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Key Concepts 4. Portfolio Management


Gamma is the greek that gives us a better understanding of how delta will change when the underlying moves. It is literally the rate of change of an option’s delta, given a $1.00 move in the underlying. For example, if a long call option has a gamma of 0.10 and a delta of 0.50, and the underlying moves up $1.00, the option will then have a delta of 0.60, all else equal. There are a few important concepts when it comes to gamma: Long option benefits, short option risks, and expiration risk.

Long Option Benefits of Gamma

Gamma is friendliest to long option holders. It accelerates profits for every $1.00 the underlying moves in our favor, and decelerates losses for every $1.00 the underlying moves against us. Since delta is the rate of change of an option’s price, and gamma increases an option’s delta as it moves closer to, or further in the money, in the example above the delta would just continue to increase. Every dollar the underlying increased would result in more and more efficient returns on the investor's capital. This phenomena also decelerates losses, as it works in the opposite way for every $1.00 the underlying moves against us.

Short Option Risks of Gamma

Because it can be beneficial for option buyers, that must mean that it can be risky for option sellers. From the seller’s perspective, it can accelerate losses, and decelerate directional gains. It is just the opposite side of the coin from the example above.

Expiration Risk & Gamma

The final aspect of gamma that is important to realize is expiration risk. As we get closer to expiration, our probability curve gets much more narrow. There is not a lot of time for the underlying to move to our far OTM strikes, and they will have a lower probability of being ITM because of that. Since we know the probability curve is more narrow, that also means our delta distribution is more narrow. The result is a more aggressive gamma. This can be good for option buyers, but especially bad for option sellers. It can quickly turn winning trades into losers, or losing trades into winners. We prefer to avoid these drastic swings, which is just another reason why we roll or close our positions 7-10 days prior to expiration.

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