The Greeks: Trading with Negative Gamma

Collecting time decay involves risk

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Option traders can enjoy positive Theta (time decay); however, those positions come with negative Gamma (rate of price changes) which can translate into the possibility of incurring a significant loss. Other traders prefer to own options, along with the possibility of earning an occasional large profit. The caveat to this position is negative Theta, meaning that the position will lose money on a consistent basis unless the asset price moves enough to offset the time decay. Whether to be a premium seller or a premium buyer is one of the major decisions for a novice options trader. 

Background information for readers who are new to the concept of using the Greeks to measure risk.

Find Your Comfort Zone

The best long-term solution for an options trader is to discover your individual comfort zone. If you decide to take the chance of owning negative Gamma positions, then the best method to avert risk is to own positions with limited risk. In other words, for every option sold, buy another less expensive option of the same type (call or put). Suggestion: Trade credit spreads instead of selling naked options

If you decide to take a position with positive Gamma, we can assume that you own one out-of-the-money call option. Here's an example:

Stock price: $74

Strike Price $80

Days to Expiration: 35

Volatility: 27

Theoretical Value: $0.61 (according to the Options Calculator)

If the stock moves higher, you can expect to earn money. However, due to negative Theta, if too much time passes, then the option may lose value, even when the stock rallies.

An Example

Consider a few stock prices and watch them for one week. Pay attention to the Gamma and how much it affects the Delta. Let's look at the table below for reference.

Stock Price

$74 $76 $78 $80
Delta 16 26 38 52
Gamma 4.4 5.7 6.5 5.9
Theta 2.4 3.3 4.0 3.5
Profit ($0.17) $0.24 $0.86 $1.78

Gamma increases as the stock moves higher—until the option delta nears 50. To understand why gamma does not continue to increase after a certain point, just think about the option delta if the stock were $200. At this price, Delta would be 100 and the option moves point-for-point with the stock. Delta cannot be above 100 and thus, there has to be a point at which Delta no longer increases.

Theoretically, Gamma remains positive, but it becomes less positive. If that is true, then there must be a point at which Gamma declines and approaches zero.

As the stock moves higher, the Delta increases, at least until it reaches 100. Thus, for each $1 change in the stock price, the Delta is higher than it was earlier and the rate at which the option gains value accelerates.

When this option was purchased, the Delta was at 19 (the Table shows a 16-Delta because that data point is taken one-week later). If the stock moved to $76, then there is an anticipated earning about $38 (2*$19). In the table, the gain was only $24. It would have been $47 if no time had passed.

As the stock climbed another 2 points, the option gained $0.62. This is considerably higher than the gain generated by the previous 2-point rally. An additional 2-point rise to $80 adds $92 in gains. Once again, the rate at which money is earned accelerates.

As the Delta increases, the rate at which call options earn money also increases as the stock moves higher. Thus, the role of Gamma in the profit/loss potential in option trading is a big deal. A 19-Delta option has become a 52-Delta option when the stock price moved from $74 to $80 in one week. Thank you, Gamma!

A Second-Order Greek

Gamma is a second-order Greek because it measures the rate of how another Greek (Delta) changes with the stock price, and not how the option price itself changes.

Remember when the Gamma changed from 4.4 to 6.5? Not only did the Gamma boost the Delta and the profits of the call owner, but it also accelerated those profits as the Gamma itself grew larger.

In conclusion, positive Gamma is beneficial to the option owner while the cost of owning that Gamma is Theta. Positive Gamma results in an increase of useful Delta (i.e., positive for call owners when stocks go higher and negative for put owners when stock prices move lower). To put it simply:

Positive Gamma makes a good thing better.

What About Negative Gamma?

If the above scenario painted a pretty picture for the option owner, then the picture must be the exact opposite for the person who sold the option, especially with no offsetting hedge. That trader has encountered negative Gamma.

  • If you are short one put option and the market is falling, then the rate at which money is lost continues to accelerate because of negative Gamma.
  • If you are short one call option and the market is rising, then the rate at which money is lost continues to accelerate because of negative Gamma.

To put it simply:

Negative Gamma makes a bad situation worse.

Earning a Profit with Negative Gamma

Why would a trader elect to take the risk that comes with owning negative-Gamma positions? For the option owner to earn a profit, the underlying stock must move in three ways.

  • Move in the right direction (up for calls, down for puts)
  • Move quickly to prevent the loss of too much money to Theta (time decay)
  • Move far enough to overcome the cost of buying the option

That is a lot of movement and most traders have a difficult time predicting market direction without a time limit. Unlike most traders, the option seller has a reasonable chance to earn money and makes negative gamma positions attractive.

Warning: If selling options sounds good, be very careful. Markets sometimes undergo unexpected price changes, and the option seller can get hurt. It is advisable to sell a spread, rather than a naked option.

When trading negative Gamma positions, use a risk graph to let you know when you are in danger of losing too much money or when the position has moved beyond your comfort zone. The Greeks -- Gamma, Theta, and Delta -- can help you estimate the price that will sound the alarm, helping you to reduce risk and gain profits.