What is Gamma?

A few months ago I wrote some posts on  the first order common Options Greeks including Delta, Theta, and Vega. Be sure to read those first if you are newer or need a refresher. We went over the main Greeks in options trading that most traders are aware of but what is Gamma? The most important option Greek is definitely Delta since it is influenced by the price movement of the underlying stock. And Gamma is what influences Delta. Gamma is the derivative of Delta or the dynamic measure that shows the rate of change of delta in the underlying stock. In other words, gamma is the greek in options trading that gives us a good understanding of how our delta might change as the stock moves. So if we have a long call option with a gamma of 0.20 and a delta of 0.40 that means if the underlying stock increases by $1.00, the option will then increase its delta to 0.60, assuming all else stays equal. 

In general if you are long an option you benefit from gamma expansion and if you are short an option you have risk with gamma expansion (aka gamma squeeze). The biggest factor that increases gamma risk is time until expiration. This is because the closer an option gets to becoming fully in-the-money or fully out-of-the-money during expiration week then the more risk of an aggressive gamma move that quickly changes an options price. Gamma also has a strong relationship with theta, since they both are higher the closer to expiration an option gets, and they are lower the farther out in time an options expiration is. Options are full of trade offs and as an option buyer you are long gamma (unlimited profit potential) and short theta (time decay working against you). As an option seller you are short gamma (limited profit potential) and long theta (time decay working for you).

Why is Gamma Important in Options Trading?

As a second order Greek in options trading, Gamma is a fundamental part of options pricing. Understanding the risk and rewards are important because gamma can be a benefit to long option holders while being a risk for option sellers. So much of options trading revolves around velocity of a move and that is where gamma comes in. From an option buyer’s perspective you want the delta of your long option to increase. Since delta is the rate of change of an option, the gamma increasing will make the options delta increase and therefore move further in-the-money, which makes the option buyer exposed to higher delta and more profit on the way up. One reason why using options can be such a capital efficient way to play a directional move in a stock is because the option buyer is usually gaining exposure to 100 shares of stock for much less delta equivalent. As the option delta moves higher and deeper in-the-money, the better the return on investment. This also makes losses decelerate on the way down because the option buyer is only risking the original amount paid for the option. If the stock drops 2 points and gamma is 0.10 then the delta may drop from 0.50 to just a 0.30 delta. 

This is different for an options seller as losses can accelerate on a move that goes against them. From a seller’s perspective if you were to sell a naked put with a 0.30 delta, you have a high probability of making a profit but also unlimited risk in theory. For example, with a gamma of 0.10 on that out-of-the-money put option, it may move to 0.50 delta on a 2 point drop in the stock. Now the option seller is long an equivalent of 50 shares and as the delta increases, so does the long stock exposure the option seller takes on. On the flip side, if the stock rallies higher after you sold a naked put, the delta starts to decay and shrink which means your upside is limited and you make less money the further the stock increases. This is simply a trade off that is made between being an option buyer or seller. 

Expiration Risk

The main takeaway that you should have with gamma is that it increases the closer an option contract gets to expiration. This is why options with 7-10 days of life left tend to move much more drastically with a stock move than options with 50-60 days of life left. That’s gamma. If you ever looked at a risk graph between several different expiration cycles you see the difference quite easily. Short options trades can move violently the week before expiration as they become closer to parity, or being fully intrinsic or extrinsic value. This can quickly turn a winning trade into a loser in the week it expires or vice versa, a losing trade turning profitable if its delta changes fast enough.

In the example risk graph above you can see Gamma vs. Time as the 3 various expiration months in AAPL I pulled are the at-the-money 175 strike. April 1st options with 4 days left have a much higher gamma shown at the pink line near the bottom of the graph, a gamma of 0.09. The April 14th expiration about 17 days away (blue line) have a gamma almost half that near 0.04, and the May options with 50 days left (orange line) have a gamma under 0.02. So you can see the difference in risk and reward just from this graph. If you are short options with little time till expiration it creates little margin for error as a quick move in the stock can take option from being out-of-the-money to fully in-the-money. This is a prime example of why buying back short options before expiration week is always a great idea from a risk perspective. Especially since there is likely not much meat on the bone in terms or premium left to collect. You are better off adjusting the position if you still like it and rolling to a further out month to have less gamma risk.

Gamma Around Different Option Strategies

As I mentioned, in general options buyers are long gamma and options sellers are short gamma. Basically if your options strategy is long vega or volatility it is considering positive gamma. Strategies like this include any type of long call or put, long debit spreads, and long straddles or strangles. Being long gamma simply means you are playing for a larger than expected move and would like to benefit from that positive directional move, or gamma. If you are short vega or volatility it is considered negative gamma. Strategies that are short gamma include naked short puts or calls, covered calls, credit spreads, calendar spreads, butterfly spreads, iron condors, and short straddles or strangles. Many of the more popular options selling techniques like credit spreads or iron condors are short gamma at their core which means you benefit from minimal movement in the stock but it’s clearly very important to understand the correct times to employ these strategies or any strategy using options for that matter. 

Simply comparing the gamma risk between two iron condors with 20 delta short strikes but different expirations is eye opening. The weekly iron condor with 4 days of life left has almost 10 times more gamma risk than the monthly iron condor with 30 days until expiration. The first risk graph below shows the weekly iron condor on SPX options. For every 10 contracts, the gamma is -1.60 which means for every point the SPX moves the delta will change by 1.60. So a 10 point move in SPX results in the delta moving 16 points. If you are short an iron condor like this in the weekly options, you are just asking for trouble with that sort of gamma risk. If a move goes against you, there is far less margin for error especially if that move happens overnight in the form of a gap.

Looking at the second graph below shows the monthly iron condor, a much smoother gamma profile as the options still have 30 days until expiration and thus the changes in delta will be less impactful based on the smaller gamma number. A Lot of newer options traders get sucked into the myth of high theta decay being apparent in the weekly options and thus will sell them since they are near expiration but it comes at the risk of much higher gamma and if you are short options, gamma is the enemy. Controlling risk should be number one as an options trader, especially as an option seller. Giving yourself a chance starts with avoiding weekly iron condors or similar tactics. As much as I like selling options, I’ve never been a fan of selling front week options with very high gamma risk, outside of when a stock has an earnings report and the implied volatility is high. The reward is just not worth the risk you take. These are just iron condor examples but the same can be said for directional credit spreads or naked options using weekly’s. The implied volatility of these is usually not high enough to justify the often high realized volatility of the underlying stock.

Takeaways:

• Gamma is the derivative of Delta or the dynamic measure that shows the rate of change of delta in the underlying stock.
• Option buyers are long gamma and option sellers are short gamma.
• Gamma increases the closer to expiration an option gets. 
• As a stock increases, a long call option owner becomes more long delta’s but if the stock decreases the option delta falls and the option owner becomes less long delta.