The Greeks: Trading with Negative Gamma

Collecting time decay involves risk

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Option traders can enjoy time decay (positive Theta)—but those positions come with negative Gamma—and that translates into the possibility of incurring a significant loss. Other traders prefer to own options, along with the possibility of earning an occasional large profit. However, these positions come with negative Theta, meaning that the position loses money on a consistent basis unless the asset price moves enough to offset that decay. Whether to be a premium seller or premium buyer is one of the major decisions for a novice option trader. 

The best long-term solution is to discover your individual comfort zone. If you decide to take the chance of owning negative Gamma positions, then the best solution to the risk problem 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). Translation: Trade credit spreads instead of selling naked options

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

A position with positive Gamma: Assume that you own one out-of-the-money call option:

Stock price: $74
Strike Price $80
Days to Expiration: 35
Volatility: 27
Theoretical Value: $0.61 (according to the CBOE calculator)

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

Consider a few stock prices—one week later. Pay attention to gamma and how much it affects Delta:

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. NOTE: Gamma remains positive, but it becomes less positive. If that is true, then there has to be a point at which Gamma declines and approaches zero.
  • As the stock moves higher, Delta increases (until it reaches 100). Thus, for each $1 change in the stock price, Delta is higher than it was earlier—and the rate at which the option gains value accelerates.
  • When you bought this option, Delta was 19 (the Table shows a 16-Delta because that data point is taken one-week later). Thus, you could anticipate earning about $38 (2*$19) if the stock moved to $76. In the table, we see 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.

The rate at which call options earn money increases as the stock moves higher because Delta increases. 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!

Gamma is a second-order Greek because it measures how another Greek changes with the stock price, and not how the option price changes.

Note that Gamma changed from 4.4 to 6.5. Thus, not only did Gamma boost Delta and the profits of the call owner, but it also accelerated those profits as Gamma itself grew larger.

Conclusion: Positive Gamma is beneficial to the option owner and the cost of owning that Gamma is Theta. Positive Gamma results in an increase in 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.

Negative Gamma

As you must be aware, if this is the pretty picture for this option owner, then the picture must be equally as ugly for the person who sold the option (with no offsetting hedge). That trader has 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.
Negative Gamma makes a bad situation worse.

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

That is a lot to ask. Most traders have a very difficult time predicting market direction without a time limit. Thus, the option seller has a reasonable chance to earn money. That makes it 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 help you estimate the price at which that will occur—and that sounds the alarm, allowing you to reduce risk.