The Key to Understanding Options: Delta and Gamma!

The two most-important concepts in option trading are delta and gamma.

Investors who don’t understand these two concepts are setting themselves up for trouble.

On the other hand, understanding them can improve your investment/option trading results immediately!

Let’s start with a simple trading question:

You are bullish on XYZ stock and are willing to use options to maximize an anticipated move up in the shares. Which of the following do you do?

A) Buy calls

B) Buy puts

C) Sell calls

D) Sell puts

If you answered A, as most people do, you just set yourself up for a potentially losing trade. You didn’t misread the question; you just fell into the most-common error in option investing.

You just saw why so many people lose with options. We never even got to the point of which option to buy, but already made a critical mistake.

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Internal Sponsorship

We didn’t discuss whether to buy a 1-month, 3-month, 6-month, or even LEAPS (or longer-dated) option.

There was no debate as to which strike price.

We just invested a lot of money and sent a wounded horse to the starting gate.

Let’s find out what the mistake is and how to correct it.

Option Values Have 2 Components

Stocks can be much-easier to trade than options. All you have to do is decide whether the stock will move up or down, i.e. the stock’s direction.

Of course, anyone who has ever invested in stocks knows that this, in itself, can be incredibly difficult.

Options have an additional component: speed. This second component is what makes options such tricky investments.

Delta measures direction, and gamma measures speed.

Although there are specific numerical measures of delta and gamma, we are only going to consider them in a much simpler, conceptual format.

Delta is a measure of direction.

  • A long call position has positive delta. In other words, the value of the call will go up (positive) as the price of the underlying stock rises.
  • Put options have negative delta; their value will go down (negative) as the price of the stock rises.

Of course, the opposite is also true. If the underlying stock goes down, calls will lose and puts will gain in value.

What if we are short a call? Then our position will have a negative delta — meaning, our position will lose value as the stock rises.

Similarly, if we are short a put, then we have positive delta; our position will gain in value as the stock rises.

It should be easy to see now that there are two ways to obtain positive deltas; long calls and short puts.

KEY CONCEPT: If you are bullish on a stock, you want positive delta for your option position. If you’re bearish, you want negative delta.

Now, what about gamma?

Gamma measures the speed component of an option. In a conceptual sense, we measure speed with time, just like any other moving object. Time premium is a way to determine gamma.

The higher the time premium of an option, the higher the gamma. Because time premium is the portion of the option’s value that erodes with the passage of time, it is this portion that is exposed to slow or no movement in the underlying stock.


XYZ Stock trading for $50

XYZ $50 call is trading for $5

XYZ $30 call is trading for $21

Here, the $50 call is all time premium. Therefore it will have a higher gamma component. The $30 call has only $1 time premium, so compared to the $50 call, its gamma component will be much lower.

You can think of gamma as a risk measure. We can say the $50 call is riskier, in terms of speed, than the $30 call. That’s because, if the stock sits still, the $30 call can only lose $1 (3.23% of value), while the $50 call can lose the entire $5 (100% of the value).

Another way to look at the risk factor is in terms of break-even points. The $30 call needs to have the stock trading at $51 by expiration in order to break even.

If the stock is $51, the call will be worth exactly $21, the price paid for the option. However, the $50 call must have the stock trading at $55 to break even.

So again, the $30 call, with respect to speed, is less risky. In other words, the $30 call does not need as much movement in the stock to break even as compared to the $50 call.

While it may seem counterintuitive, long calls and long puts both have positive gamma.

This is because you need speed in the underlying stock in either case in order to make up for the time premium you paid.

KEY CONCEPT: If you are looking for quick speed of movement in the underlying stock, your option position should have positive gamma.

If you expect the stock to move slowly or sit flat, your option position should have zero gamma or even negative gamma.

Now let’s put it all together …


We are bullish on XYZ trading at $100

1-month $105 call is trading at $7

1-month $95 put is trading at $5

We determined at the beginning of this lesson, that most investors are inclined to buy calls when they are bullish. So let’s "buy" a call and see what happens!

Here, we are long the $105 call at $7. At expiration, the stock is trading at $110.

The question now is, are we correct in our bullish assumption?

There is no question that we are. The stock is up a whopping 10% in a month (that may not seem like a lot, but that’s an annualized rate of over 200% — at that rate, you would more than triple your money in a year).

So just how much of a killing did we make on our call?

The $105 call will be trading for $5, exactly the intrinsic amount. We paid $7 and sold for $5, yet we were correct in our bullish assumption.

That’s a 28% loss on the investment for being correct!

Sound familiar?

Now that we know about deltas and gamma, let’s see if we can correct the trading mistake we discussed earlier.

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Internal Sponsorship

This trader just made the classic mistake of trading options only on delta — the direction of the stock.

Let’s Polish up the Trade a Bit

We know the trader is bullish, so he should have positive delta — either long calls or short puts.

But now let’s say we ask the trader, "How quickly do you think the stock will move?"

Let’s say he says, "I think it will move up, but slowly."

Now we are in position to set up a winning tradeassuming the trader’s assumptions are correct.

We now know he wants positive delta (because he’s bullish) but also needs negative gamma (because he believes it will move slowly). The following chart should help us determine what we should do:

So How Can We Get Positive Delta & Negative Gamma?

We can short the puts, which will give us the opposite signs as listed in the table above.

Long puts have negative delta and positive gamma, so a short position will have positive delta and negative gamma — exactly what the trader needs!

Now, if he shorts the $95 puts, he will receive $5 and keep the entire $5 instead of losing $2 as he did with the calls.

What if the trader doesn’t want to be short or doesn’t have the option approval level to be short? We could do a credit spread (selling a higher-priced option and purchasing a lower-priced option at the same time) that would lessen the risk.

Or, we know he desires negative gamma, so a gamma close to zero would also work.

Remember, "time premium" is synonymous with gamma, so to get a gamma of zero (or close to it), we could also look at deep-in-the-money calls.

  • With XYZ at $100, the $80 call may be trading in the neighborhood of $20.50 ($20 intrinsic value + a small amount of time premium).
  • If he buys the $80 call, he will spend $20.50.
  • With the stock closing at $110, he will be able to sell the option for $30, for a profit of $9.50 (46% gain).

This is certainly better than the 28% loss taken when he traded only on direction alone.

Now you should be in a better position to answer the question asked at the beginning.

The correct answer is this: We should have clarified the gamma component with the investor.

In other words, is the investor bullish quickly or slowly?

Once we determine that, we can then recommend either long calls or short puts … or even a host of other strategies that would properly align the deltas and gammas with his directional opinion of the stock.

Bottom line: It should now be evident that you need to determine both direction and speed when dealing in options.

In order to make a profitable trade:

  • A position with positive gamma must move up.
  • A position with negative gamma does not have to move up; it just cannot move down.

These are two very different situations. If you don’t consider both, you will almost certainly set yourself up for a losing trade.

Always Watching Your Chickens,

James DiGeorgia

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