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Delta Neutral Trading - Condors etc.

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wayneL

VIVA LA LIBERTAD, CARAJO!
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There have been a couple of questions on delta neutral trading both on the forum and via PM; I'd promised to start a thread, but have been slack thus far, so here we go.

Feel free to ask questions as we go along.

But first we need to understand a couple of Greeks, starting with "delta" itself.

The short version:
The amount an option's price will change for a corresponding one-point change in the price of the underlying security.
Click to expand...
To explain it further, we need to understand that all trading instruments have delta. Delta is expressed as a fraction of 1 or -1 (Except if discussing "position delta" which we'll go into in a minute), therefore any derivative's rate of change is that fraction of change compared to the long underlying.

So if we're talking stock and stock options, we know that the delta of long stock is 1. Another way of looking at it is that for every dollar the stock goes up, we make one dollar... easy.

Therefore if we look at short stock; for every dollar the stock goes up, we will lose one dollar, so short stock has a delta of -1.

Options, in the vast majority of cases have a delta of some fraction of 1 or -1.

An ATM long call has a delta of approximately 0.5, so if the underlying stock goes up $1.00, then theoretically the option will go up by $0.50. Similarly, an ATM long put has a delta of approximately -0.5 and will lose $0.50 for every dollar the underlying rises.

When you write (short sell) options, the delta is reversed, just like if you short sell a stock; short calls have -delta and short puts have +delta.

Position delta (sometimes referred to as deltas) is the sum of all the individual deltas in a position.

So if you own 100 shares in a stock, your position delta is 100. Or it can be stated that you have 100 deltas.

If you own one ATM call contract (presuming a contract size of 100 options), your position delta is ~50, or 50 deltas.

to be continued.
 
So onto "Delta Neutral".

Delta neutral is simply a term to denote any position where your position delta is zero, though in common usage, it refers to a few select strategies which we will get into soon.

But just for the exercise, hear are a couple of delta neutral positions to help understand this concept before we go onto the next important Greek.

1/ Buy 100 XYZ stock and sell XYZ CFDs. We add the deltas of the two positions together, i.e. 100 + -100 = 0. Voila, delta neutral.

2/ Buy 100 XYZ stock, sell 1 XYZ ATM call contract and buy 1 XYZ ATM put contract, i.e. 100 + -50 + -50 = 0. (this position is called a conversion)

Barring any possible arbitrage profits, the above two positions have zero delta and have no possibility of profit or loss, no matter what the stock does, because the deltas all cancel each other out.

So what would possess someone to go delta neutral?

Enter - GAMMA.....
 
One of the things that separates the pricing of options as opposed to CFDs and other derivatives is that delta <> 1 or -1.

In fact option delta can vary significantly depending on where the striking price is in relation to the underlying price. As mentioned, a long ATM call option's delta is about 0.5, but a very very deep ITM call option can have a delta of 1 or very close to it. Likewise a very far OTM call option can have a delta of 0 or very close to it. Delta varies at all points in between.

The rate at which delta changes in response to changes in the price of the underlying is called Gamma. Gamma is expressed as the amount that delta changes per 1 point move in the underlying.

For example: Say we have a long call option whose delta is 0.5 and the stock moves up $1 and we now find that the delta is now 0.6. The gamma of that option is 0.1.

As all options have a theoretical gamma figure, we can calculate the change of delta for any position we have. In total this is called "position gamma". The position gamma of 1 contact of 100 options in the above example is 100 x 0.1 = 10. i.e the position delta of that one call contract will increase from 50 to 60 if the underlying moves up one dollar.
 
A couple of things I should add about gamma:

1/ You can only acquire gamma by acquiring an option position. Stocks, CFDs, Futures, Bonds etc do not have gamma.

2/ Gamma can also be positive or negative. All long options have positive gamma, whereas all short options have negative gamma.

