Delta Neutral Trading

Delta Neutral Options Strategy

The delta of an option is the rate of change in an option's price relative to a one unit change in the price of the underlying asset. For example, if a call option has a delta of 0.35 and the price increases by one dollar, the option's price should increase by 35 cents.

In the example above, the option has a delta of 0.35. Traders and brokers refer to that as "35 deltas." Simply multiply the delta by 100 to make it a percentage. Please be aware of that common convention. However, make sure you understand that "35 deltas" really means 0.35.

For the purpose of our discussion, whenever we mention the delta of an option, we are referring to the actual decimal value because that is what's actually used in all mathematical models. --The PitMaster

What exactly is Delta Neutral?

The term "Delta Neutral" refers to any strategy where the sum of your deltas is equal to zero. For instance, if you buy 10 call options, each having a delta of 0.60, and you also buy 20 put options, each having a delta of -0.30 you have the following:

(10 x 0.60) + (20 x -0.30) = 6.00 + -6.00 = 0

Your position delta (total delta) is zero, which means you are delta neutral.

The technique you are about to learn, is just one application of delta neutral. It is a general trading approach that is used by some of the largest and most successful trading firms. It allows you to make money without having to forecast the direction of the market. You can use it on any market (stocks, futures, whatever), just as long as options are available and the market is moving. It doesn't matter whether or not the market is trending, but it won't work if the market is really flat.

The principle behind delta neutral is based upon the way an option's delta changes as the option moves further in or out of the money.

Consider the following example:

	Statistical Volatility	25.00%
	90 day Tbill rate	05.00%
	Option Strike Price	100
	Days remaining	30

Price	Call	Put	Delta
of	option	option	of
underlying	delta	delta	underlying

80	0.0013	-0.9987	1.0000
85	0.0148	-0.9852	1.0000
90	0.0843	-0.9157	1.0000
95	0.2668	-0.7332	1.0000
100	0.5371	-0.4629	1.0000
105	0.7805	-0.2195	1.0000
110	0.9226	-0.0774	1.0000
115	0.9795	-0.0205	1.0000
120	0.9958	-0.0042	1.0000

You will notice the following characteristics of an option's delta:

	The absolute value of the delta increases as the option goes further in-the-money and decreases as the option goes out-of-the-money.
	At-the-money call and put options have a delta that is right around 0.50 and -0.50 respectively.
	Put options have a negative delta, which means if the price of an asset goes up, the price of a put option on that asset goes down.
	Deep in-the-money call options have a delta that approaches +1.00. Conversely, deep in-the-money put options have a delta that approaches -1.00.
	Deep out-of-the-money calls and puts have deltas that approach zero.
	The delta of the underlying asset itself always remains constant at 1.00.
	All of the deltas mentioned above assume that you are buying the options or the underlying asset, that is, you have a long position. If instead, you sold the options or the asset, establishing a short position, all of the deltas would be reversed. In the example above, if you sold a call option with a strike price of 100, and the price of the underlying asset was 110, the delta would be 0.9226 x -1 = -0.9226.
	If you short the underlying, the delta would be -1.0 instead of +1.0.

Keeping all of this in mind, we can construct the following delta neutral trade:

	Tbond futures price	110
	Statistical Volatility	8.00%
	90 day Tbill rate	5.00%
	Option Strike Price	110
	Days remaining	30

Price	Option	Option
of	theoretical	delta
underlying	price

108	2.14	-0.73
109	1.43	-0.58
110	0.91	-0.42
111	0.53	-0.28
112	0.28	-0.16

Buy 2 Tbond futures at 110
Buy 5 Tbond futures put options (110 strike price) at 0.91 each

Delta of Tbond futures	2 x 1.00	= -2.00
Delta of put options	5 x -0.42	= -2.10
Total position delta	2.00 + -2.10	= -0.10

How it works:

If Tbond futures increase from 110 up to 112:

	Profit on Tbonds = 2 x 2.00 = 4.00
	The put options will decrease from 0.91 down to 0.28 (each)
	Loss on put options = 5 x (0.91 - 0.28) = 5 x 0.63 = 3.15
	Net profit = 4.00 - 3.15 = 0.85

If Tbond futures decrease from 110 down to 108:

	Loss on Tbonds = 2 x 2.00 = 4.00
	The put options will increase from 0.91 up to 2.14 (each)
	Profit on put options = 5 x (2.14 - 0.91) = 5 x 1.23 = 6.15
	Net profit = 6.15 - 4.00 = 2.15

We can summarize this delta neutral approach as follows:

If you buy the underlying and buy put options so your position is delta neutral:

	When the market goes up, you have a profit on the underlying and you have a smaller loss on the options (because their delta decreased), so you wind up with a net profit.
	When the market goes down, you have a loss on the underlying but you have a bigger profit on the options (because their delta increased), so again you have a net profit.

If you sell (short) the underlying and buy call options so your position is delta neutral:

	When the market goes up, you have a loss on the underlying but again you have a bigger profit on the options (their delta increased), so you have a net profit.
	When the market goes down, you have a profit on the underlying but once again, you have a smaller loss on the options (their delta decreased), so you still have a net profit.

When you do this kind of delta neutral trading, you need to follow a few rules:

	Always initiate the position with a total position delta of zero or as close to zero as possible. So, your starting position is "delta neutral."
	When the market moves enough so your total position delta has increased or decreased by at least +1.00 or -1.00 delta (or more), you make an "adjustment" by buying or selling more of the underlying asset to get your position back to delta neutral. You can also sell off some of your options to get back to delta neutral. But the point is, you make profits consistently by making these adjustments.
	If the price of the underlying asset doesn't move around much, close out the entire position. You need some price action for this approach to work. If the market just sits there, time decay will eat away at this position.
	Keep an eye on the implied volatility of the options you're using. If it moves toward the high end of its 2 year range, stay away from this position for a while. Otherwise, you might have excessive time decay in your options when the implied volatility starts to drop.
	The options you buy should have at least 30-60 days remaining before expiration. Remember that time decay accelerates as the option's expiration date approaches, so if you allow more time, you minimize the time decay.
	As you have seen, these trade positions benefit by price movement in the underlying asset. It puts you in the enviable position of being able to take full advantage of big price moves, in any direction. In fact, when the Dow dropped 171 points recently, delta neutral positions in the S&P 500 did extremely well.