What it means
Options are affected by several sensitivities, known as the Greeks. Delta measures how much an option's price changes for a small move in the underlying asset, and gamma measures how quickly delta itself changes.
A portfolio with high gamma sees its delta swing rapidly as the market moves. A delta neutral position is protected against small price moves at one moment in time, but if gamma is large, the position stops being neutral as soon as the price shifts.
The trader then has to trade again and again to rebalance. A gamma neutral portfolio reduces this problem, because delta stays close to zero across a wider range of prices.
To become gamma neutral, a trader adds options to offset the portfolio's gamma. The underlying shares or futures cannot do the job, since they have a gamma of zero and only affect delta.
The usual approach is to buy or sell a different option on the same asset, calculate the number needed to cancel the gamma, and then trade the underlying to restore delta neutrality. Market makers and options desks use this approach to manage risk when they hold large books of options.
It is particularly important when big price moves, scheduled events or approaching expiry make gamma high. Sellers of options are often short gamma, which means they lose when the market moves sharply in either direction, and gamma hedging reduces that exposure.
The nuance is that gamma neutrality is not free. The offsetting options cost money or earn less time decay income, and the hedge only works for the assumptions of the moment, so it must be monitored as volatility, time and prices change.
It also covers only small moves, and a very large jump can still cause losses.
In practice
Real-world examples.
Example
An options market maker has sold a large number of short-dated options and is short gamma. She buys a different set of options on the same stock to bring the book's gamma to zero. She then trades the stock to remove the leftover delta.
Example
A hedge fund expects a company results announcement to cause a big price jump. Its traders reduce the portfolio's gamma to near zero beforehand so that the delta does not swing wildly when the news arrives. They accept that the position will not profit much from the move either.
Example
A bank's trading desk runs a risk report each morning showing net delta, gamma and vega. The head of risk sets a limit on gamma so that no trader can build a position that would become unstable in a sharp market. The limit is reviewed every quarter.
Formula
Calculation
Number of hedge option contracts = - portfolio gamma / (hedge option gamma per share x shares per contract)
The result is then adjusted with the underlying to restore delta neutrality.
Suppose a portfolio has a gamma of -600 (its delta falls by 600 shares for every $1 rise in the underlying). A hedge call option has a gamma of 0.05 per share, and each contract covers 100 shares, so each contract adds 0.05 x 100 = 5 of gamma. Contracts needed = 600 / 5 = 120 bought. Net gamma = -600 + (120 x 5) = 0. If each call has a delta of 0.50, the 120 contracts add 120 x 100 x 0.50 = 6,000 shares of delta, so the trader sells 6,000 shares of the underlying to bring delta back to zero.Case study
Seen in the real world.
Tidewater Derivatives is an illustrative, fictional trading firm that sold a large number of options on an index. A sudden jump in the index showed that its delta hedge had stopped working, and the desk lost money chasing the market.
The head of risk asked the team to measure the book's gamma and found it was strongly negative. She instructed the desk to buy options to bring gamma close to zero, accept a smaller income from selling options, and rebalance delta twice a day.
In the illustrative follow-up, a similar jump happened a few weeks later, and the losses were a fraction of the first event. The firm accepted the cost of the hedging options as a form of insurance, and wrote that cost into its pricing.
Watch out
Common mistakes.
- Trying to fix gamma by trading the underlying asset, which only changes delta because shares and futures have no gamma.
- Assuming gamma neutral means risk free, when volatility changes, time decay and very large price jumps can still cause losses.
- Forgetting to rebalance delta after adding hedge options, which have their own delta.
Questions
People also ask.
What is the difference between delta neutral and gamma neutral?
Delta neutral protects against small price moves right now, while gamma neutral also keeps delta stable as prices change.
Why do sellers of options worry about gamma?
Short option positions lose when the market moves sharply, and gamma measures how fast those losses can build up.
Is gamma neutral hedging expensive?
It can be, because the options bought to cancel gamma cost money and can reduce the income earned from time decay.
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