Our recent stint of Greek exploration has taken us from odds assessment with delta to clock watching with clock watching with theta and finally to volatility betting with vega. Before we conclude our brief but illustrative tour of the Greeks, we have one more stop on the list – gamma.
At first blush, gamma can seem a bit complex, yet many are already familiar with how it influences an option’s behavior. They just may not know that gamma is the culprit for these particular quirks. Though a comprehensive exploration of gamma is outside the scope of one article, we can at least put a dent in your understanding of this esoteric Greek. Let’s take a look at three key properties.
1. Gamma measures the rate at which delta changes when the underlying stock moves $1.
Option enthusiasts will recall that an option’s delta approaches 1 as it moves deeper in-the-money while approaching 0 as it moves further out-of-the-money. Delta is in a constant state of flux, rising and falling as the stock lurches to and fro.
Gamma provides the ability to measure the rate at which delta changes. When gamma is high, delta behaves like a rabbit on speed. Any slight move in the underlying stock’s price can cause a large change in delta. When gamma is low, delta behaves more like a mammoth stuck in the mud. It takes a large move in the stock to cause a noticeable change in delta.
2. Gamma is highest for short-term, at-the-money options.
As options approach expiration, gamma builds, particularly for at-the-money options. A one day, at-the-money option would have a rather large gamma, while a one-year, deep-in-the-money or far out-of-the-money option would have a very small gamma. The behavior of the one-day option would be much more erratic and arguably much more difficult to manage. This illustrates in part why short-term options are more risky.
3. Gamma can be either positive or negative.
Like the other Greeks, gamma can be either positive or negative. Here is one key difference to remember: positive gamma positions will see their gains accelerate and losses decelerate while negative gamma positions will see their gains decelerate and losses accelerate.
Any time traders buy options they acquire positive gamma. Think of the behavior of a long call or put for example. If I buy a call option and the stock rises in value, the call will move deeper in-the-money, causing its delta to grow and thus my profits to accumulate quicker. Alternatively, if the stock falls, the call will move further out-of-the-money, causing its delta to shrink (towards zero) and thus, my rate of accumulating losses will diminish.
Positive gamma, then, is the property of options that makes purchasing them so alluring. If you’re correct, your rate of profit accumulation will surge. If you’re wrong, your rate of accumulating losses will diminish. Not a bad proposition.
When traders sell options, they acquire negative gamma. Strategies like covered calls, short puts, vertical credit spreads, and iron condors all possess negative gamma. As mentioned above, that means that if the stock moves adversely, all of these types of strategies will see the rate of loss accelerate (e.g. the delta position gets bigger). Conversely, if the stock moves in a favorable direction, the rate of profit accumulation gets slower and slower (e.g. the delta position gets smaller).