Long Gamma and Short Gamma Explained
The gamma of an option indicates how an option's delta is expected to change when the stock price changes.
However, long gamma or short gamma take things a step further and indicate whether an option position's delta will become more positive or more negative when the stock price changes. A long gamma position is any option position with positive gamma exposure, while a short gamma position is any option position with negative gamma exposure. More specifically:
A position with positive gamma (long gamma) indicates the position's delta will increase when the stock price rises, and decrease when the stock price falls.
A position with negative gamma (short gamma) indicates the position's delta will decrease when the stock price rises, and increase when the stock price falls.
When the stock price increases, gamma is added to delta. Conversely, gamma is subtracted from delta when the stock price decreases. As a result, the delta of long gamma strategies changes in the same direction as the stock price, and the delta of short gamma strategies changes in the opposite direction as the stock price.
To explain these concepts in more detail, let's walk through some basic examples.
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Long Gamma Example
Position | Position Delta | Position Gamma | New Delta: $1 Share Increase | New Delta: $1 Share Decrease |
|---|---|---|---|---|
Long Call | +75 | +3 | +78 | +72 |
Long Put | -50 | +5 | -45 | -55 |
In this table, the positions with positive gamma are said to be long gamma. As you can see here, long gamma positions benefit when the stock price moves in favor of the position because the directional exposure of the position grows in the same direction as the stock price.
To demonstrate this concept, let's look at some real examples.
The following visual demonstrates how a long call's delta increases as the stock price increases:
As we can see here, the long call's position delta grows from +25 to +75 as the stock price increases. With a delta of +25, the long call trader is expected to make $25 for each $1 increase in the stock price, and lose $25 for each $1 decrease in the stock price.
However, when the delta grows to +75, the long call trader is expected to profit by $75 when the share price rises by $1 and lose $75 when the share price falls by $1.
So, the long call trader wants the stock price to rise to profit from the increased positive delta exposure.
In the next visual, we'll look at a long put position. Note how the long put's position delta falls as the stock price decreases.
As we can see here, the long put's position delta falls from -37 to -80 as the stock price decreases. With a delta of -37, the long put trader is expected to make $37 for each $1 decrease in the stock price, and lose $37 for each $1 increase in the stock price.
However, when the delta falls to -80, the long put trader is expected to profit by $80 when the share price falls by $1 and lose $80 when the share price rises by $1. So, a long put trader wants the stock price to fall to profit from the increased negative delta exposured.
Short Gamma Example
Position | Position Delta | Position Gamma | New Delta: $1 Share Increase | New Delta: $1 Share Decrease |
|---|---|---|---|---|
Short Call | -25 | -3 | -28 | -22 |
Short Put | +30 | -4 | +26 | +34 |
The positions with negative gamma are said to be "short gamma." As you can see here, short gamma positions are harmed when the stock price moves against the position because the directional exposure of the position grows in the opposite direction as the stock price movements.
Let's look at some real examples to demonstrate short gamma.
The following visual illustrates how the position delta of a short call grows more negative when the stock price increases:
As we can see here, the short call's position delta falls from -27 to -85 as the stock price rises. With a delta of -27, the short call trader is expected to lose $27 for each $1 increase in the stock price. However, when the delta falls to -85, the short call trader is expected to lose $85 when the share price rises by $1. So, a short call trader does not want the stock price to increase because their losses will become more significant if the stock price continues to rise.
Next, we'll look at a short put position. Note how the position's delta increases as the stock price decreases.
As we can see here, the short put's position delta rises from +30 to +80 as the stock price falls. With a delta of +30, the short put trader is expected to lose $30 for each $1 decrease in the stock price.
However, when the delta rises to +80, the short put trader is expected to lose $80 when the share price falls by $1. So, a short put trader does not want the stock price to fall because their losses will become more significant if the stock price continues to decrease.