In the Winter 2015 edition of thinkMoney, an option trader asked a question about a butterfly trade. The trader had initiated a new butterfly trade a few days before expiration. The trader had correctly speculated on where the underlying's price "would go," but complained that, despite the correct calculation, the butterfly "barely increased in value" (12).

What happened? the option trader asked. As part of the answer, thinkMoney's Trader Guy explained, "A butterfly's value depends on the likelihood of the stock landing on the middle strike." Moreover, he added, "Close to expiration, there's less uncertainty where the stock will land, and butterflies whose strikes are close to the stock price begin to have higher prices." Because the situation had forced the trader to pay a higher price for the butterfly, there wasn't as much opportunity for a big profit.

Because this question and answer so aptly illustrate the interplay of time, implied volatility, and the price of butterflies, I thought a visual example might be appropriate. The option trader's question didn't supply specifics. Which stock was the underlying? What constitutes the "just a few days to expiration" at which the option trader entered the butterfly trade? When did the stock "go to the middle strike"? Was that sometime between the trade's initiation and expiration? Or was it at expiration? The option trader mentioned that "the butterfly barely increased in value."

We're going to have to make some assumptions.

Let's Use AAPL for November 2014's Expiration:

Early that November expiration week, "just a few days to expiration," AAPL was hovering near 114. Let's imagine that, on Tuesday, our hypothetical trader had postulated that AAPL might head back up toward 116, a level it had temporarily hit and exceeded on that Monday.

Hypothetical Five-Contract Butterfly Established at 8:45 am CT Tuesday, November 18, with a Central Strike at 116:

Let's assume that the trader's intention was not to let this trade expire, with the attendant risk of assignment and other problems, but rather to capture a moment during Thursday or Friday of option expiration week when AAPL tested 116. That trader could then close the trade and lock in the profit. This graph shows that the trade, as constructed, had a maximum potential loss of a little over $600 ($617.50, to be exact, with commissions of $1.25/contract) but had a maximum potential gain of slightly over $800.

AAPL did test 116 by Thursday of opex week.

AAPL tested 116 again on 9:30 AM CT on Thursday, November 20:

The theoretical profit at that point, a day before expiration and with AAPL sitting squarely on the 116 central strike, would have been $330.00, according to OptionNET Explorer. That's a hefty 53 percent of the maximum margin in the trade, but to the trader setting up this trade a few days earlier and eyeing that potential $800+ profit, that gain might have proven disappointing. That close to expiration, the trader might have expected to capture a heftier portion of that maximum potential profit.

I once had a SPY butterfly that sat right on the central strike for more than an hour on the last day the options traded, and I was disappointed at my gains, too. I don't remember my earnings in that particular case, but they were certainly a less hefty percentage of my risk in the trade than in this theoretical AAPL trade.

Trader Guy's conclusion had been that the trader might have paid too much for that butterfly when butterflies were getting expensive closer to expiration. In our hypothetical case, the 116 strike wasn't all that far from AAPL's 114.31 price when the theoretical trade was entered. Butterflies with central strikes at nearby levels were likely expensive. Also, imagine that during a moment when prices were bouncing around, the trader hadn't been able to fill the original order until he offered $0.20/contract higher than the mid-price for his five contracts. That would have meant that trader would have paid $0.20/contract x 5 contracts x 100 multiplier = $100 more for those five butterflies than in our hypothetical example. The trader would have reaped only $230 in theoretical profit when AAPL hit $116 on 11/20. Imagine that it hadn't been easy to exit those flies when AAPL hit 116, either, and there was more slippage on the exit. Flies were already expensive and a jittery market that forced a bad fill would have cut into the potential profit even more. This is an entirely plausible situation. Slippage is often encountered, and we don't know how much slippage this trader was forced to buy when entering the trade and give up when exiting it.

Another point made in Trader Guy's answer was that the further away from expiration the trade was entered, the more uncertainty there would be about AAPL's price at expiration. That uncertainty would have rendered the butterfly less expensive to purchase than the one purchased just a few days before expiration.

Same Butterfly, Same Strikes, Entered 11/4 with AAPL at 109, Trade Carried to 11/20 with AAPL at 116:

We can't compare apples to apples with this trade--pun intended--because AAPL wasn't at the 114 entry price in the weeks before expiration.

The flies were indeed cheaper, but that was due to two greater uncertainties and not just one: the greater uncertainty that AAPL would land at 116 from its then-current 109 price and the greater uncertainty due to the longer time period before expiration. Those uncertainties resulted in cheaper flies. This trade offered much more reward and the risk had been lower, too, at $140.00 for the same five-contract trade centered at 116. On November 20 at 9:30 AM CT, it offered a theoretical $808 profit after commissions, a whopping 577 percent of the maximum risk in the trade. Whether someone could characterize a theoretical $330 gain on a trade that cost $617.50 as "not much" of an increase in value, everyone would agree that a theoretical $808 gain on a trade that cost $140 offered a much larger potential gain in value. If a hypothetical trader had found it necessary to pay $0.20 more than the mid-price per contract to enter this trade, the extra expense wouldn't have hurt as much as it did with a trade entered a few days before expiration or when the underlying's price was further away from the central strike.

What's the point? Should traders never enter speculative butterflies the week of expiration? No, of course that's not the point. They're not my cup of tea, but if everyone traded only the way I do, we'd have a stodgier market. One point is to be aware that you're paying more for those butterflies as expiration nears and if the central strike is near the price of the underlying. You need to be more of a bargain hunter if you're trading that way. Your entry price really matters. Start pricing some expiration week flies before you dive into these or at least trade them with small lots until you're familiar with pricing. Trading in small lots means that commission costs and slippage will eat up a lot of your profit--which may also have contributed to the "not much" gain in value that the inquiring trader experienced--but those who insist they can't learn with simulated or back-tested trade can at least manage their risk this way while they're learning. When learning a new trade or an unfamiliar way of managing a trade, your primary goal is not losing your trading capital or confidence, not making huge bundles of money.

Now let's test ourselves. If those flies are more expensive as expiration approaches and if the central strike is close to the current price, what would we find if we priced butterflies on the same "few days before expiration" and with the same size wings but with the central strike further away from the then-current price? In other words, what if our hypothetical trader had thought AAPL would go to 118 from its 114 price rather than 116?

Five-Contract Fly Centered at 118 with Three-Point Wings, Theoretically Established on 11/18 at 8:45 AM CT with AAPL near 114:

As we should have anticipated, this was a cheaper setup than our original 116 fly established on 11/18. Although the size of this fly, both in number of contracts and wing span, was the same, it cost only $300 rather than the $617.50 the originally discussed fly cost. More uncertainty about outcome has been introduced, not because of an increased time to expiration but because of the increased distance of the central strike to the current stock price.

Of course, AAPL didn't hit the 118 strike on 11/20. However, when it hit the same 116 level on 11/20 as had been used to test profit on the other two flies, ONE shows that the theoretical profit was $255, not that far behind the $330 of the original fly centered at 116.

I thought it might be fun and educational to take a Q&A from another source and look at how it plays out on a risk chart or analysis page.

Linda Piazza