Calendar vs. Butterfly: The Ultimate Premium Smackdown

A popular strategy for many option traders is to try to profit from the passage of time. Positions like iron condors and short vertical spreads spring to mind, for example. But two other strategies traders could turn to are the long calendar and long butterfly.

If you looked at the risk graph of each strategy, you might think they’re twins. Both trades profit if the stock is near the short strike at expiration. And both lose value as the stock moves away from the short strike, regardless of direction (See Figures 1 & 2).

But dig a little deeper, and you’ll see there’s a difference between the two. It’s not obvious from the risk graph. But your choice could potentially have a big impact on how the trade performs.

Fly or Calendar?

Butterflies and calendars can be created using either all call options or all put options. You can also do a little call/put “mix and match” to arrive at these strategies. But let’s keep it simple. We’ll consider these strategies using all call options, and focus on the long version of both.

The long butterfly (or “fly”) uses three strike prices in the same expiration. It’s created on a 1:2:1 ratio, where the strikes are the same distance apart. The single options on the outside of the fly are long options, or the wings. And the two options in the middle are short options—they make up the body. Get the visual now?

Using the theoretical prices in Table 1, and with the stock trading at $145, you could buy the 140/145/150 call butterfly, that is, buy one 140 call, sell two 145 calls, and buy one 150 call for a net price of $2.50. In the real world, you’d also tack on transaction costs. The risk graph (Figure 1) reveals that this fly hits its max profit if the stock settles at the body—short strike—at market close on expiration date. 

On the other hand, if the stock moves away from the short strike in either direction, the trade would show less profit. It would likely break even eventually, or possibly reach a total loss if the stock price moves to or past the wings.

Long calendars, on the other hand, use just one strike, but spread the options between two different expiration periods. Going back to Table 1, you might buy the November 145 call and sell the October 145 call, for a net price of $1 ($3 – $2). The risk graph in Figure 2 tells a similar tale: max profit if the stock settles at the short strike at expiration, with less profit as the stock moves away from the strike, eventually reaching a full loss if the stock moves far enough away in either direction.

Since both strategies profit if the stock is near the short strike at expiration, why would you choose one over the other? In a word: volatility.

What’s Vol Got to Do With It?

Calendars and butterflies look similar on the risk graph. And their greeks are also similar. With the stock sitting near the short strike, calendars and butterflies will both be close to delta-neutral, with short gamma and long theta. Keep in mind that theta indicates the profit as time passes. But when you look at how these trades react to changes in volatility, you’ll see a difference. Here’s where vega kicks in.  

Vega isn’t vol. But the two are related. Suppose a stock is suddenly expected to have a larger range than was previously thought. The option’s implied vol could increase to reflect the stock’s bigger expected range. And that means option prices could also increase.

But just how much an option price goes up will depend on the option’s vega—defined as “the dollar amount an option will change when the implied volatility changes by one percentage point.” In other words, if implied vol increases, the option will increase by vega’s amount. And if implied vol drops, the option price will drop by vega’s amount.

Here’s an example. Going back to the theoretical values in Table 1, the November 145 call is worth $3.00 and has a vega of 0.25. If vol jumps two points (all things being equal) from 16% to 18%, the call is expected to increase by $0.50 (0.25 x 2 = $0.50). It also works in the other direction. If vol drops by three points, and goes from 16% to 13%, this call will then be expected to drop by $0.75, from $3.00 to $2.25 (0.25 x -3 = -$0.75).

If the single option changes price, will spreads change price? It depends. But you can also use vega to forecast what happens to spread prices if vol changes. For spreads that have all their options in one month, like the fly, it’s as straightforward as adding up the vegas for each option to arrive at a vega for the spread. (Remember, short options have short vegas.)

Who Reigns Supreme?

The calendar is a little different. When you compare the same strike, vega may be higher for options further out in time. With the calendar, the long November 145 call has 0.25 of vega, and the short October 145 call has -0.15 of vega. As a spread, the calendar nets out with vega of 0.10—positive vega, that is. So if vol goes up by one point, assuming vols change by same number of points in both expirations, the calendar will likely profit $0.10. And if vol drops by one point, the calendar will likely lose $0.10.

So, the calendar is a long-vega trade, while the butterfly is a short-vega trade. And your assessment of whether vol is high or low, and whether it’s going to move higher or lower, should help you choose one strategy over another.

If implied vol is high, we can expect butterflies to be cheaper. And if vol drops, the fly will likely profit, even though the spread has two long options. That’s because the vega of the at-the-money (ATM) option is larger than the vega of options that are either in the money (ITM) or out of the money (OTM).

Calendars, however, are going to be more expensive in a high-vol environment, where a drop in vol can hurt your trade. The long option could lose more value than the short option because it has a bigger vega. So overall, the calendar could lose value.

In general, low-vol environments are often better suited for calendars. They can be cheaper, and can profit if vol rises. Butterflies, on the other hand, are often more expensive and can lose profit potential if vol goes up.

More to Think About

With either strategy, don’t go into the trade and expect the underlying stock to settle exactly at the short strike on expiration day. You may get lucky, but that’s a low-probability expectation.  Instead, consider these strategies for stocks you think will be range-bound, and not likely to stray far from the short strike.

Another difference? Calendars are more easily rolled out when expiration nears. Of course, if you held an expiring butterfly on a stock you felt was going to remain stagnant, you could close that butterfly and open another one in a different expiration. But that’s trading potentially six different strikes (three to close, three to open) with transaction costs. In contrast, rolling a calendar on a stock you think isn’t going anywhere fast—that requires only rolling the expiring strike out to a longer expiration.

Only time will tell you whether the strategy you chose was the “right” one. Calendars and butterflies are designed to profit from time decay if the stock finishes near the strike at expiration. And both might eventually lose their entire value if the stock moves far enough away from the strike. These strategies are also closely related in many of their greeks. But it’s their vega that separates them into strategies that can perform better in different vol environments.