# Gamma hedging trading strategies : Part I

By Simon Gleadall, CEO of Volcube.

In this article we’ll look at some more ideas around gamma hedging and some of the typical ways traders formulate a gamma hedging strategy. At the outset, you should know that if anyone has discovered the optimal gamma hedging strategy, they are keeping it quiet! In all likelihood, there is no such thing as an optimal strategy; only strategies that work better in certain markets and at certain times than others. But it is essential for any options trader to understand the different approaches so that when opportunities arise, they grab them.

## Introduction to gamma hedging essentials

Let’s start with the useful formula that is worth committing to memory.

### Gamma profit = ½ Γ x²

where Γ is the portfolio gamma and x is the distance the underlying product price has moved. This is an approximation of the profit you make from gamma for a certain move in the spot price. Let’s take an easy example. If you have 100 gamma and the underlying product moves 1 point, by hedging your gamma at that point you would make ½ * 100 * 1² = 50. Depending on the contract multiplier of your options, this could be $50 or $5000 or whatever. Let’s say $50 for now. The ‘half gamma x squared’ formula is a useful one to keep up your sleeve.

The most revealing part of this formula is the ‘squared’ term. Look at our profit from 100 gamma in a spot price move half as far. Assume the spot price moves 0.50 instead of 1. Now the formula tells us our gamma profits are only 12.5. (½ * 100 * 0.5² = 12.5). So for half the size of move, we only make a quarter the profit. The ‘squared’ term is doing the exponential damage here. Look what happens if the spot moves 2 points instead of 1. Double the gamma profits? No: (½ * 100 * 2² = 200). **Profits quadrupled!** This is the most important aspect of gamma trading and hedging. Profits are not linear; they are exponential. Spot price travelling twice as far before you hedge leads to four times the profit. Half as far, and profits are quartered. 10 times as far and you could be retiring early.

Lastly, remember that the short gamma situation is exactly reversed. For convenience, in these articles we will generally take the perspective of the long gamma position but the above example means precisely the same but in reverse; *losses* are a quarter as big for short gamma hedges half the distance away and four times as big for moves twice as far. Moves 10 times as far and you could be retiring early, but perhaps not to your yacht moored at your private tropical island.