I entered a January butterfly trade on schedule. However, I also took an honest look at the geopolitical landscape at that time and decided to enter with a smaller position than I typically would. I'm glad I made that decision. This last week, I closed that trade at a loss, although for less than the planned maximum loss I intended to take. This article is about an interim period during the course of that trade.

In the long grind up on fiscal-cliff-resolution hopes, I was forced to roll butterflies several times. When butterflies are rolled to the upside, you often take a big hit due to the difference in price in the ones you're selling and ones you're buying. You build in some take-notice realized losses that then have to be overcome.

How does the trade overcome them? In the case of my trade, it never did. But in the normal course of these trades, it's time. You spend more time in the trade than would have been needed to meet the target profit prior to the adjustment. At the particular period discussed here, on 12/27, the tent shape of my butterfly was resting on swampy land and my profit-and-loss line had sunk below ground level due to the hit the trade had taken on adjustments. I'd been vigilant about adjustments, but sometimes trades just don't work the way you want them to work.

However, the trade still looked viable, with plenty of profit to be had and more adjustments available, too, if the RUT just behaved reasonably well. Otherwise, the trade would have been closed.

Butterfly Trade on 12/27/12:

Notice that the delta for the entire position is -14.54, a mildly negative delta. This was a position that had started out as a 9-contract position and then been reduced on delta-managing adjustments to a 7-contract one. For those not used to watching the Greeks of the trade, delta measures how much a price movement impacts the trade over a short distance, with the negative value meaning that the trade was going to benefit approximately $14.54 if the RUT dropped a point and lose about that much if it gained a point. Of course, movements during this time period were often accompanied by big changes in the implied volatilities. Vega, this far out before expiration, was still much bigger an impact on the trade than that relatively flat delta. However, I want to isolate gamma and talk about that.

The delta might have been mild, but notice that gamma is -3.12, with that negative gamma having negative implications for the trade. Gamma measures how much the delta is theoretically going to change for each one-point move in the underlying. With the benefit of hindsight, we now know that there was a whole lot of upside yet to go for the RUT.

One trick to remembering the way delta will move when gamma is negative is to remember the saying that "negative gamma is bad on the way up and on the way down." I'm not certain who first said that, but I first heard it on a CBOE webinar by former market maker Dan Sheridan. In other words, with gamma being negative, the delta is going to grow more negative with each point climb and more positive with each point the RUT declines. Now that this period has passed and we know what happened with the RUT, we can see that the trade was going to be hit far harder by the upward price movement than that -14.54 delta suggested it would be.

Neither the gamma nor the delta was too bothersome just yet on 12/27 when this chart was snapped and this article roughed out. That negative gamma did mean that the trade would have to be adjusted sooner than it would if the gamma were -0.31 rather than -3.12.

Another problem is that the absolute value of the gamma grows bigger as expiration approaches. We now know what happened since this chart was snapped and this article roughed out on 12/27, but we didn't know that on 12/27. It was possible that the fiscal-cliff negotiations could completely fail and the markets could fall apart. Traders need some way of seeing into the future of various what-if scenarios, and that's what I do with these risk or analysis graphs.

As of 12/27, I rolled the date forward two weeks and looked at the graph and the Greeks again. You'll notice that the delta will have grown much more negative. That's something that I would have long-since addressed before it grew so negative and did address via several adjustments last week that ultimately could not rescue the trade. I would not be in the trade two more weeks, as it turned out. However, we're examining the effects of time on gamma and isolating that as we looked forward as of 12/27, imagining what might happen.

Date Moved Two Weeks Forward:

With these new theoretical parameters, gamma would theoretically have dropped (dropped because it's a negative number with a bigger absolute value) to -9.59. The delta would grow rapidly more negative on any jump higher in price. As this chart was examined on 12/27, it's possible to see the hurt that negative delta and gamma could do to the profit-and-loss line if the RUT runs up higher from this point. Again, we know that the RUT didn't just sit at this price, but this was meant to be an illustration that isolated the effect of time to expiration on gamma. This graph moved the date forward to a time when there would be one week left before expiration. That gamma effect was about to speed up even more.

