Gamma, or why the hedge has to start over

Definition

Gamma measures how much delta changes when the index moves 1 point. High gamma means delta moves fast, so the hedge goes stale fast.

Two properties to memorize:

• gamma is highest at the money and falls as you move away from it;
• at the money, gamma rises as expiration approaches. A 0DTE option at the money has enormous gamma; the same option three months out has little.

Long gamma, short gamma, and the direction of the hedge

An option buyer is long gamma: when price rises, his delta increases; when it falls, his delta decreases. An option seller is short gamma: the opposite.

For the rebalancing market maker, that yields two mechanical behaviors:

• Long gamma: price rises, his delta turns positive, he sells ES. Price falls, his delta turns negative, he buys. His hedging runs against the trend. It dampens.
• Short gamma: price rises, his delta turns negative, he has to buy. Price falls, he has to sell. His hedging runs with the trend. It amplifies.