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Definition of Delta Hedging Delta hedging is a strategy in which an investor hedges the risk of a price fluctuation in an option by taking an offsetting position in the underlying security. That means that if the price of the option changes, the underlying asset will move in the opposite direction. The loss on the price of the option will be offset by the increase in the price of the underlying asset. If the position is perfectly hedged, the price fluctuations will be perfectly matched so that the same total dollar amount of loss on the option will be gained on the asset. In general, hedging is a strategy used to reduce risk. An investor hedges a position in a particular security to minimize the chance of a loss. The nature of a hedge, though, also means the investor will give up potential gains as well. For example, an investor with an options contract for Company ABC that benefits from the stock price falling would purchase shares of that company just in case the stock price rose. Understanding Delta Options Delta is the measure of an option’s price sensitivity to the underlying stock or security’s market price. It is the expected change in options price with a 1c change in security price (positive if it rises/falls with a rise/fall in market price; negative otherwise). For call options, the delta ranges between 0 and 1, while on put options, it ranges between -1 and 0. For example, for put options, a delta of -0.75 implies that the price of the option is expected to increase by 0.75, assuming the underlying asset falls by a dollar. The vice-versa is the same as well. 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. Trade Example: Hedging Long Stock With Long Puts In this example, we’ll look at a scenario where a trader owns 500 shares of stock. Being long 500 shares of stock results in a position delta of +500. If the trader wanted to reduce this directional exposure, they would have to add a strategy with negative delta. In this example, the negative delta strategy we’ll use is buying puts. Since the trader is long 500 shares of stock, we’ll purchase five -0.35 delta put options against the position. Here is how the position looks at the start of the period: As we can see here, buying five -0.35 delta puts against 500 shares of stock reduces the delta exposure by 35%. Let’s take a look at the P/L of each of these positions when the stock price falls: Charts courtesy of projectfinance.com. In the middle portion of this graph, the P/L of the long shares and the long puts are plotted separately. As you can see, when the stock price collapses, the long stock position loses money, but the long puts make money. In the lower portion of the graph, the combined P/L of the long stock and long puts is plotted. The key takeaway from this chart is that the stock position by itself experiences a drawdown greater than $10,000. However, with the long puts implemented as a delta hedge, the combined position only experiences a $4,000 drawdown at the lowest point. By adding the negative delta strategy of buying puts to the positive delta strategy of buying stock, the directional exposure is less significant. Pros of Delta Hedging Delta hedging provides the following benefits: It allows traders to hedge the risk of constant price fluctuations in a portfolio. It protects profits from an option or stock position in the short term while protecting long-term holdings. Cons of Delta Hedging Delta hedging provides the following disadvantages: Traders must continuously monitor and adjust the positions they enter. Depending on the volatility of the equity, the investor would need to respectively buy and sell securities to avoid being under- or over-hedged. Considering that there are transaction fees for each trade conducted, delta hedging can incur large expenses. What Is Delta-Gamma Hedging? Delta-gamma hedging is an options strategy. It is closely related to delta hedging. In delta-gamma hedging, delta and gamma hedges are combined to cut down on the risk associated with changes in the underlying asset. It also aims to reduce the risk in the delta itself. Remember that delta estimates the change in the price of a derivative while gamma describes the rate of change in an option's delta per one-point move in the price of the underlying asset. Conclusion Delta hedging is an options trading strategy that aims to hedge the directional risk associated with price movements in the underlying. It uses options to offset the risk of a single holding or an entire portfolio. The goal is to reach a delta neutral state and not have a directional bias. Delta hedging is a great way to manage the delta (price exposure) of both a position and your overall portfolio. For premium traders, it is a particularly powerful tool to keep your delta neutral positions and portfolio… delta neutral. There is more to cover on this topic. It is important to note, that before using options to delta hedge, you need to fully grasp the dynamic delta behaviors of your hedges. New traders should consider risk-defined (pre-delta hedged) positions at trade entry. It is important to match your strategy not only to your strategy’s criteria and objectives but also to your options trading ability and knowledge.

