# Realizing profit with Gamma Trading doubt

Lets suppose we have a delta-neutral portfolio and that we want to trade the gamma.

If we are long gamma, we can profit from every rebalancing to keep the portfolio delta-neutral.

### Lets suppose the following portfolio:

• long 100 x call ATM (∆=50%, constant gamma = 10)
• short 50 x stocks ($100). ### 1) Underlying's prices goes down by$1:

• Call's delta goes down (∆=40%)

• I need only -40 stocks to remain delta-neutral, so I buy +10 stocks and realized immediate profit.

Gamma PnL = (1/2) * (10) * ($$1)^2=$$5 USD;

Or assuming that delta is discrete and goes from 50% to 40% immediately; -10*($$99-$$100) = $10 USD.  ### 2) Underlying's price goes up by$1:

• Call's delta goes up (∆=60%)

• I need -60 stocks to remain delta-neutral, so I sell more -10.

And we will sell this additional -10 in a price above that the initially sold.

If price goes down further, we will buy it, and again realize immediate profit.

### But what if the price just goes up?

If price's only goes up, and we close the position, we will finally have to buy the underlying, buying it for a higher price, losing money on the underlying by itself.

This loss in the underlying may or may not be followed by a profit on the options (call's price can goes up, but we have Vega, Theta, etc, that can make the option's value decrease).