Delta Neutral Hedging

In options trading, the "Greeks" provide valuable understanding of risk associated with a particular option.

Theta tells us how much we are receiving or paying every day, vega tells us how much we can gain or lose because of volatility, and delta tells us how much an option's value will change as the price of the underlying fluctuates. 

Delta is a somewhat unique "Greek," because the term may also be used to describe the directional exposure of a position. 

For example, if a trader buys a naked long call, this position will have a "long delta" because we gain as the underlying goes up. Here the risk is defined because the trader can lose only the premium he has paid for the call.

The term "delta neutral" refers to a strategic trading approach that attempts to neutralize directional exposure, using the underlying security of the option. In simple terms, trading delta neutral can help traders reduce their exposure if a position moves against them. However, he certainly has to pay a price for risk mitigation, which can be a substantial part of his profit.

Traders use Delta-neutral strategies to profit from either IV or from time decay of the options. Usually, traders purchase securities that are inversely related to their original position. In case of adverse price movement, the inversely related security will move in the opposite direction, acting as a hedge against the losses. Let’s take an example to understand it better.

Imagine that two different traders decide to invest in a certain stock, say XYZ Ltd. which is currently trading at ₹200 per share, and the company is set to report earnings in two weeks.

Intending to profit on a quick rise in the stock price after a good earnings report, both traders decide to purchase 200 options of the 220 strike calls that expire in three weeks. They each pay ₹5 for the 220 strike calls, which equates to an outflow of ₹(5*200) = ₹1000.

Suppose, Trader A decides to sit tight with the naked calls while Trader B decides to hedge himself and create a delta neutral position. This means that Trader B will use the underlying stock to “neutralize” the long delta exposure of the calls.

Trader A: Trader A purchases 200 of the 220 strike calls for ₹5. Trader A does not take any position in stock against the long calls. 

Trader B: Trader B purchases 200 of the 220 strike calls for ₹5. The 220 strike calls have an associated delta of .35, and Trader B decides to hedge the position "delta neutral." This means Trader B sells 70 shares of stock XYZ short against his call position.

Now let's look at some hypothetical situations for the day of earnings, and see how each of the respective traders (A and B) perform :

Scenario #1: Company XYZ reports fantastic earnings and the stock opens trading ₹240 after earnings are released. 

• Trader A: Trader A paid ₹5 for 200 calls that are now worth ₹20. Trader A makes a profit of ₹3,000 on the trade (15 x 200).
• Trader B: Trader B also paid ₹5 for 200 calls that are now worth ₹20. However, Trader B additionally sold 70 shares of stock XYZ short for ₹200/share. That means Trader B has made ₹3,000 on his call position, but lost ₹40/share on the short shares (40*70 = 2,800). Trader B, therefore, makes a profit of ₹200 on the trade (3000-2800).

Scenario #2: Company XYZ reports fantastic earnings, but simultaneously announces accounting irregularities at the firm that are currently being investigated. Stock XYZ opens at ₹180/share after earnings are released. 

• Trader A: Trader A paid ₹5 for 200 calls that are now worth nothing, very likely will expire worthless. Trader A will likely lose his entire ₹1,000 investment in the call premium.
• Trader B: Trader B also paid ₹5 for 200 calls that are now likely to expire worthless too. Trader B will likely lose his entire ₹1,000 investment in the call premium. However, Trader B also sold 70 shares of stock XYZ short for ₹200/share. That means Trader B has made a profit of ₹20/share on the short shares (20*70=1400). Trader B therefore makes a profit of ₹400 on the trade (1400-1000).

This shows how a delta-neutral trading approach affects profit and loss for a position.

Traders can use this framework to ensure they have deployed a position that matches their outlook, expectations, and risk profile. 

Any position, no matter how complex, is simply the sum of its parts. By breaking down the P/L of each component of a trade, traders can best understand how different moves in an underlying will affect the overall position, and more importantly, the bottom line.