two vertical spreads that had the same distance between the strike prices. The fact that the vertical spreads making up our butterfly are the same width — that is, they have the same distance between the strike prices — means that the spread that is closer to at-the-money is going to be more expensive than the one that is further from at-the-money. This is what generates the potential profit for a butterfly seller, but it also means the butterfly buyer has to pay the net cost and the butterfly buyer ends up with a trade structure that has a fairly narrow profit window and a miniscule window to realize the maximum profit. Since a butterfly is a spread of two vertical spreads, couldn't we change the width of the spread that is further out of the money, thereby collecting more for selling it as part of a long butterfly, and reducing or eliminating the cost of the entire trade? We'd end up with a trade that wasn't symmetrical, which is why it's often called a broken butterfly.

While the buyer of a regular, symmetrical butterfly loses all of the premium paid if the underlying stock isn't between the strike prices of the wings, the buyer of a broken butterfly can often put the trade on without paying any net premium. But we know there's no free lunch, so what's the downside of a broken butterfly if it doesn't cost us any premium? The potential loss is greater if the underlying makes a big move, a move that extends beyond the most distant strike price. In Figure 11.15, we look at some call option prices in XOP, the crude oil and natural gas exploration and development exchange-traded fund and examine a broken butterfly we might execute.

Call Options and Buying a Broken Call Butterfly in XOP

FIGURE 11.15 Call Options and Buying a Broken Call Butterfly in XOP

This is a butterfly because we're buying a nearby vertical call spread — the 80/82 in this case — and selling a further out-of-the-money vertical call spread — the 82/85 call spread in this case — that shares a strike with our first call spread. It is a broken butterfly rather than a traditional butterfly because this butterfly is made up of spreads that aren't the same width; the spread we're buying is $2 wide, while the spread we're selling is $3 wide.

Observant readers will note that we're buying this broken butterfly because we're buying the outer strikes, the wings, but we're also collecting a little net premium. If we're buying the wings we're buying the butterfly and while we might collect some premium in doing so, we're paying elsewhere, probably in the fact that we've changed the risk, the maximum potential loss, as we'll see. This is one of the very few instances when we might say we're buying a spread while collecting premium.

What will be the profit or loss for this broken butterfly at expiration? Previously, we've built a complete profit and loss table and generated the results for a bunch of strike prices or we've created a payoff chart. Those can both be helpful, and we'll create a traditional payoff chart later, but instead of creating a profit and loss table with every single strike, let's create a smarter profit and loss table with only the inflection points. We see this in Table 11.4.

As long as XOP is below 80.00 at expiration, we'll get to keep the 0.08 we initially collected, all the options will expire worthless, and we can reevaluate. With XOP at 82.00 at option expiration, the 80/82 call spread will have achieved its maximum value of 2.00, the 82/85 call spread will be worthless, and we will also have our original 0.08. At the body of the broken butterfly, our

TABLE 11.4 Profit and Loss for Our Broken Call Butterfly at the Inflection Points

Inflection Point

80/82 Vertical Call Spread Profit/Loss

82/85 Vertical Call Spread Profit/Loss

80/82/85 Broken Butterfly Profit/Loss

80. 00

-0.68

0.76

0.08

82.00

1.32

0.76

2.08

85.00

1.32

-2.24

-0.92

profit will be 2.08, which is the net we originally collected plus the width of the first spread.

Once XOP has passed beyond the most distant strike, the 85 strike in this case, we will sustain our maximum potential loss: we'll lose more from shorting the 82/85 call spread than we'll make from buying the 80/82 call spread, and the 0.08 we originally collected won't make up the difference. Our loss will be the difference in the widths of the spreads — 1.00 in this case (3.00 width minus 2.00 width) — less/ plus the initial net premium collected/paid.

Let's extend the prices we look at to make certain this 0.92 loss is our maximum loss and see where we sustain that loss. You can see this in Figure 11.16.

The maximum loss for our broken butterfly is 0.92, and that occurs with XOP at or above 85.00 at option expiration. This greater potential loss is the price we pay for the fact that we actually collected 0.08 when we initiated this trade rather than paying as we would with a traditional, symmetrical butterfly.

