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Experienced investors and traders hedge their portfolios using various approaches. Delta hedging ranks among the more widely used risk mitigation strategies, and we will discuss how delta hedging with options functions.

Retail traders may know the term hedge or hedging from hedge funds, which naturally hedge their portfolios if they implement long-short strategies. However, market participants must differentiate between operational procedures at hedge funds and what they can implement in personal portfolios. Delta hedging offers a useful hedging strategy but it is not well-suited for all investors and traders.

We will discuss how to delta hedge, cover the advantages and disadvantages of a delta hedging strategy, evaluate delta-neutral hedging, and provide a delta hedging example to help you decide if this strategy is appropriate for your risk management.

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Delta hedging is an options strategy that attempts to lower directional risk associated with price action in the underlying asset.

- Delta is a risk metric option traders use to estimate how a one-point move in the underlying asset, for example, a $1 move in Company ABC from $35 to $36, will impact the option price.
- Call options will have a value between 0.00 and 1.00, and the closer the contract moves to its expiry date and time, the closer the delta for in-the-money call options will move to 1.00. Put options range between 0.00 and -1.00, and the delta for in-the-money put options moves closer to -1.00 as the contract approaches its expiry date and time.
- Delta also provides relevant information on achieving the desired hedge ratio and estimates if an option will finish in-the-money or out-of-the-money.
- Hedging refers to lowering market risk through various strategies. It is an active strategy and requires ongoing monitoring and adjusting, making it most suitable for advanced, full-time traders.

Market participants who use delta hedging often want to accomplish a delta-neutral portfolio, having no directional bias. While delta hedging can lower or eliminate directional risk, it cannot shield portfolios against the time decay of options or market volatility. Therefore, many investors and traders who prefer delta hedging implement a delta-gamma hedge, which adds another layer of complexity to trading strategies.

Gamma is a derivative of delta, and a delta-gamma hedge provides a directional hedge associated with the underlying asset, via the delta component, and price fluctuations in delta, via the gamma component.

The core of delta hedging, and the most simplified approach, is a market participant who buys and sells call and put options and then mitigates directional risk by buying or selling an equal amount of the underlying security.

#### An Example of Delta Hedging a Call Option

- Assume a trader buys one call option in Company ABC
- The delta is 0.70
- The trader wants to implement a delta hedge to achieve a delta-neutral portfolio

Therefore:

- A trader would sell 70 shares of Company ABC to achieve a delta hedge since one option contract equals 100 shares
- In this example, a $1 change in the share price of Company ABC in a portfolio will result in a $70 move, equal to holding one call option with a delta of 0.70
- Since the trader bought a call option and sold 70 shares of the underlying security, the portfolio is delta-neutral

Using a delta hedge for put options follows the same principle, with two differences. The delta of a put option is negative, for example, -0.70, and the trader would buy 70 shares of the underlying asset.

Financial businesses may use delta hedging to mitigate the directional risk of price movements in the underlying asset to option contracts. It also offers an opportunity to profit from short-term counter-positions moves while keeping longer-term positions intact. The final usage depends on the sub-sector of the financial businesses.

For example, a hedge fund will use delta hedging to shield its portfolio from unexpected price moves and profit from short-term fluctuations. A commodity firm could seek to lock in long-term contracts and protect against daily price variations.

Delta hedging options strategies offer an insurance policy against directional market risk but also carry costs, which can counter any positive impacts of delta hedging. Financial businesses use delta hedging to achieve desired hedge ratios in line with their risk management protocols or to estimate whether options contracts will finish in-the-money or out-of-the-money.

It requires ongoing monitoring and adjusting of delta hedges to maintain ratios. The time-consuming and labor-intensive effort requires financial companies to either employ a dedicated delta hedging team or make a considerable investment into automated delta hedging software that requires less supervision, often manageable by one or two individuals.

Below are two examples of delta hedging, one where a trader uses equities to hedge options and the other where a trader uses options to hedge equities.

- Assume a trader has one put option in Company ABC
- The delta is -0.70

Therefore:

- Buying 70 shares in Company ABC achieves delta-neutrality
- Buying 35 shares results in a hedge ratio of 50%

- Assume a trader buys 500 shares in Company ABC (delta equals 5.00)
- The delta of an associated put option is -0.50 or at-the-money

Therefore:

- Buying 10 put options results in a delta-neutral position
- Buying 5 put options achieve a 50% hedge ratio

Before evaluating option delta hedging, market participants must understand option contracts, how delta functions, what it reveals, know its shortfalls, and then consider delta hedging as a risk mitigation approach.

Delta is one of the five Greek letters derivative traders use to evaluate options, assess risk, and implement as part of their trading strategies. The other four are gamma, theta, vega, and rho, where gamma is often part of delta hedging, which we will explain later.

Delta tells option traders how much the price will move if the underlying asset moves by one point. It also provides the hedge ratio and a probability for option contracts to finish in-the-money (ITM) or out-of-the-money (OTM).

Options contracts grant holders the right but not the obligation to exercise the option at the strike price. American-style option contracts equal 100 shares, an important metric to consider when delta hedging.

Traders use call options if they believe the value of the underlying security will increase, which is why the delta for call options ranges from 0.00 to 1.00. For example, a trader buying a call option for Company ABC at $35 analyzed an upward move in price action. Should Company ABC move to $38 before the option contract expires, the option holder has the right but not the obligation to exercise the option, netting a profit of $3.00 per share or $300 since one contract equals 100 shares.