Example

Let say we have one trader with an ATM call option with gamma as per the example in the above post. The delta of the option will be about +0.5 and a positive gamma of +0.1. Therefore as per the example, the delta of the option will rise to 0.6 if the underlying stock goes up $1.

But another trader has a short ATM put option, and like the long call option above, it also has a delta of +0.5. However the gamma is negative at -0.1. What this means is that the delta of the put option decreases to 0.4.

Sorry this is all so long winded, but it is vital in understanding delta neutral strategies.
 
So how do we profit from being delta neutral

Delta neutral strategies can be either long gamma (+gamma) or short gamma (-gamma).

In long gamma strategies it is the gamma that delivers the profit, by manufacturing deltas. The most common long gamma, delta neutral position is the long straddle. That is, long an ATM call and long an ATM put.

The atm long call has a delta of about +0.5, and the atm long put has a delta of about -0.5. We add the delta together to get the delta of the position: 0.5 + -0.5 = 0. So these two options cancel each other out.

However (and using the example above where gamma is 0.1) as the underlying moves, the delta of these options will change.

Lets say the underlying goes up one dollar. The delta of the call will become 0.6 and the delta of the put will become -0.4 as the gamma add o.1 to each delta.

So now the strategy has some delta, which has been manufactured by the gamma. 0.6 + -0.4 = 0.2

As the share value increases this change in overall delta accelerates the profit as the share moves away from the striking price, eventually, if the share goes far enough, to 1.0 as the long call's delta will increase from 0.5 to 1.0 and the put's delta increases from -.5 to 0

Likewise, if the share goes down one dollar the delta of the call will become 0.4 and the delta of the put will become -0.6.

So now the strategy has again some delta, negative this time, which has been manufactured by the gamma. 0.4 + -0.6 = -0.2

We want negative gamma if the stock is moving down and it will become -1.0 if the stock moves down far enough.

So in the long straddle's case, it is a bet each way on stock prices.

What's the catch?

Next Greek - Theta
 
Good stuff, Wayne. It takes a fair bit of time to write such detailed posts!

For those whose head is spinning - I suggest breaking it down and digesting small bits at a time. I well remember how my head hurt when reading options theory in the beginning. It's pretty much learning another languague and time, effort and exposure seems to be the only way to master it.

I initially used post-it notes on my monitor and found it a helpful reference when reading options theory eg.

+ delta: expect market to rise
- delta: expect market to fall

+ gamma: expect market to move in direction of long strike
- gamma: expect market to stay away from the short strike

+ vega: expect IV to rise
- vega: expect IV to fall

etc, etc...

 
You it explain it well Wayne, it's tough simplfying it so keep up the good work
 
G’Day Everyone.

Wayne on one his posts mentioned that one method of defending a short position that’s gone wrong would be to introduce some opposite delta in the form of buying/selling the underlying, effectively neutralizing delta (or close to neutralizing). At what stage should this be implemented?, i.e when the underlying hits your short contract strike or would you do this as the underlying approaches your strike, say 2 strikes out on a $30 contract?

I’m interested to hear from traders that use this form of defence on shorts, ATM all I use on naked positions that have gone bad is diagonal rolling, normally this works for me but I got caught on the hop recently with an early assignment.
 
Thanks peeps,

If anything is not clear or causes a , please jump inand ask for clarification.


That's such an important question, but if I can answer that one later, after we talk about short gamma strategies, ut would make more sense in the context of the thread.

We'll get there.
 

Dont pick up the underlying, depending on how far out I am & in what month I might start to defend by selling a spread to create a condor or if I like the way the greeks are set up a double diagonal of sorts. Difficult to say, different strategies for different set ups.
 
Just a quick point going back to "position delta". When you are in a delta neutral position, or one that started off neutral, think of position delta as "exposure" and analogous to holding that number of shares. If your position delta is +200, it is the same exposure as being long 200 shares of the underlying; -50 is like being short 50 shares.

This may be wanted or unwanted, depending on what you're trying to do, but always know this number.

