Greek of the Week: Gamma

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Editor’s note: This post, part of a four-part series about options Greeks, was originally published on Monday, August 20, 2018.

We previously looked at delta. Delta measures how much an option changes in price when the underlying stock or ETF fluctuates. Calls have positive delta because they move in the same direction as the underlier, while puts have negative delta because they move in the opposite direction. Remember that delta is expressed as cents on the dollar.

Now let’s turn to Gamma: G is for “gaining delta.”

  • Gamma shows how much delta an option gains or loses when the underlier moves.
  • Gamma shows the absolute or simple change in delta for an option based on the underlier moving $1. This is important because delta isn’t constant.
  • Gamma can be understood as “leverage on leverage.” Knowing how to maximize or minimize it can help you better plan option trades.

The screenshot below shows calls and puts on the SPDR S&P 500 ETF (SPY) for the weekly contracts expiring Friday, August 24, 2018. Notice how the highest gammas are closest to the money.

A trader buying the 286 calls would have an initial delta of 0.47, but his or her delta will change as SPY ticks up or down. How much? Gamma tells us they will gain 0.14 delta if SPY rises $1, and lose 0.14 delta if it slips $1.

This is where it gets interesting. If SPY rises $1, they will make more than just 0.45. Why? Because on its way up $1, delta grows incrementally. If SPY rises $0.50 to $286.20, their delta will already be over 0.50. They’ll make more money the higher SPY goes. In other words their leverage will increase.

Just the opposite is true to the downside. Say they’re wrong and SPY moves $1 lower. In that case they’ll lose less than $0.45 because their delta will decrease. (Time decay, or theta, also kicks in. We’ll address that in a coming post.)

Hopefully you see the nice thing about gamma: It rewards you when you’re right and cushions you when you’re wrong.

Gamma can be extremely useful for directional traders looking to profit from relatively small moves. Calls and puts just out of the money can provide much more leverage, which lets you risk much less capital. That can also let you own more contracts, opening the door to even more leverage if you get a nice move in your intended direction.

For example, compare the 286 and 287 calls:

  • The 286s cost $1.01 and have 0.47 delta.
  • The 287s cost $0.55 and have 0.32 delta.
  • The 287s cost 46 percent less but only have 32 percent less delta. So, they can give you more bang for your buck if SPY moves higher.
  • Even better, their gammas are almost identical. That means you’ll gain delta at pretty much the same speed, despite paying barely half as much in premium.

It’s important to remember that these values will change quickly because the contracts are out of the money. If SPY falls over the next week none of this will be true after expiration. Greeks are useful but not magic. A directional trade always needs to get the direction right!

Still, we can see the differences in leverage by assuming that SPY rallies. Say it ends the week at $290. In that case the 286s will be worth $4, or 296 percent more than their current price. The 287s, on the other hand, will be worth $3, a gain of 445 percent. This difference in leverage is another way to understand the effect of gamma.

SPDR S&P 500 (SPY) options chain. Contracts mentioned in post marked in yellow. All prices as of August 20, 2018.

Looking further out the options chain, there’s something else important about delta and gamma: Deeper-in-the-money contracts (lower strikes for calls, higher strikes for puts) have much lower gamma. Notice that their deltas are also much closer.

For instance, the 282 calls only have 0.05 more delta than the 283s, but cost a full $0.93 more. Also notice that their gamma is just 0.06. So you pay much more on a premium basis and get much less rewarded for being right if SPY rallies. In other words, these options have much less leverage because they have much less gamma. (Even worse, they have wider bid/ask spreads, which we will also address in a future post.)

These principles are also useful to clients selling options. If you’re short calls or puts that are near the money, gamma can work against you. Some people learned that the hard way back in February.

In conclusion, think about driving a car. The gas pedal is delta because it controls its speed, but gamma is the signal from your brain telling your foot what to do. Delta is in control, but gamma controls delta. That’s why the useful phrase to remember is:

Gamma: G is for “gaining delta.”


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