Hedge with and for Options

Study Notes:

Hedging is one of the most popular uses of equity options. Options can be used to hedge an individual stock position or an entire portfolio. For example, an investor may choose to hedge a long Apple stock position against a downward move by purchasing downside puts in Apple or they may want to hedge a well-diversified portfolio with either index or index-based ETF options. An investor can use options to hedge both long and short positions. Hedging is defined as a strategy used to limit investment losses by taking an equal and opposite position in a related asset.

A good way to think about hedging is insurance. A person gets car insurance to protect against damage caused by an accident, or homeowners’ insurance to protect the value of their house in case it is damaged or destroyed. In both cases the investor is paying to protect their position. Questions that investors ask themselves are, how much they should pay to protect themselves and at what price level does the potential loss become worth the premium paid for hedging? It is the answer to those questions that determine the strike as well as deciding to hedge one-to-one or using the delta of the option to determine the risk level.

In this lesson we will focus on using options for hedging individual stocks as well as hedging an option with stock. As with any options strategies there are risks and rewards. The following examples are meant to suggest ways to use option hedging to potentially protect an established position from loss on an underlying movement that goes against the position. It is important to remember that each investor’s portfolio is different and may have different hedging needs. The following are broad based examples to help illustrate some hedging strategies. A common risk of hedging is that an investor may over hedge, buying too much protection and unnecessarily incur losses on the hedging instrument.

 Hedging a single equity position on a one-to-one basis is defined when:

• The investor who is long 100 shares of stock ABC would buy one put in ABC beneath the current trading price and be protected from any moves occurring from the stock moving below the strike price minus the premium paid for the option up until the option expires.
• The investor who is short 100 shares of stock XYZ would buy one call in XYZ above the current trading price and be protected from any losses occurring from the stock moving above the strike price plus the premium paid for the option up until the option expires.

Using this strategy, the investor can hedge every underlying share position individually within a portfolio.

Hedging using a one-to-one strategy

In this example the investor is long 1,000 shares of company ABC whose stock is trading at $100. If the stock price rises the value of the investment rises. However, if the stock falls the value of the stock drops and the investor loses money. In an extreme circumstance, the stock goes to zero and the investor loses their entire investment. The investor may want to hedge their long stock position by purchasing a downside put. Watch the PNL plot change as 10 downside puts at the 95 strike are added to the portfolio. The investor is no longer at risk of losing their entire investment if stock goes to zero. The loss is limited to ABC stock trading at or below the strike price of 95 minus the premium paid. No matter how low the stock goes prior to expiration the investor is protected from further loss. However, if the stock stays above the put strike up to expiration the investor is out by the amount of premium paid for the put option.

Let’s assume that the 95 put contract is trading at $1.50. Since equity options represent 100 shares of stock the overall cost of one put option contract is $150. To hedge their ABC long position of 1,000 shares using a one-to-one delta strategy the investor spent $1,500.

What is option delta?

Delta is defined as the rate of change in an option’s theoretical value for a one-unit change in the price of an underlying. A call option’s delta will be between 0 and 1.00 and a put option’s delta will be between 0 and –1.00. 0 represents the furthest out–of-the money option with little or no chance of having value at expiration and 1 or -1 represents the furthest in-the-money and having the same rate of change in value as the equity it is derived from. 

Consider a call option with a 0.20 delta (sometimes referred to as a 20 delta). Since an option contract equals 100 shares of stock, the value of the option should increase for a call by $0.20 for every dollar the stock goes up and decrease for a call by $0.20 every dollar the stock goes down. Conversely, for a put whose delta is 0.2 (or simply 20 delta) its value should increase by $0.20 for each $1 the stock declines and decrease in value by $0.20 for each $1 that the stock increases.

It also signifies that there is a 20% chance that the option will be in-the-money at expiration. Another way to think of it is the option is the equivalent value of 20 shares of stock given the strike price and the current stock price. The delta of the option is a dynamic value that will change as the stock price gets closer or further away to the strike price. This feature of delta is very important when using a delta neutral hedging strategy.

How to hedge a stock position using delta

Going back to our previous example, the investor is long 1,000 shares of ABC stock and wants to offset some of their downside risk from a downward move in the price of the stock. The investor decides to use the 95 put which is currently a 20 delta, which signifies that the stock currently has a 20% chance of trading at that value or lower at expiration. Instead of buying 10 puts they decide to hedge by purchasing two 95 puts for $1.50 each.

20% x 1,000 shares = expected value of 200 shares

2 puts = 200 shares

The overall price the investor pays for this protection is $300 versus the $1,500 paid in the previous example. As you can see from the chart the puts purchase offers some protection, but unlike buying 10 95 puts, the investor will continue to lose money if the stock drops below 95.

• The advantage of this strategy is that the investor is spending less on protection when they believe there is an 80% chance that the stock will close at expiration above 95 and the option will be worthless.
• The disadvantages are:
  •  If the stock falls toward the strike, the delta of the put increases and the trader must decide on whether they will purchase more of the puts at possibly a higher price than $1.50.  For example, stock has dropped $1.50, and the 20 delta puts the investor previously purchased are now a 40 delta, and are trading for $2.15. The investor needs to decide whether they purchase another two puts since there is now a 40% chance the puts will expire in-the-money or risk a greater chance of being unhedged?

(2 x $150) + (2 x $2.15) = $550

• The stock could continue to fall, and the investor may need to either purchase more puts at a higher level or run the increasing risk of losing more value of their equity position thus spending more than the initial $1,500 required to hedge on a one-to-one ratio.

Delta Neutral Option Trading

Delta is an important aspect of option trading. Many option traders prefer to remain delta neutral and will hedge their option positions with the corresponding shares of stock. The same logic applies as we discussed above. There are several ways to hedge an option trade both with other options and stock but the four most basic are:

• Long call positions can be hedged with short stock
• Long put positions can be hedged with long stock
• Short call positions can be hedged with long stock
•  Short put positions can be hedged with short stock

For example, the investor bought 10 ABC 105 calls, currently a 0.30 delta.  The overall delta of the trade is 300.

0.30 x 100 x 10 = 300

The investor then sells 300 shares of ABC stock, and their position is now delta neutral.

Call delta = 300

Stock Delta = -300

As time progresses toward expiration, the delta will change due to stock movement and/ or time decay. The investor will need to continue to monitor their position and trade more stock to remain delta neutral. To better illustrate this are two examples

• Stock ABC increases from $100 to $103; the 105 calls are now a 0.45 delta. For the position to remain delta neutral the investor would need to sell an additional 150 shares of stock.
• Stock ABC decreases from $100 to $97; and the 105 calls are now a 10 delta. For the position to remain delta neutral the investor would need to buy back 150 shares of stock.

Notice in each scenario the investor is either selling stock ABC for a higher price than the original trade or buying it back for a lower price than the original trade. If the investor was short the call the opposite would be true to remain delta neutral.

Hedging is a risk management strategy that enables the investor to offset potential losses in an individual asset or across an entire portfolio.