# What does it mean to be long gamma?

When you are "long gamma", your position will become "longer" as the price of the underlying asset increases and "shorter" as the underlying price decreases.

My intuition tells me that if you're long gamma, all that means is that if gamma increases, so does the value of your portfolio. Correct me if I'm wrong, but this seems to conflict with the quoted definition above (it is possible for gamma to decrease while the value of your portfolio goes up). Am I totally wrong? Does being long gamma simply mean your portfolio has a positive gamma as the quoted definition suggests?

• Long gamma means that the gamma of your portfolio is positive. Your gamma could get shorter (i.e. smaller, but still positive) while you make money and vice versa. – Tal Fishman Dec 14 '11 at 1:19
• I see, that makes perfect sense now. I guess my intuition was wrong (wouldn't be the first time, hehe). – sooprise Dec 14 '11 at 1:26

$$...\frac{1}{2}\frac{\partial^2C}{\partial S^2}(\Delta S)^2...$$
Notice that the $\Delta S$ (change in stock price) term is squared, meaning that the gamma term is positive when long regardless if $\Delta S$ is positive or negative. (This comes from the derivation of BS using Ito's Lemma.) What this means is that if you are long gamma (long a call or put option) then the P/L attributed to your position from gamma will increase regardless of the direction the stock moves.