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Delta-Neutral Trading

The Delta of a stock option is a measure of how much the option can be expected to gain or lose per $1 move in the stock price. A Delta-Neutral option position is one in which there is no gain or loss on the position due to stock price movement.

A stock investor may hear about the concept of Delta-Neutral trading and be completely mystified. This is because a stock investor cannot gain from a stock that doesn't move. If a trader is long stock, the stock must rise to make a gain. If a trader is short stock, the stock must fall to show a gain.

A perfectly Delta-Neutral stock position would be long and short the same number of shares of the same stock at the same time. No matter what the stock did, the overall position would not gain or lose.

A stock investor usually brings these ideas with him when he starts trading options. He looks for strategies that will benefit if a stock rises, or benefit if a stock falls. But options are affected by more than just stock price movement. Two of the most important things affecting options in addition to stock price are volatility and the passage of time.

This means an options trader has additional ways to profit. The options trader can profit from options that gain or lose value due to rising or falling volatility, and/or the trader can profit from options that gain or lose value due to the passage of time.

"Delta-Neutral" is a way of saying an options strategy is designed to profit from something besides stock movement. In fact, a Delta-Neutral trade is set up so it is NOT very affected by the stock moving a little bit higher or lower. Then the trader can focus on just the volatility, or just the passage of time, or both.

For instance, an options trader could set up a Delta-Neutral trade that included selling options that were historically overpriced. If the options then returned to normal pricing, even with the stock at the same price, the trader could close out the entire position with a gain.

Another Delta-Neutral trade would be to set up a Delta-Neutral position that included buying historically underpriced options. If the stock stays put, but the options return to normal pricing, the trade can be closed for a gain.

Using time decay to his advantage, the Delta-Neutral trader could set up a trade that included selling fairly valued options. If the stock price and volatility stay put, just the passage of time will reduce the value of the sold options, meaning he can close out the trade with a gain.

To understand how an entire position can be Delta-Neutral, you must understand:

  • What Delta means.
  • What the Delta is for each leg of a position.
  • What the total Delta of a position is.

The Delta of a stock or option means how much the stock or option can be expected to gain for each $1 movement in the stock. See The Option Greeks for more information about Delta if you need it.

Stock always has a Delta of 1, since a $1 gain in the stock means a $1 gain in a position consisting of one share of stock.

Calls have a Delta of anywhere from 0 to 1, since a $1 gain in the stock will result in either no price change for a very OTM call, or a higher price for the call if it is ITM or ATM.

Puts have a Delta of anywhere from 0 to -1, since a $1 gain in the stock will result in either no price change for a very OTM put, or a lower price for the put if it is ITM or ATM.

The Delta for each leg of a position is calculated by:

  • The individual Delta x the number of shares represented x (-1 if short).


  • Long 500 shares of stock = 1 x 500 = a leg Delta of 500.
  • Short 20 ATM calls = .5 x 2000 x -1 = a leg Delta of -1000.
  • Short 10 ATM puts = -.5 x 1000 x -1 = a leg Delta of 500.

The Delta of an entire position is the sum of the Delta for each leg. So if a trader had the position in the example above, the position Delta would be 500 - 1000 + 500 = 0. The position would be perfectly Delta Neutral at the current time. A graph of the position is shown below.

Delta Neutral Option Graph

Notice that the graph shows the stock could move anywhere from about $48.50 to $51.00 on the day of entry, without much of a gain or loss on the position. A relatively flat entry line near the stock price at entry is a hallmark of a Delta-Neutral position.

If a trader entered the position shown, he would be hoping for the stock price to stay close to where it is now. Then, just from the passage of time and not from stock price movement, he could take a good gain in just 20 days, as shown by the green time line. The reason for his gain on this particular trade is that he sold a total of 30 contracts of options. Since options lose value with the passage of time, all other things remaining equal, his sold options will be worth less 20 days from now, and he can buy them back for less than he sold them for, taking a gain.

Just establishing a Delta-Neutral option position is no guarantee of making gains. You can set up Delta-Neutral positions that lose because of options returning to a more normal volatility, or lose because of the passage of time. So before entering a Delta-Neutral position, the option trader needs to know exactly how the position will gain. Usually this means the trader must always sell overpriced options, buy underpriced options, and/or or sell time.

For instance, a straddle position might look Delta-Neutral when you enter it, but if you don't pay attention to volatility and time it would have a very tough time making a profit. If you buy overpriced calls and puts to make the straddle, they will both lose value if volatility returns to normal. And since a Straddle Purchase uses long options, the position is losing time value as each day passes.

Even if a position is Delta Neutral when entered, there is no guarantee it will stay that way. The stock price moving up means the calls will be more ITM, and therefore have a higher Delta, and the puts will be more OTM and therefore have a less negative Delta.

If the example stock moved up after entry, and the Delta on the calls rose to .6 and the Delta on the puts rose to -.4, the position would be:

  • Long 500 shares of stock = 1 x 500 = a leg Delta of 500.
  • Short 20 ATM calls = .6 x 2000 x -1 = a leg Delta of -1200.
  • Short 10 ATM puts = -.4 x 1000 x -1 = a leg Delta of 400.

And the overall Delta is now 500 - 1200 + 400 = -300.

A position with overall negative Delta means the position will lose value if the stock goes up and other factors remain the same. This can be seen from a position consisting of just short stock. Short stock has a negative position Delta, and it will lose value if the stock rises.

An overall negative Delta is also an estimate of how much the position will lose if the stock rises by $1. A position with a position Delta of -300 can be expected to lose $300 if the stock rises by $1.

A position with overall positive Delta means the position will gain value if the stock goes up and other factors remain the same. A total position Delta of 100 would mean the position can be expected to gain $100 if the stock rises $1.

Some practitioners of Delta Neutral trading will simply close out a position if the position Delta moves too far away from being neutral. They may have a gain or a loss at the time, but they use the position Delta no longer being neutral as a reason for exit in either case.

Others may adjust the trade so it is once again Delta-Neutral, and from that point they can continue to benefit from volatility or time decay working in their favor. The trade from the example, that moved to a position Delta of -300, could be adjusted back to neutral by buying 300 shares of stock, because 300 shares of stock have a Delta of 300. Or looked at another way, owning another 300 shares of stock will prevent the position from losing $300 by the stock going up $1.

Almost all successful practitioners of Delta-Neutral trading take gains early and small losses whenever they have them. They profit overall by having more and larger gains, and fewer and smaller losses. Let's look at the graph of a ten contract calendar call and see why taking gains early makes sense.

A Calendar Call is the classic Delta-Neutral strategy. It uses near-term short ATM calls, which for a ten contract position would have a leg Delta near -500, and far-term long ATM calls, which would have a leg Delta near 500, making the overall position Delta-Neutral. The goal is to profit from the passage of time, and not stock price movements.

Notice that on the day of entry, the blue time line is relatively flat, demonstrating the neutral positioning at that time. Even if the stock were to rise $3.65 on the day of entry, the position would only lose about $70.

With one week to expiration of the near options, the green time line is showing a position gain of about $500 with the stock at $50. Now if the stock rises $3.65, the gain would only be about $100. The same amount of stock movement causes a $400 loss of value instead of $70.

As the graph shows, the longer you hold on to a calendar call, the more gains you risk. If the stock were to be at $50 and then rise $3.65 on expiration day, you would see a gain of $1242 completely evaporate. For this reason, many calendar call traders either take a small loss whenever they have it, or close the position with a week remaining to the first expiration, no matter what. They know that they risk losing more and more of their gains on any move in the stock price, and that the risk increases every day.


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