how delta hedging works
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 exchange traded fund etf shares investors may want to offset their risk of moving in the option or the underlying stock by using delta hedging strategies more advanced options 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 any exposure to the risk of an asset delta is a ratio between the change in the price of an options contract and the corresponding movement of the underlying asset s value so 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 let s assume 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 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 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 has a strike that s equal to the stock s price 1reaching delta neutralan 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 delta gamma hedging is closely related to delta hedging it 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 a brief primer on optionsthe value of an option is measured by the amount of its premium which is 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 asset 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 contract equals 100 shares of the underlying stock or asset holders of american style options 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 expiration date also depending on the value of the option the holder of either style of options may decide to sell their contract to another investor before expiration 2for 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 of 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 3delta hedging with equitiesan 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 4advantages and disadvantages of delta hedgingdelta 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 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 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 an option s time value impacts the premium cost for that option since options with a lot of time value typically have higher premiums than those 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 5allows traders to hedge the risk of adverse price changes in a portfolioprotects profits from an option or stock position in the short term without unwinding the long term holdingnumerous transactions might be needed to constantly adjust the delta hedge leading to costly feesover hedging may occur if the delta is offset by too much or the markets change unexpectedlyexample of delta hedginglet 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 represents 100 shares of ge s stock the stock declines considerably and the trader has a profit on the put option then recent events push the stock s price higher however the trader sees this rise as a short term event and expects the stock to fall again as a result a delta hedge is put in place to help protect the gains in the put option ge s put option 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 investor buys 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 