# Gamma

## What is Gamma

Gamma is the rate of change in an option’s delta per 1-point move in the underlying asset’s price. Gamma is an important measure of the convexity of a derivative’s value, in relation to the underlying. A delta hedge strategy seeks to reduce gamma in order to maintain a hedge over a wider price range. A consequence of reducing gamma, however, is that alpha will also be reduced.

## Basics of Gamma

Gamma is the first derivative of delta and is used when trying to gauge the price movement of an option, relative to the amount it is in or out of the money. In that same regard, gamma is the second derivative of an option’s price with respect to the underlying’s price. When the option being measured is deep in or out-of-the-money, gamma is small. When the option is near or at the money, gamma is at its largest. All options that are in a long position have a positive gamma, while all short options have negative gamma.

## Gamma Behavior

Since an option’s delta measure is only valid for a short period of time, gamma gives traders a more precise picture of how the option’s delta will change over time as the underlying price changes. Delta is how much the option price changes in respect to a change in the underlying asset’s price.

Gamma is an important metric because it corrects for convexity issues when engaging in hedging strategies. Some portfolio managers or traders may be involved with portfolios of such large values that even more precision is needed when engaged in hedging. A third-order derivative named “color” can be used. Color measures the rate of change of gamma and is important for maintaining a gamma-hedged portfolio.

### KEY TAKEAWAYS

- Gamma is the rate of change for an option’s delta based on a single-point move in the delta’s price.
- Gamma is at its highest when an option is at the money and is at its lowest when it is further away from the money.

## Example of Gamma

Suppose a stock is trading at $10 and its option has a delta of 0.5 and a gamma of 0.1. Then, for every 10 percent move in the stock’s price, the delta will be adjusted by a corresponding 10 percent. This means that a $1 increase will mean that the option’s delta will increase to 0.6. Likewise, a 10 percent decrease will result in a corresponding decline in the delta to 0.4.