Gamma, Your Option’s Silent Accelerator and Decelerator Pedal

What is Gamma?

Gamma is one of the least understood of the Greeks affecting an option’s price. Many investors are familiar with the Greek variable delta: the change in the underlying option’s price with respect to the change of the underlying stock price. Gamma is the rate of change in delta per $1 dollar move in the underlying asset’s price. Because it measures the rate of change of delta, gamma is the first derivative of delta, or the second derivative of the underlying stock price. Since delta is not a constant measure, as a stock price changes, the change in delta is measured by gamma. An option’s sensitivity to gamma is also not constant and is more pronounced as the option approaches expiration, especially for options where the strike price is close to the current price of the stock, ETF or index.

Accelerator and Decelerator

If delta is the “speed” of an option, gamma tells investors about its “acceleration” – i.e. the rate of change in the speed or delta of an option. Gamma tends to be at its highest when the option is near or at-the-money, while deep in or out-of-the-money options will have a low gamma. For investors trading options set to expire in less than 3 weeks, the accelerator and decelerator effects have the largest impact on the value of an option. Near-the-money options that are close to expiration are extremely sensitive to small movements in the underlying stock. If we look at the chart below, we see that short-dated options (1 month) will have a higher gamma when they are near the current price of the stock (peak) compared to a 6-month option. Additionally, gamma is most sensitive and highest for options that are close to the current price (centre of chart) versus options that are either far “in-the-money” or far “out-of-the-money” (left side and right side).

Chart 1: Gamma Sensitivity vs. Time & Moneyness

Source: Options Industry Council

Gamma with Calls

For a call option, as the stock price rises, delta increases due to gamma, creating the option’s unlimited profit potential. As the stock continues to rise, delta will increase up to 1, creating an upside risk profile that resembles being long the stock. Gamma is effectively increasing the sensitivity of the option to the stock price as it rises, accelerating the gains. In contrast, as the stock price decreases, gamma will reduce delta towards 0. This creates the “limited risk” factor of a call option, since as the stock declines, the option becomes less sensitive to further declines, decelerating the losses. Consider the following example: $BMO’s June 2021 $116 call option has a delta of 0.50 and a gamma of 0.02. If $BMO increases by $1, the delta will increase by the gamma value to 0.52. If $BMO decreases by $1, the delta will decrease by the gamma value to 0.48.

Chart 2: BMO Call Option

Source: OptionsPlay

Gamma with Puts

For a put option, as a stock price declines, delta increases due to gamma, creating the substantial profit potential associated with a put option. As the stock continues to decline, delta will increase up to 1, creating an upside risk profile that resembles being short the stock. Gamma is effectively increasing the option’s sensitivity to the stock price as it declines, accelerating the gains. In contrast, as the stock rallies, gamma will reduce delta towards 0. This creates the “limited risk” factor of a put option, since as the stock rallies, the option becomes less sensitive to further rallies, decelerating the losses. Consider the following example: $BMO’s June 2021 $117 put option with a delta of -0.50 and a gamma of 0.02 will see delta move to -0.52 if $BMO decreases by $1 and to -0.48 if the price increases by $1.

Chart 3: BMO Put Option

Source: OptionsPlay

Long vs. Short Gamma

Option strategies can be divided into long gamma and short gamma strategies. Long calls and puts are considered long gamma strategies, while short calls and puts are short gamma strategies. Long gamma works in the investor’s favour when the stock moves in the expected direction by accelerating the gains. Moreover, if the stock moves in the opposite direction, it can decelerate the losses. Short gamma strategies work against the investor when the stock moves in the opposite direction than what is expected by accelerating losses, while decelerating gains as the stock moves in the expected direction.

Table: Gamma vs. Delta 

Source: OptionsPlay

While gamma can be a somewhat tricky concept to grasp at first, it is important for investors to understand the difference between long gamma and short gamma strategies and how this can impact changes in option pricing. The most important concept to remember is that gamma acts as an accelerator and decelerator on the gains and losses of an option as the stock moves higher and lower. While the four types of strategies can be confusing at first, long calls and puts are long gamma and short calls and puts are short gamma. As an option approaches expiration it will have a higher gamma, especially options with a strike price that is near the current price of the stock. This will result in an accelerator or decelerator that is very sensitive to the value of the option as the stock moves in favour of or against the investor’s desired direction.

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Originally Posted on June 1, 2021 – Gamma, Your Option’s Silent Accelerator and Decelerator Pedal

Dollars expressed are in CAD

Disclaimer:

The strategies presented in this blog are for information and training purposes only, and should not be interpreted as recommendations to buy or sell any security. As always, you should ensure that you are comfortable with the proposed scenarios and ready to assume all the risks before implementing an option strategy.

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