What is Delta Hedging? One major principle that many of the spread types share is the concept of delta hedging, a technique used to reduce the directional exposure of the underlying stock. This allows us to create lower risk positions. While many options spreads have built-in delta hedges, the positions Delta can still change with price movements by the underlying stock. We can also use delta hedging to maintain the desired delta set at trade entry. This is the more conventional definition and use of delta hedging. Let’s take a short put as an example: A significant risk to the premium seller is being Short Gamma. Gamma defines the expected change of delta for a $1 price move in the underlying. While gamma doesn’t affect the P/L of the position outright, it does change the delta of the position. The changing delta exposes the seller to more and more price risk until the position behaves like a long stock position. Instead of being subject to the markets every twist and turn, we can use delta hedging to maintain a more consistent delta despite price moves. This hedging approach can be applied at a trade level or a portfolio level so long as all the positions in the portfolio are beta weighted to a common reference. In short, as our position or beta-weighted portfolio delta becomes more negative or positive (whichever is the undesirable direction) we can “balance” the position using Delta Hedges. So let’s take a look at the various delta hedging methods we have at our disposal. Delta Hedges in Our Trading Quiver Here’s a short description (review) of the strategies used for creating positive delta hedges: Setup Description Long stock How it Hedges: 1 share of stock will provide 1 overall delta to the position. Stock provides “static delta”. Unlike with the use of options in Delta hedges, stock will maintain a delta of 1. It’s important to remember the option contract’s multiple – if the contract is for 100 shares of stock, then a deep-in-the-money option will have an option of “1” which is equivalent to 1x100 = 100. Trade-Offs: This is the most effective positive delta hedge but is coupled with high capital requirements. Furthermore, while you protect yourself from growing delta as prices increase, you could lose if the price action sharply reverses and your original options position is a defined-risk spread. Long calls How it Hedges: Like stock, the long call will hedge growing negative delta, but with a much lower capital requirement. Trade-offs: While this hedge is less capital intensive, it is still an expensive delta hedge to hold due to the negative theta from buying the calls. It is important to remember that when putting on this type of hedge, that you are still buying calls regardless of its title of a “hedge”. Short puts How it Hedges: Short puts have a positive delta which can offset any growing negative delta position. The premium received is the maximum protection against price moves. Trade-offs: This hedge is much cheaper than buying long calls or stock but has limited effectiveness for big price moves and is coupled with increased margin requirements and the commitment to buy the underlying at lower prices. Long call spreads How it Hedges: An alternative to a long call. This strategy involves the buying of a lower strike price call and the selling of a call with a higher strike price than the underlying asset (bullish). Trade-offs: A long call spread is a great hedge for a range. However, the long call spreads’ delta will reduce to 0 as the price increases past the short call in the spread. Short put spreads An alternative to a short put. With a similar tradeoff as seen between long calls and long call spreads. … and many others The strategies used for creating negative delta hedges include: Setup Description Short stock How it Hedges: Shorting stock means to sell stock that you do not own. This negative delta hedge is the inverse of long stock and hedges delta in price declines. Trade-Offs: This is the most effective negative delta hedge, but it is coupled not only with high margin requirements but also carry costs (interest and dividend obligation) related to borrowing the stock to short. Long puts How it Hedges: Exactly like the long call from the example above, but this time providing a growing delta hedge (if out of the money) up to -1 for each contract. Trade-offs: Like the long call, this hedge is less capital intensive than shorting stock, but still more expensive than shorting stock due to theta as well as the generally higher IV usually seen on the put side vs. the call side. Short calls How it Hedges: Short calls have negative delta and provide a hedge like short puts from the positive delta hedge. Trade-offs: This hedge is much cheaper than buying long puts, however, short calls are in theory “unlimited risk” positions. If the price action of the underlying reverses quickly (think earnings, etc) the trader could be looking at growing losses. Short call spreads How it Hedges: An alternative to a short call. This strategy involves the selling of a lower strike price call and the buying of a call with a higher strike price. Trade-offs: The short call spread provides some cheap negative delta right away, but the hedge is limited to certain trading ranges, similar to the long call spread. Long put spreads How it Hedges: An alternative to the long put and added to the position via a debit. Trade-offs: This one is like term life insurance vs. whole-life. It’s a lot cheaper, but the coverage is only good for a limited range. ..and many others Delta Hedging Example Using Best Buy Corporation (BBY) I will demonstrate how delta hedging works using Best Buy Corporation (NYSE: BBY) as the underlying asset. BBY was trading at around $77 a share at the time of this writing. Our demonstration will involve five series from the October 19 calls/puts to create the positive/negative