Also think of it as your "hedge" ratio. In other words, to get back to delta neutral, this is the number of shares you need to trade to acquire the opposite deltas.

If you've got 30 deltas, you need to short 30 shares to acquire the -30 deltas to get back to 0, if that's what you need to do (depending on the strategy), or the equivalent deltas via options (long puts or short calls).
 
wayneL said:
So in the long straddle's case, it is a bet each way on stock prices.

What's the catch?

Next Greek - Theta
Click to expand...

Well anybody who has ever traded a straddle will know what the catch is; it's time decay.

With the straddle, because we have two long options per straddle, we get a double dose of it.

Theta measures the rate of time decay. Often "theta" is used in place of time decay, I'm guilty of this, but it's wrong, theta measures the rate of it.

I didn't want this to end up a treatise on greeks, so brushing over these really, just picking out the important bits as far as delta neutral is concerned. For a bit more discussion, refer to by blog post here: http://sigmaoptions.blogspot.com/2008/05/time-time-decay.html (really must develop that a bit more)

So if an option has a theta of 0.03, all other things being it will decay by three cents for that day. That means position theta will be $30 per contract of one hundred options and $60 per straddle.

So our straddle must manufacture deltas faster than theta to be profitable. Theta increases when at the money as time goes by.

So with long gamma strategies such as long straddles, we want a move... somewhere.... NOW .... FAST!

There is one further trap with long straddles and that is volatility crush... vega risk. I won't go too much into that now but here is a blog post on one such situation. - http://sigmaoptions.blogspot.com/2006/12/nike-straddle-just-do-it.html
 
We can also trade delta neutral strategies with gamma on the short side (-gamma), meaning that we will be writing options instead of buying them.

This is what the vast majority of delta neutral traders trade for a number of reasons.

Look at the long straddle from the previous post. The simplest short gamma delta neutral strategy (and maybe the least traded) is the short straddle. Instead of buying ATM puts and calls, we sell them instead.

With the long straddle, I said we need the underlying to go somewhere NOW and FAST. But the reality is that this isn't what usually happens and long term and systematic straddle buying is a loser... heavily. Most of the time stocks go up a little bit, retrace a little bit, go up a little bit again, then go down, etc, frustrating the straddle buyers into bankruptcy.

This is exactly what we want from the short straddle, for the stock to go nowhere, just sit there twiddling it's thumbs. Gamma is our enemy and time decay is our friend. We don't want that gamma manufacturing any deltas, and we want time decay gobbling up the option value so we can keep all, or most of the premium we collected.

But the problems with shorts straddles are:

  1. Gamma is highest at the money, and we don't want gamma.
  2. Theta is also highest ATM; we want that, but the gamma can cause problems.
  3. The risk is theoretically unlimited if that blinkin' underlying decides to take off

There are a number of things we can do to mitigate those risks, but I urge you not to get too carried away with the unlimited risk thingy. Remember that a straight stock purchase or short has more dollar risk of loss than an equivalent size short straddle, but the short straddle has risk in both directions.

...and just because we are trading options doesn't mean we're bloomin' stupid. The stock trader will have a stop loss, and so will we (or a means of defending and rescuing a profit ).
 
The other thing about short straddles is that if you let it go to expiry, and unless the stock pins itself exactly to the strike you've written, on of your written options is going to be in the money and you will most like end up with a stock position... not what we want.

So if you do write straddles you will want to either:

  1. Close early
  2. Roll out to the next expiry if it makes sense
  3. Metamorphose it into something else as stock movements develop

Taming Gamma (a little)

Because of the high gamma of the ATM strikes of the straddle, many traders will write strangles instead. This strategy writes OTM options instead of ATM options.

For example (with XYZ trading at $50):

Instead of writing a both calls and puts at the $50 strike, the strange might be constructed by writing a $45 put and a $55 call.

This widens out the break even points, reduces gamma and lessens the risk of one option finishing ITM. This will be at the expense of a lower maximum profit (presuming the same number of options are written), but maximum profit instead of being bang at $50, will be anywhere in between $45 and $55.

