By Guy Bower of www.guybower.com*
In the first article of this four-part series, we had a quick look at the concept of the delta. You will recall that the delta is a measure of how an option will move, given a change in the underlying. We all know the term is thrown around quite a bit by some options advisors and most warrant issuers. But, there is a lot more to it than the simple definition might indicate.
Over the next few articles in this series, we will be showing the different ways to look at the delta. The last article laid the foundation of knowledge. This week’s does a little more of that by looking at the delta of a total position.
Delta is not just used for analyzing individual options, but positions that involve multiple options. That is, you can actually measure the delta for a total position rather than just one single option.
Let’s say you bought one NAB Oct $34.00 call and one Oct $35.00 call. In the table shown subsequently, we see these options have a delta of 0.59 and 0.39, respectively.
| October NAB options | ||
| Strike | Call | Put Delta |
| $30.00 | 1.00 | -0.02 |
| $31.00 | 0.96 | 0.00 |
| $32.00 | 0.90 | -0.23 |
| $33.00 | 0.79 | -0.23 |
| $34.00 | 0.59 | -0.40 |
| $35.00 | 0.39 | -0.62 |
| $36.00 | 0.20 | -0.83 |
| $37.00 | 0.11 | -0.92 |
| $38.00 | 0.05 | -0.87 |
| $39.00 | 0.01 | -0.89 |
| $40.00 | 0.00 | -0.90 |
Now, what would happen if the stock moved 10c higher? According to the deltas, we would see an increase of approximately 6c in the $34.00 call and 4c in the $35.00 call. Now, to be exact, the theoretical movement would be 5.9c and 3.9c. So, together, your position has moved up 9.8 cents (5.9+3.9=9.8c). You could say that the delta of the total position (the two long calls) is 0.59 + 0.39, or +0.98. That is, the fair value of your two options together will mimic the underlying almost tick-for-tick.
This is a really important point: The delta of a total position is equal to the sum of the individual deltas that make up that position. It is a very simple concept, but an important one. In the example I used earlier, if we have five contracts each, the position delta would be 4.90 (0.98*5).
The same rule applies for put options or any combination of options. A position delta is simply the sum of the individual option deltas.
For example, if you have five of the $34.00 puts, each with a delta of -0.40, your total delta will be -2.0. That is, for every one point gain in the underlying market, your two puts will collectively lose two points in value.
If you then buy an equivalent amount in the underlying stock (2000 shares), your total delta will be zero (-0.40*5 + 2.0 = zero). That is, if the underlying market rallies one point, you will make money on the shares and lose on the options.
Therefore, you will see no change to your total profit and loss. This scenario is called “delta neutral”. A “delta positive” position, on the other hand, is one in which your total delta is positive. That is, an increase in the underlying will result in an improvement of your total profit and loss position.
Naturally, “delta negative” refers to the scenario of a negative total delta. A negative delta position will lose money when the underlying market rises and profit when the market falls.
A point to note is that the talk, so far, has been on deltas for options, assuming we were long. Because the profit and loss on a short option is the exact opposite of the profit or loss on a long option, the delta for a short position is simply the opposite of that of a long position.
For example, if you go short on an option with a delta of +0.50, the delta for your position is -0.50. If you are short a put option with a delta of -0.40, the delta of your position is +0.40.
Now that you have an understanding of the examples described previously, you can now apply the concept of delta to common option strategies. This table summarizes various positions:
| Position | Description | Delta |
| Long call | Long call | Positive |
| Long put | Long put | Negative |
| Long straddle or long strangle | Long call and long put | Neutral |
| Short straddle or short strangle | Short call and short put | Neutral |
| Bull call spread | Buy call; sell furter out-of-the-money call | Positive |
| Bear put spread | Buy put; sell further out-of-the-money call | Positive |
| Short calendar spread (call options) | Sell short-term call option; buy long-term call option | Slightly positive |
| Short Calendar Spread (put options) | Sell short-term put options; buy long-term put options | Slightly Negative |
You will notice that there is no mention of more complex strategies, such as ratio spreads. This is because the delta on these positions is not so clear-cut. It is very much dependent on your choice of strikes.
For example, in the case of a ratio call spread, if there is a large gap between the bought strike and the sold strike, the sold component will have a small delta, relative to the bought component, thereby having little impact on the net delta. If the sold strike is close to the bought strike, it will have a greater impact and may even cause the net delta to be negative.
All this information, along with that provided in the previous article, has built the foundation for our next level of understanding of options. Next time, we will start looking at specific strategies and how you can use delta figures to understand your risk and, of course, make some money.
Our objective is to understand how the delta concept applies to real-world trading. This article and the previous one really only talked about the theory, but, in the next two articles, you will see how the theory can benefit your trading immensely.
*Reprinted (and modified) with permission from Guy Bower of www.guybower.com