Tuesday of Expiration Week:

Gamma is now a much bigger factor, at -27.23. Of course, to be honest, I would have been a happy camper if the RUT had stayed in the same place for two and a half weeks and the profit line rose up toward its expiration line in this manner. Instead of closing out the trade at a loss, I would have long since have locked in profit and closed the trade since my profit target was far lower than $7,000. I have no intentions of bringing a trade into expiration week if I can help it.

That bigger gamma effect as expiration draws near is the reason I don't want to bring trades into expiration week if there's any way I can help doing so. I like to keep my PnL line relatively flat over a one-standard deviation move, a task that will become increasingly difficult as expiration approaches and that gamma effect becomes more pronounced. At the time this article was roughed out, a one-standard deviation move for the RUT was running about 9.31. We now know that the RUT was going to move multiples of a standard deviation the next week, 2.5 standard deviations on Wednesday, for example. However, we did not have that knowledge on 12/27 and needed to work with theoretical profit-and-loss charts.

By the Thursday before opex week, represented by that second theoretical graph, gamma was already going to make it harder to keep that PnL line flat. It was changing the delta value by 9.59 for each of those 9.31 points for a standard-deviation move.

James B. Bittman, in Trading Options as a Professional, provides graphs showing how gamma changes over time, showing an in-the-money call, an at-the-money call, and an out-of-the-money call (101).

Graph from Bittman's Book, Page 101:

He sums up the information by saying that gammas increase as expiration approaches, and are also largest when options are at the money (99). Of course, when you've sold options as part of a spread such as a butterfly, the effect to the overall trade is negative, resulting in that negative gamma for the overall position as long as the underlying's price stays nearer the center of the butterfly than the outside edges or even beyond the expiration breakeven. That's the "money" part of the butterfly, where the butterfly trader wants prices to be as expiration approaches. That middle graph, however, shows what starts happening to the gamma on those at-the-money options as expiration approaches: they explode higher.

What's the point? This article addresses the effect of negative gamma on your ability to manage the profit-and-loss of a trade as expiration nears. If you're in a complex trade such as a butterfly or iron condor in which your sold options are nearer to the money than your long options, you may see this gamma effect as expiration approaches. Your trade may be harder to handle. Some traders are adept at handling this, and some can handle the stress but just don't want to do so.

Bittman's book is dry reading but is a great resource. However, you don't have to know all the nitty gritty stuff about the Greeks of trading. Just know this: if you're in a butterfly and price is anywhere near the middle of that fly, you're going to think it's been transformed into a bucking bronco as expiration approaches. Of course, changes in implied volatility can and do impact it more strongly, but just understand that your PnL line can change more than you are accustomed to seeing it change with a certain price movement as expiration draws nearer.

Unfortunately, price was nowhere near the middle of my butterfly this last week, despite my concerted efforts to keep moving those butterflies. My butterflies just couldn't fly fast or high enough. I hope you had better luck, but losses are a part of this work we do. Except for those trading pure directional trades, who likely either had lots of fun or lots of dismay, most options traders likely struggled this last week. Trades such as butterflies are built on the premise that prices will stay in certain ranges over certain periods of time, and the RUT, at least, defied gravity.

As a last note, 900 must be singing a siren song for the RUT traders. Balance that against the knowledge that RVX and VIX both test low levels from which they often reverse, with equity indices reversing along with them and head to the downside. A return of more volatility can be difficult to handle, so some cheap OTM puts might be in order to help hedge your trades. Just don't spend so much on them that you swamp your trade. A better idea might be to keep trades smaller until we figure out whether volatility indices are going to trend at low levels, as they did in the mid 2000's or if they're about to reverse higher.