In order to truly evaluate this broken butterfly, we have to compare it to the generic butterfly we might have executed. If we'd bought the 80/82/84 call butterfly,

Broken Call Butterfly in XOP

FIGURE 11.16 Broken Call Butterfly in XOP

we would have bought the 80/82 call spread for 0.68 (so far the two trades are identical) and would have sold the 82/84 call spread for 0.56 (this is where the two trades differ), meaning we pay a net of 0.12 for this traditional butterfly versus collecting 0.08 for buying the broken butterfly. The difference between the two trades is 0.20, and that makes sense, as this was the difference in price between the 84 strike call which was trading at 0.76 and the 85 strike call which was trading at 0.56.

Since we would have paid 0.12 for the traditional butterfly, that would have been our maximum loss, and we would have lost that full amount with XOP above 84.00 or below 80.00 at option expiration.

Instead, with the broken butterfly we collect 0.08, but our maximum loss is 0.92 and we sustain that with XOP above 85.00 at option expiration. This leads to the question, is the extra 0.20 we save worth the added risk?

Let's use the tools at OptionMath.com to determine the likelihood that we'll lose that entire 0.92. If we do that math, we find that the delta for this 85 strike call is 19, meaning there's a 19 percent chance we lose the full 0.92. It's no accident that 19 percent of 0.92 is 0.175, or almost exactly the 0.20 we're saving (the difference between 0.20 and 0.175 is generated by the bid/ask spreads of all the options; for our purposes the numbers are essentially equal). So are you better off buying the broken butterfly or the traditional butterfly? The math says you're equally well off, but your insight into what XOP is going to do, your ability to initiate the trade effectively (it's made up of 3 legs and 4 options so execution is going to be key), and your ability to manage the trade prior to expiration will make the difference.

You could apply the same principle and generate a broken put butterfly that could be initiated for no net premium or that would generate a small net credit. By buying a put spread and then selling another put spread that is both wider and more out-of-the-money, you'll spend less money up front, and maybe generate that small credit, but face more risk if the underlying drops below the lowest strike price.

As such, broken butterflies, whether using calls or puts, are trades that expect a moderate movement in a specific direction — up for a broken call butterfly, down for a broken put butterfly — but think a large move that would take the underlying past the furthest strike by expiration is unlikely.

Call Butterfly Cheat Sheet

Long Call Butterfly

Short Call Butterfly

Description

Long one OTM call

Short two further OTM calls

Long one even further OTM call

Short one OTM call

Long two further OTM calls

Short one even further OTM call

Example

ATM = 100

Long one 105 call

Short two 110 calls

Long one 115 call

ATM = 100

Short one 105 call

Long two 110 calls

Short one 115 call

Pay or Collect Premium

Pay

Collect

Needed Directionality

Passage of Time without Market Movement

– –

+ +

Increase in Implied Volatility without Market Movement

+

Payoff Thumbnail Chart

Maximum Risk

Cost of the butterfly

Difference between wing strike and body strike minus net premium received

Maximum Profit

Difference between wing strike and body strike minus net premium paid

Premium received

Breakeven Points

Lowest strike + Net premium paid

Highest strike – Net premium paid

Lowest strike + Net premium paid

Highest strike – Net premium paid

Put Butterfly Cheat Sheet

Long Put Butterfly

Short Put Butterfly

Description

Long one put

Short two further OTM puts Long one even further OTM put

Short one put

Long two further OTM puts Short one even further OTM put

Example

ATM = 100 Long one 95 put Short two 90 puts Long one 85 put

ATM = 100 Short one 95 put Long two 90 puts Short one 85 put

Pay or Collect Premium

Pay

Collect

Needed Directionality

Passage of Time without Market Movement

– –

++

Increase in Implied Volatility without Market Movement

+

Payoff Thumbnail Chart

Maximum Risk

Cost of the butterfly

Difference between wing strike and body strike minus net premium received

Maximum Profit

Difference between wing strike and body strike minus net premium paid

Premium received

Breakeven Points

Lowest strike + Net premium paid Highest strike — Net premium paid

Lowest strike + Net premium paid Highest strike – Net premium paid

 
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