I think of gamma, one of the Greeks of option pricing, as "a woman scorned." When we options traders first start learning about the Greeks of options pricing, we tend to concentrate on delta, theta and, if we're astute traders, vega. These Greeks estimate how much the value of an option, a position or a portfolio is likely to change with a one-point change in price, a one-day change in time or a one-percent change in implied volatilities, respectively.
Gamma tells us how much delta changes with a one-point change in price of the underlying. For example, if a position's delta is 10.15 and the gamma 0.33, a one-point rise in price in the underlying will theoretically result in a new delta of +10.15 + 1*0.33 = +10.48. A one-point drop in price in the underlying would theoretically result in a new gamma of +10.15 -1*0.33 = +9.82. It's the second derivative of the formula for options pricing with respect to the price of the underlying. For some of us, the ones who may hate the phrase "second derivative," gamma is just no fun and way more than we want to know about options pricing. Delta is enough, they reason, to anticipate how the option's price will change.
I, however, am one of those who loves dashing off phrases such as "second derivative." Moreover, as options traders go, I rank among the cautious end of the spectrum. In real life and in options trading, I just don't like to ignore anyone or anything.
Besides, we know the rest of the saying about a woman scorned, don't we? Gamma can get quite vengeful when she's ignored for too long or the underlying ventures too close to the sold strikes in a complex options trade. To understand what happens, let's have a little primer on gamma. Gamma is positive for both calls and puts, and the gammas of calls and puts at the same strike are about equal. When you sell an option, gamma is negative. A complex position with both long and short options can be either positive or negative gamma, depending on the proportion of long to sold positions, the underlying's proximity to the longs or shorts or the time left until expiration. Gamma will change as time goes on and the underlying moves, and a long-gamma complex position can become a negative-gamma one, and vice versa.
There's a little something to remember about a negative-gamma position, whether that's a single option, a position or an entire portfolio. It works against you. Jim Bittman sums up the effect of negative gamma in Trading Options as a Professional, "Stock up; position delta down, or stock down, position delta up" (125). Dan Sheridan, former market maker and presenter on CBOE webinars explains simply that negative gamma is bad on the way up and bad on the way down. If your underlying is going up, the delta gets ever more negative, so you either make less or lose more money than you would have. On the way down, your delta gets more positive, so that you make less or lose more. If the absolute value of gamma is relatively small when compared to the size of your trade, this negative-gamma effect isn't particularly important, but gamma shouldn't be ignored as it can grow more negative.
Let's use one of my trades as an example. This trade has already been closed for a profit. I'm experimenting with adjustments, so I'm keeping a journal complete with snapshots of the trade at various intervals. By showing my actual trade, we can see the effects of gamma on the trade. That effect won't be particularly large in this trade because I was watching it, but we can see how gamma changes under different conditions. Because the sizing requirements for these articles is different than that when I was snapping these pictures for my trading journal, it may be difficult to read the Greeks, but I'll list them after I've shown a chart. The Greeks are listed in the "Live" line under the chart.
At inception, this trade has a delta of 2.10 and a gamma of -.34. The low delta value and the small negative gamma meant that the trade wasn't going to be impacted much by price move over a relatively large range. This is reflected in the flat "T+0" or "today" line, the white line in the chart. That white line is difficult to spot toward the right side of the chart because it's nearly flatlined at the "0" level. This white line shows what will happen to the profit or loss as price moves, if volatility stays relatively steady. The idea was to set up the trade and then adjust to keep the trade relatively immune from price movement while theta or time-related decay was allowed to work. This was January 27, 49 days until the expiration of these March options.
By February 16, 29 days until the March expiration, the RUT had charged up high enough that I had moved the original butterfly contracts. I had made other adjustments to keep the deltas flat, and gamma remained in control, too.
At the Close on February 16:
It may be difficult to read the Greeks on the live line, but delta was -9.30 and gamma, -0.42. The white line was still relatively flat.
I knew that would likely soon be changing. To quote Bittman, "gammas are biggest when options are at the money, and they increase as expiration approaches" (99). Of course, this means that if your position is negative gamma, it will grow more negative. He further warns that "gammas of at-the-money options are very small and nearly constant, rising only slightly, until about one month before expiration. Then they rise dramatically until immediately before expiration" (102). Gammas of the in-the-money and out-of-the-money options would behave differently. They would also rise until about a month before expiration, but then they would begin dropping off rapidly. So, while I could even out the deltas before the close, I might have more difficulty evening out those gammas as they began changing more rapidly. That meant that the delta that I attempted to flatten wouldn't stay that way long. It was due to this known "gamma effect" as expiration grew nearer, in particular, that I had planned to exit 7-14 days before expiration. The gamma effect is hard to handle the week before expiration week and even harder on expiration week. A big move then can totally derail what had been a profitable trade, and I didn't want to risk that possibility until the trade was more familiar.
By February 23, 22 days until expiration, I had made other adjustments, including buying some long debit call spreads, to flatten the risk. The white today line was rising as some profit began accumulating. But gamma was also becoming more negative, the absolute value rising.
At end of the day, February 23:
Delta was -12.64 and gamma a smaller number, at -1.17. However, consider what this means for delta. If the RUT were to rise 7 points, that would change the deltas by 7 x -1.17 = -8.19, bringing the delta to -12.64 - 8.19 = -20.83. I would lose $20.83 for each further point the RUT rose. Morever, because the gamma was negative, that trade would suffer similarly if the RUT dropped 7 points. My delta would grow more positive by 8.19 points than it had been, and would be approximately -4.45 at the end of that 7-point drop. The trade would benefit less and less from the drop. If a drop were deep enough, the delta would eventually become positive. The RUT had been churning and could have broken out to either direction. Obviously, this trade was not in any trouble, but I'm using this real-life journal of my trade to show how the gamma was changing and how that could have impacted the trade. With this three-lot trade, the effect wasn't big, but I eventually plan to trade this in at least a 10-lot size, when the effect would be magnified.
This gamma effect is the reason that I elected to close this trade for a lower profit when I feared the RUT was due to break out of the coil in which it had been churning back and forth. By February 28, I closed down one of the three butterfly contracts and some of the long positions, and the next day, I closed the rest for a profit of $917.50 after commissions. My profit target had been $300-500 per butterfly contract, and I had a three-lot position, so I met that lower end of the profit target. If I'd stayed in longer, I would have been able to squeeze out more profit. While I'm testing this trade, however, I didn't want to risk the RUT breaking out of that coil and running hard either direction while I was having to deal with a big delta effect and also manage a gamma that was growing rapidly more negative.
I've talked about Bittman's book before. It's dry reading. I use it as a resource, not for engrossing information. I've talked to other traders who use it the same way. Other books exist, and I'm not pumping Bittman's book, but perhaps you might consider finding a resource book like this one. Keep an eye on gamma, too, and don't let her be the scorned woman that you didn't give enough attention.