Put options function similarly but in the opposite direction, which is why they range between 0.00 and -1.00. For example, a trader buying a put option for Company ABC at $35 believes price action will contract. Should Company ABC move to $30 before the option contract expires, the option holder has the right but not the obligation to exercise the option, netting a profit of $5.00 per share or $500 since one contract equals 100 shares.

#### A Delta Example for a Call Option

- Assume Company ABC trades at $35
- An associated call option for Company ABC trades at $1.75
- The delta is 0.70

Therefore:

- A price move in Company ABC from $35 to $36 will move the options price by $0.70 since the delta is 0.70, or from $1.75 to $2.45

#### A Delta Example for a Put Option

- Assume Company ABC trades at $35
- An associated put option for Company ABC trades at $1.95
- The delta is -0.65

Therefore:

- A price movement in Company ABC, from $35 to $34, will move the options price by -$0.65, since the delta is -0.65, or from $1.95 to $1.30

Knowing the delta allows market participants to achieve desired hedge ratios. Traders can use a spreadsheet, but brokers usually provide delta directly from their trading platforms. Delta is not constant and requires ongoing adjustments to maintain a hedge ratio or delta-neutral portfolios. Traders must consider the trading costs associated with delta hedging.

Delta Δ = (Of – Oi) / (Sf – Si)

Where:

- Of = Final value of the option
- Oi = Initial value of the option
- Sf = Final value of the underlying stock
- Si = Initial value of the underlying stock

#### Delta Depends on Where the Option Trades

- In-the-money options (call options from 0.51 to 1.00 put options from -0.51 to -1.00), higher premium plus intrinsic value
- At-the-money (call options at 0.50 and put options at -0.50)
- Out-of-the-money (call options from 0.49 to 0.00 and put options from -0.49 to 0.00), lower premium, no intrinsic value

Most delta hedging mistakes derive from incorrect inputs in the Black-Scholes option pricing model, of which delta is one component. Volatility ranks as the most notable drawback and can cause trading mistakes and losses. Gamma attempts to counter delta hedging mistakes associated with volatility.

Delta hedging mistakes from the Black-Scholes option pricing model include the below assumptions:

- Constant values for the rate of risk-free return and volatility
- Continuous trading free of trading costs, ignoring liquidity risk and broker fees
- Lognormal pattern or geometric Brownian motion pattern
- No dividend payments
- No early exercise of options contracts, making delta unsustainable and less relevant for American-style options
- No margin requirement for short sellers
- No arbitrage trading
- Tax-free trading

Delta hedging errors, made by market participants, include:

- Overtrading
- Ignoring costs associated with delta hedging
- Lack of monitoring and adjustments of active delta hedges to maintain hedge ratios
- Lack of knowledge related to when to implement and when to break a delta hedge
- Insufficient trading capital

Investors and traders must consider the advantages and the disadvantages of delta hedging before considering it as part of their market strategy and risk management.

- Provides a portfolio hedge against short-term price fluctuations
- Protects profits of short-term positions
- Maintains long-term portfolio profitability
- Allows short-term counter-directional profit opportunities on long-term positions if the portfolio is not delta-neutral

- Time-consuming and labor-intensive
- Requires ongoing monitoring and adjustments of active delta hedges
- Trading costs can accumulate to make delta hedging unsustainable
- Delta constantly changes with each move in price action
- The chance of errors directly related to the limitations and incorrect assumptions of the Black-Scholes option pricing model
- Requires gamma to create a delta-gamma hedge and counter some of the Black-Scholes option pricing model errors
- A danger of overtrading with underfunded trading accounts
- Lack of knowledge by market participants about when to use a delta hedge and when to break it
- Effective and efficient delta hedging requires costly software to assist with the monitoring, adjustment, and execution of a delta hedge

Delta hedging offers market participants a risk management strategy to protect portfolios against short-term directional risk with options contracts. Given the time and labor-intensive nature of delta hedging, beginner traders should consider if they have the trading infrastructure to delta hedge. Potentially high trading costs are another drawback and given the limitations and flaws of the Black-Scholes option pricing model, of which delta is one component, a gamma hedge becomes necessary to cover some of the shortfalls of delta hedging.

**When should you use delta hedging?**

Delta hedging suits experienced traders who want to protect their long-term portfolio holdings against short-term price fluctuations. It also benefits short-term traders who want to profit from counter-position directional moves via derivative contracts while maintaining long-term physical positions.

**When shouldn’t you use delta hedging?**

Beginner traders should not use delta hedging, as they lack the knowledge on when to apply a delta hedge and when to break it. They often do not have the necessary trading infrastructure and cannot commit the required time and capital. Market participants who do not understand the flaws and limitations of the Black-Scholes option pricing model should also avoid delta hedging.

**Why do commodity investors use delta hedging?**

Commodity traders may use delta hedging and a delta spread to secure long-term contracts, protect them against short-term price movements, and profit from price action.

**How do you conduct a delta hedge?**

Assume a trader buys one call option in Company ABC with a delta of 0.70. Achieving a delta hedge would have the trader sell shares in Company ABC. For example, selling 35 shares would result in a hedge ratio of 50%, while selling 70 shares creates a delta-neutral position.

**How do you practice delta hedging?**

There is no substitute for learning by placing delta hedges in live trading accounts, with real money, under developing market conditions. Many sources will point beginners to a demo account to practice delta hedging. Since the trading psychology component does not apply, a demo account fails to provide valuable educational lessons.

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