Delta Hedging

What Is Delta Hedging?

Delta hedging is an options trading strategy that aims to reduce, or hedge, the directional risk associated with price movements in the underlying asset. The approach uses options to offset the risk to either a single other option holding or an entire portfolio of holdings. The investor tries to reach a delta neutral state and not have a directional bias on the hedge.

Closely related is delta-gamma hedging, which is an options strategy that combines both delta and gamma hedges to mitigate the risk of changes in the underlying asset and in the delta itself.

Understanding Delta Hedging

The most basic type of delta hedging involves an investor who buys or sells options, and then offsets the delta risk by buying or selling an equivalent amount of stock or ETF shares. Investors may want to offset their risk of move in the option or the underlying stock by using delta hedging strategies. More advanced option strategies seek to trade volatility through the use of delta neutral trading strategies. Since delta hedging attempts to neutralize or reduce the extent of the move in an option's price relative to the asset's price, it requires a constant rebalancing of the hedge. Delta hedging is a complex strategy mainly used by institutional traders and investment banks.

The delta represents the change in the value of an option in relation to the movement in the market price of the underlying asset. Hedges are investments — usually options — taken to offset risk exposure of an asset.

Delta Hedging Explained

Delta is a ratio between the change in the price of an options contract and the corresponding movement of the underlying asset's value. For example, if a stock option for XYZ shares has a delta of 0.45, if the underlying stock increases in market price by $1 per share, the option value on it will rise by $0.45 per share, all else being equivalent.

For the sake of discussion, let's assume that the options discussed have equities as their underlying security. Traders want to know an option's delta since it can tell them how much the value of the option or the premium will rise or fall with a move in the stock's price. The theoretical change in premium for each basis point or $1 change in the price of the underlying is the delta, while the relationship between the two movements is the hedge ratio.

The delta of a call option ranges between zero and one, while the delta of a put option ranges between negative one and zero. The price of a put option with a delta of -0.50 is expected to rise by 50 cents if the underlying asset falls by $1. The opposite is true, as well. For example, the price of a call option with a hedge ratio of 0.40 will rise 40% of the stock-price move if the price of the underlying stock increases by $1.

The behavior of delta is dependent on if it is:

A put option with a delta of -0.50 is considered at-the-money meaning the strike price of the option is equal to the underlying stock's price. Conversely, a call option with a 0.50 delta is has a strike that's equal to the stock's price.

Reaching Delta Neutral

An options position could be hedged with options exhibiting a delta that is opposite to that of the current options holding to maintain a delta neutral position. A delta neutral position is one in which the overall delta is zero, which minimizes the options' price movements in relation to the underlying asset.

For example, assume an investor holds one call option with a delta of 0.50, which indicates the option is at-the-money and wishes to maintain a delta neutral position. The investor could purchase an at-the-money put option with a delta of -0.50 to offset the positive delta, which would make the position have a delta of zero.

A Brief Primer on Options

The value of an option is measured by the amount of its premium — the fee paid for buying the contract. By holding the option, the investor or trader can exercise their rights to buy or sell 100 shares of the underlying but are not required to perform this action if it is not profitable to them. The price they will buy or sell at is known as the strike price and is set — along with the expiration date — at the time of purchase. Each options contract equals 100 shares of the underlying stock or asset.

American style option holders may exercise their rights at any time up to and including the expiration date. European style options allow the holder to exercise only on the date of expiration. Also, depending on the value of the option, the holder may decide to sell their contract to another investor before expiration.

For example, if a call option has a strike price of $30 and the underlying stock is trading at $40 at expiry, the option holder can convert 100 shares at the lesser strike price — $30. If they choose, they may then turn around and sell them on the open market for $40 for a profit. The profit would be $10 less the premium for the call option and any fees from the broker for placing the trades.

Put options are a bit more confusing but work in much the same way as the call option. Here, the holder expects the value of the underlying asset to deteriorate before the expiration. They may either hold the asset in their portfolio or borrow the shares from a broker.

Delta Hedging With Equities

An options position could also be delta hedged using shares of the underlying stock. One share of the underlying stock has a delta of one as the stock's value changes by $1. For example, assume an investor is long one call option on a stock with a delta of 0.75 — or 75 since options have a multiplier of 100.

In this case, the investor could delta hedge the call option by shorting 75 shares of the underlying stocks. In shorting, the investor borrows shares, sells those shares at the market to other investors, and later buys shares to return to the lender — at a hopefully lower price.

Pros and Cons of Delta Hedging

One of the primary drawbacks of delta hedging is the necessity of constantly watching and adjusting the positions involved. Depending on the movement of the stock, the trader has to frequently buy and sell securities to avoid being under or over hedged.

Also, the number of transactions involved in delta hedging can become expensive since trading fees are incurred as adjustments are made to the position. It can be particularly expensive when the hedging is done with options, as these can lose time value, sometimes trading lower than the underlying stock has increased.

Time value is a measure of how much time is left before an option's expiration whereby a trader can earn a profit. As time goes by and the expiration date draws near, the option loses time value since there's less time remaining to make a profit. As a result, the time value of an option impacts the premium cost for that option since options with a lot of time value will typically have higher premiums than ones with little time value. As time goes by, the value of the option changes, which can result in the need for increased delta hedging to maintain a delta-neutral strategy.

Delta hedging can benefit traders when they anticipate a strong move in the underlying stock but run the risk of being over hedged if the stock doesn't move as expected. If over hedged positions have to unwind, the trading costs increase.

Real World Example of Delta Hedging

Let's assume a trader wants to maintain a delta neutral position for investment in the stock of General Electric (GE). The investor owns — or is long one put option on GE. One option equals 100 shares of GE's stock.

The stock declines considerably, and the trader has a profit on the put option. However, recent events have pushed the stock's price higher. However, the trader sees this rise as a short-term event and expects the stock to fall again eventually. As a result, a delta hedge is put in place to help protect the gains in the put option.

GE's stock has a delta of -0.75, which is usually referred to as -75. The investor establishes a delta neutral position by purchasing 75 shares of the underlying stock. At $10 per share, the investors buy 75 shares of GE at the cost of $750 in total. Once the stock's recent rise has ended or events have changed in favor of the trader's put option position, the trader can remove the delta hedge.