Gamma is the rate at which an option's delta changes relative to a one-dollar move in the underlying asset's price. If you own an option with a delta of 0.60 and a gamma of 0.05, a $1 increase in the stock price means your delta will rise to approximately 0.65. Gamma is the second derivative of the option's price with respect to the underlying asset—it measures the curvature of the price relationship rather than the slope itself.
How It Works
Gamma exists because options don't have a fixed delta. As the underlying asset moves, the delta changes, and gamma tells you the speed of that change. At-the-money (ATM) options have the highest gamma because small price movements create the biggest shifts in intrinsic value probability. Out-of-the-money (OTM) and in-the-money (ITM) options have lower gamma because they're further from the critical strike price threshold.
Gamma is always positive for long options and negative for short options. This asymmetry matters: when you're long gamma, you benefit from price swings in either direction. When you're short gamma, volatility works against you.
Why It Matters for Investors
Gamma risk is about hedging stability. If you use options to hedge a portfolio position, gamma tells you how often you'll need to rebalance. High gamma positions require frequent adjustments, creating transaction costs and slippage. Conversely, if you're speculating on volatility, high gamma amplifies your gains when you're right about direction.
For angel investors and venture-backed entrepreneurs using equity options for compensation or hedging, gamma explains why delta-hedged portfolios need constant maintenance. It's particularly relevant when implied volatility spikes—gamma risk becomes acute near expiration dates or around major corporate events.
Example
Imagine you buy a call option on a stock trading at $100 with a strike of $100. The delta is 0.50 and gamma is 0.03. If the stock rises to $101, your new delta is approximately 0.53 (0.50 + 0.03). If it rises to $102, delta becomes roughly 0.56. But if the stock instead drops to $99, your delta falls to about 0.47. Gamma made your position more sensitive to directional moves—the delta didn't stay flat at 0.50.
Key Takeaways
- Gamma measures how quickly delta changes; it's the velocity of your hedge's effectiveness.
- At-the-money options carry the highest gamma; gamma decays as options move deeper ITM or OTM.
- Long gamma positions profit from volatility; short gamma positions lose money when markets move sharply.
- High gamma requires active rebalancing; low gamma means more stable delta hedging needs.