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Delta Hedging Your Options Strategies


All traders begin with an introduction to call and put options.  However, it's rare (apart from short puts) that an experienced trader would use these contracts by themselves. Instead, we primarily trade options spreads. There are many benefits to spreads. The variety of spreads are targeted to various market criteria and market environments.

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:

 

  1. long call spread, and
  2. short put spreads

 

And for the negative delta hedge, we will use the:

 

  1. short call spread, and
  2. 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 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.

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Thanks for your article Drew. I'm thinking you may not have picked up the correct price for the 75 calls in both your long call and short call spread examples thereby affecting your calculation of hedge value on both.

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