By Guy Bower of www.guybower.com*
“The problem with change is that it just never stays the same.” That sounds like something Yogi Berra might have said. However, in options trading, not understanding change can be quite a risk.
In the last few articles, we have looked at the concept of the delta and, specifically, the interpretation of the delta of individual options and total positions. Once you have delta information (from many software packages or the AFR), it’s a pretty straightforward process understanding it all.
Here is a quick summary:
- The delta measures the variability of an options price versus small changes in the share price.
- Each individual option has its own delta.
- Delta is expressed in either decimal or percentage figures.
- Call deltas will range between 0 and +1.0 (or 0% and +100%). Out-of-the-money call deltas will approach zero, and in-the-money deltas will approach +1.0. An at-the-money call has a delta of close to +50% (or normally just a bit higher).
- Put deltas will range between 0 and -1.0 (or 0% and -100%). Out-of-the-money put deltas will approach zero, and in-the-money deltas will approach -1.0. An at-the-money put has a delta of close to -50% (or normally just a bit higher).
- The delta for the underlying is always +1.0 for a long position or -1.0 for a short position.
- A delta for a total position is calculated by simply adding up the individual deltas.
- Interpretation is simple: A delta of +50%, for example, will mean the option position will move 5c for every 10c move in the stock. A -50% delta would mean the option position loses 5c for a 10c gain in the stock.
OK, so the previous information is pretty straightforward stuff. The delta is an important figure to know with respect to understanding the position you have. Let’s say I have the following position:
| Long / Short | Contracts | Call / Put | Strike |
| Long | 1 | Call | $36.00 |
| Short | 2 | Call | $37.00 |
This is a ratio call spread and is a mildly bullish position, assuming these strike prices are out-of-the-money. Now, what if I were to ask you how the position would react to say a 30c increase in the price of the stock?
Here, you could hazard a guess, but you could only make a good estimate by knowing your position delta:
| Option | Option Delta | Position Delta |
| $36.00 call | 0.27 | +0.27 |
| $37.00 call | 0.15 | -0.15 * 2 |
| -0.03 or +3% |
Now, this position delta of -0.03 suggests a small increase in the stock will have little or no impact on the options position. In this respect, it is not a bullish position at all; it is close enough to neutral (zero delta). You would only know this by knowing your delta.
It is highly recommended that you start looking at the delta of your option(s). It will not take too long until you start to get a feel for the concept of delta.
Now, it is about at this point when a lot of literature on the delta will stop, possibly for fear of confusing the reader. We don’t have that fear here, right? To be honest, the next step is not really that complex and, normally, takes one or two re-reads to appreciate.
The thing is: Many think that, if you buy a call option with a delta of say +0.50, it’s fixed. For the whole time you keep that option, you will make 5c on every 10c gain in the share and, likewise, lose 5c for every 10c drop. No matter what the share price does, no matter how far it moves, your delta stays at +0.50. Wrong!
Think about this. This is not logical. As we know, a call with a delta of +0.50 is approximately at-the-money. A deep in-the-money call has a delta closer to +1.0. Now, what if after you buy this call, the market rallies and rallies and the option ends up to be deep in-the-money? Your delta would no longer be +0.50. It would be closer to +1.0.
In other words, your delta does not stay constant. A delta will change over time (a topic for another article), and a delta will change relative to changes in the underlying share price as previously illustrated.
You would not believe it, but there is a way to measure this change. In keeping with the Greek or mathematical theme, this one is called the gamma. We will have a quick look at the numerical examples here, but what is important is knowing the concept.
The gamma measures the rate of change of the delta, given a change in the underlying price.
At first thought, the gamma does not seem like a very important measurement, but it really is. If the delta never changed throughout the life of your position, risk would be very easy to quantify. But, if a market starts to trend, your delta can change dramatically. And, if the trend is not in the direction you want it to be, you could be in trouble!
Gamma Facts
- Like delta, the gamma of a total position is calculated by adding the sum of each component.
- Gamma is largest for at-the-money options (where deltas are close to 50%). Put another way, the delta of an option that is close to or at-the-money can rapidly change in response to a change in the underlying price.
- As the delta approaches zero or approaches +1.0 (-1.0 for puts), the gamma gets smaller. Put another way, the delta tends not to change very much the further in-the-money or out-of-the-money you go.
- The delta of the underlying is always equal to one. It never changes. Therefore, the gamma of the underlying is always zero
- Modern options trading software should be able to display individual and position gammas.
The best way to start thinking about gamma is not in its numerical form. Think about the concept itself, not its measurement. Think about your total delta when you buy some calls, sell a strangle or buy a bull call spread. Think about how small and large changes in the market will affect your delta and your profit and loss. A changing delta simply means a changing risk profile.
However, as a numerical example, let’s go back to that ratio call spread and see how gamma affects things. Let’s say we have the market trading at $34.50, and we expect, not a small move, but a large one, say, an increase of $1.50 in the very short term.
| Long / Short | Contracts | Call / Put | Strike | Position Delta at $34.50 | Position Delta at $36.00 |
| Long | 1 | Call | $36.00 | 0.27 | 0.52 |
| Short | 2 | Call | $37.00 | -0.15*2 | -0.36*2 |
| -0.03 | -0.20 |
See what has happened to the delta! In fact, we don’t even need to look at the option prices in this example to see things have moved against us. The deltas have increased in response to the change in the market price. This has meant that the delta for the total position has also changed. Forget the numerical measure of gamma. This is gamma right here.
It is clear that this position was close to delta neutral for a smaller movement in the market, but, given a big move, the whole picture changes. The change in the deltas for the two short positions has simply blown away the change in the delta on the single long call.
After an increase of $1.50 in the share price, the ratio call spread now looks entirely different. By reading the total position delta, you can see that it is nothing but a bearish position. The total position delta is negative, suggesting the position will improve on a fall in the market. (It should be noted that this position is also affected by time decay, but that’s another story.)
As an options trader, I think understanding how your position will move, given a change of any magnitude in the market, is paramount. This means you must know your delta and your gamma.
As an options trader, you must constantly re-evaluate your total risk and make sure it fits with your objectives. Do not be afraid to exit a position because the market has moved in such a way that your delta and gamma have moved against you.
For the novice, any new concept can be a little confusing. But, if you begin to understand that these figures are simply designed to measure change, you can start to appreciate them. Understanding also comes with practice. It is worth following the delta of an option or a number of options and watching how it moves.
Next time, we will look at the concept of how a delta will change relative to time. The purpose here will be to show how the profit or loss potential of a position can change, simply given the passage of time. It is a most important concept for any strategy.
*Reprinted (and modified) with permission from Guy Bower of www.guybower.com