I do write straddles sometimes, but more often than not morph them to strangles via trading vertical spreads over the top.

Now we are firmly on the trail of the Condor.
 
The main objection to short straddles and strangles is the supposedly "unlimited" risk. I don't necessarily go along with that a 100%, but in many cases it is most certainly a worry.

A few examples where a short straddle/strangle could be like playing Russian roulette:

Oil and Energy products
Gold and precious metals
Coffee in the Brazil winter
Stocks with news risk
plus pretty much everything else.

So, how do we limit the risk on short straddles and strangles? The answer is very simple, we just go long some wings further otm than our sold strikes.

What we end up with is a sort of synthetic butterfly (if short a straddle) called an "iron" butterfly or a synthetic condor (if short a strangle) called an iron condor.

Voila! Limited risk. (BUT our greeks change a little bit)

Supposing we have the underlying at $50:

eg If you are short the $50 straddle, you buy the $45 put and the $55 call (all same expiry)

eg If you are short the $45 - $55 strangle, buy the $40 put and the $60 call.

So the natural butterfly is

Buy 1 x 45 call
Sell 2 x 50 calls
Buy 1 x 55 call (or can be done all puts)

and bought for a debit

The iron butterfly is

Buy 1 x 45 put
Sell 1 x 50 put
Sell 1 x 50 call
Buy 1 x 55 call

and sold for a credit

The natural condor

Buy 1 x 40 call
Sell 1 x 45 call
Sell 1 x 55 call
Buy 1 x 60 call (or all puts)

and bought for a debit

The iron condor

Buy 1 x 40 put
Sell 1 x 45 put
Sell 1 x 55 call
Buy 1 x 60 call

and sold for a credit

There are also other delta neutral strategies such as calender spreads and backspreads which we can go into if there is any interest. But I'll go into defense of these first.
 
quote by waynel "A few examples where a short straddle/strangle could be like playing Russian roulette:"

Oil and Energy products
Gold and precious metals
Coffee in the Brazil winter
Stocks with news risk
plus pretty much everything else.


hi wayne
thanks for all the info
i gather this i where indexes could come into play as they do not have the large volitile movement risk associated with stocks

the only thing in favor that i can see with stock is the ability to purchase to cover sold calls if needed and to take delivery of a stock in the event of a short put being assigned . this gives a small sense of security with these strageties for myself even though taking on the stock is a large risk in itself

the inability to utilise stock as a backup has kept me from dipping my toes into the index so i will be interested in your future comments and ideas on defending these positions

gary
 
hi waynel

just wondering whether there will be any further instalments to this thread as i have just dipped my toes into index options condors so would be interested in any further posts

gary
 
jackson8 said:
hi waynel

just wondering whether there will be any further instalments to this thread as i have just dipped my toes into index options condors so would be interested in any further posts

gary
Click to expand...

Yep,

Stay tuned Gary, I've just got to be in a concentrating mood so I dont spout bs.

Cheers
 
jackson8 said:
hi waynel

just wondering whether there will be any further instalments to this thread as i have just dipped my toes into index options condors so would be interested in any further posts

gary
Click to expand...

While your waiting for one of Waynes prolific posts, something to munch on.

Think about how you are going to manage your IC in the environment we are in, they tend to work best when there is little to no movement. Seeing that is not the case at the moment, you might want to think about tighter wings or heavier wings & be ready for adjustments.
 

thats the bit i am interested in how to make adjustments . at this point have only sold wotm calls with a protective bought call next strike above , but this has a very limited profit potential . so would like to sell bit closer to the money but i dont really know of the stragety if my strike is threatened

the way i see it i could buy an itm call to protect but this would leave me open to the down side , plus the loss of time premium that i would be paying for....or open another sold call above to reduce any loss over the threatened strike but that just introduces another strike which could be taken out in the event of a big move up , or just take the hit.
 
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