Gamma Hedging

It sounds like a term describing when you help your grandma trim her topiaries (which itself sounds like a euphemism of some kind...best to just move on).

Gamma hedging is a technique used in the derivatives market. The process gets complicated to describe, mostly because gamma itself is somewhat esoteric.

Let's start with hedging. In general, hedging involves limiting the risk of some situation.

You're playing roulette. You put some money on black 22. Obviously, you have a low chance of hitting this bet, so you decide to hedge. You also put some money on red. Both bets can't win at once. If red hits, then the black 22 bet loses. If the ball lands on 22, then your red bet loses.

However, your losses for either bet are limited, because of the win you'll collect with the other bet. By placing both bets, you limit your losses.

Before we get to gamma, we have to say something about delta. And talking delta requires a bit of basics about derivatives, which are contracts based on some other asset. The most common forms are options and futures. Options give you the right to buy or sell an asset at some time down the road. So you might buy an option to purchase 100 barrels of oil at $72, with the option expiring in two months.

The price of your option is based on the price of the underlying asset. When oil prices go up, the value of your option goes up. Oil prices at $75 mean your option is in-the-money. You can purchase barrels at $72, sell them in the open market and pocket the difference.

Meanwhile, oil trading at $69 doesn't do you much good. Your option is out of the money...not something you want. As oil prices fall, so does the value of your option.

The relationship between the two prices is called delta. The amount of change in the price of an option compared to the price change in the underlying security...that ratio represents delta.

Okay, now we're ready for gamma. Gamma is a second derivative of delta. It represents the relationship between changes in the price of the underlying asset and changes in delta.

As prices change, so does delta. Prices near the barrier between in-the-money and out-of-the-money are more meaningful than if the price is way in one direction or another. So if oil is sitting at $85 a barrel and falls to $84 a barrel, that doesn't affect your option value too much. It's still well above $72. However, if oil is trading at $72.50 a barrel, then a drop to $71.50 makes a big difference in the price of your option.

So the goal of a gamma hedge is to hold delta constant. Gamma measures changes in delta...you want to lock that in place. You want gamma to remain steady. You are trying to get your option position closer to a situation called "gamma neutral."

By hedging gamma, you are making the delta constant...every dollar change in the underlying asset should have the same impact on the price of your option.

The first step to a gamma hedge is to hedge delta. If you hold an option to buy a stock, for instance, the easiest way to hedge delta is to take a short position in the underlying asset. So if you hold an option to purchase oil...at the same time, you put in a short sale on the spot price in oil.

This limits changes in delta. Generally speaking, a delta-hedged position is protected against smaller fluctuations in the price of the underlying asset. However, you are still vulnerable to sudden big swings in price. Neutralizing gamma protects against this.

To set up a gamma hedge, you would take an opposite options position at a different strike price. So if you have an option to purchase oil at $72 a barrel, you would sell an option at some other price (the price depending on how much you plan to hedge the gamma...complicated math gets utilized here).

Hedging a position completely is pointless. You end up with a series of positions where you break even no matter what happens. You might as well stay home and watch TV (think: betting the same amount on both black and red in roulette...though in that case, you still have to worry about zero and double-zero).

So most positions aren't hedged completely. The goal is to limit extremes, so you can have a more predictable outcome.