hedges. To keep things simple in these examples, and focus on the delta hedging effects, we will assume that the trader is holding or shorted 100 shares of BBY at $77/share. This allows us to assume that the original position has a “Static Delta” of 100 and is much simpler than considering a position of options which would all with their own dynamic deltas. Selected October 19 Call/Put series for BBY Calls Strike Premium Implied Volatility Delta 72.50 6.63 32.49% +0.70727 75.00 5.75 31.89% +0.62246 77.50 3.90 31.14% +0.53083 80.00 3.15 30.74% +0.43739 82.50 2.26 30.32% +0.34763 Puts Strike Premium Implied Volatility Delta 72.50 0.77 34.88% –0.30216 75.00 1.49 34.06% –0.38159 77.50 2.58 33.66% –0.46722 80.00 4.03 33.54% –0.55275 82.50 5.82 33.60% –0.63300 For each call and put strike price shown, you can see its corresponding implied volatility (IV, which is the expected change in the value of the underlying stock) and delta. You can see a higher IV for the puts (where the average IV = 33.95%) than the calls (average IV = 31.32%). Position Delta Impact on $1 Movement The varying deltas are indicators of what price-change expectations you have of the position for each $1 of movement (either up or down). Gamma is an indicator that describes the change to the position delta with the same $1 price movement. Therefore, note that delta and gamma are reported as a snapshot in time and are both dynamic as time goes by and the underlying moves in price. Also, notice that the further in-the-money the option from the options chain above (up to 72.50 for the BBY calls and up to 82.50 for the BBY puts), the greater the premium and the greater the delta. So, a trader that delta hedges by selling 1 Oct 72.50 Call at 6.63 will offsets a delta of 100 from 100 shares of stock in the stock by nearly 71% (0.70727). This hedge is also known as “converting the position to a covered call”. Of course, this means that the trader has a short-term bearish outlook on BBY and a hope that an exercise does not take place before the expiration of the short call. If the short call expires worthless, the trader will pocket the $663 profit ($6.63 × 100). Alternatively, the use of spread (bull put/call, bear put/call) provides a way to offset delta and limit either upside or downside risk to a certain degree. We’ll explore some examples below demonstrate this point. Let’s take this information for BBY and apply it to selected examples of delta hedging to illustrate how the setup works. Setups for Positive and Negative Hedging Let’s look at how this hedging works a bit closer. For the purpose of the examples that follow, we will focus on two positive delta hedges: long call spread, and short put spreads And for the negative delta hedge, we will use the: short call spread, and long put spread. Long Call Spread – Positive Delta Hedge Here’s the scenario for using a Long Call Spread as a positive delta hedge: Buy 1 OCT 75 Call –$5.75 × 100 = –$575.00 Sell 1 OCT 80 Call +$3.15 × 100 = +$315.00 Hedge Initial Positive Delta = +0.62246 - 0.43739 = 0.1851 delta Net debit = –$2.60 × 100 = –$260.00 Maximum Hedge = Difference in strike prices (5) – Net debit (2.60) × 100 = $240.00 Short Put Spread – Positive Delta Hedge Here’s a positive delta hedge scenario using the Short Put spread as opposed to the Long Call spread: Sell 1 OCT 80 Put +$4.03 × 100 = +$403.00 Buy 1 OCT 75 Put –$1.49 × 100 = –$149.00 Hedge Initial Positive Delta = –0.38159 – (-0.55275) = 0.1712 delta Net credit = +$2.54 × 100 = +$254.00 Maximum Hedge = Net credit (2.54) × 100 = $254.00 Short Call Spread – Negative Delta Hedge Making a switch, let’s look at how a Short Call spread is used to create a negative delta hedge: Sell 1 OCT 75 Call +$5.75 × 100 = +$575.00 Buy 1 OCT 80 Call –$3.15 × 100 = –$315.00 Net credit = +$2.60 × 100 = +$260.00 Initial Negative Delta = -(+0.62246) +0.43739 = -0.1851 delta Maximum Hedge = Net credit (2.60) × 100 = $260.00 Long Put Spread – Negative Delta Hedge The last setup is an illustration of the use of the Long Put spread as a hedge to create a negative delta: Buy 1 OCT 80 Put –$4.03 × 100 = –$403.00 Sell 1 OCT 75 Put +$1.49 × 100 = +$149.00 Net debit = –$2.54 × 100 = –$254.00 Initial Negative Delta = –0.55275 – (–0.38159) = -0.1712 delta Maximum Hedge = Difference in strike prices (5) – Net debit (2.54) × 100 = $246.00 Conclusion I hope this article gave you a flavor of how delta hedging can be used and was a useful brush-up on the basic arithmetic of delta hedging. Delta hedging is an options trading strategy that aims to hedge the directional risk associated with price movements in the underlying. It uses options to offset the risk of a single holding or an entire portfolio. The goal is to reach a delta neutral state and not have a directional bias. Delta hedging is a great way to manage the delta (price exposure) of both a position and your overall portfolio. For premium traders, it is a particularly powerful tool to keep your delta neutral positions and portfolio… delta neutral. There is more to cover on this topic. It is important to note, that before using options to delta hedge, you need to fully grasp the dynamic delta behaviors of your hedges. New traders should consider risk-defined (pre-delta hedged) positions at trade entry. It is important to match your strategy not only to your strategy’s criteria and objectives but also to your options trading ability and knowledge. Drew Hilleshiem is the Co-Founder and CEO of OptionAutomator, an options trading technology startup offering a free options screener that leverages Multi-Criteria Decision Making (MCDM) algorithms to force-rank relevancy of daily options opportunities against user’s individual trading criteria. He is passionate to help close the gap between Wall Street and Main Street with both technology and blogging. You can follow Drew via @OptionAutomator on Twitter.