Delta Explained

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What is Options Delta?

I am not joking when I say that gaining an understanding of delta changed my trading life forever. And I promise that this four-part series will be one of the most important and influential investing lessons you’ve ever had.

Even if you don’t trade options, you should still read this, because it can significantly reduce your risk in this market. You can learn how to replace your overpriced stock with call options — but you MUST know which options to buy, or else you might actually increase your risk instead.

Learning about delta and using it to make better trades is not really complex, so don’t be intimidated. Just remember the two most important things:

In other words, if you have 100 shares of Capital One Financial (COF), and want to close the position at $21.60, you will have $2,160. To establish an option position, you should buy only one call option contract (which represents 100 shares). If you buy the COF Jan 15 Call and pay $8 per contract (an $800 investment), then you should put the remaining $1,360 in a safe, interest-bearing security, such as a money-market fund or Treasuries.

This four-part series will help you understand why it’s important to buy in-the-money call options in place of stock (as opposed to at-the-money or out-of-the-money options).

What is Delta?

The “delta” of an option measures how much the option changes in price when the underlying security moves one point. (Lean about the other option Greeks.)

Let’s say that ExxonMobil ( XOM) is trading at $65 per share, and the XOM Jan 65 Call is selling for $5. (NOTE: Because XOM’s stock price is the same as this option’s strike price, this option is trading at-the-money.)

When XOM rises one point (from $65 to $66), the Jan 65 Call should then sell for $5.50. Thus, the option only increases by 50 cents when the stock rises by one full point. This at-the-money option is said to have a delta of 0.50.

Decoding the Delta

The delta of an option is a number that ranges from 0.00 to 1.00, and the delta of a put option is a number that ranges from -1.00 to 0.00. A call with a delta of 0.70 implies virtually the same thing as a put with a delta of -0.70.

You will notice that when a call option is far out-of-the-money (for example, the XOM Jan 95 Call is 30 points out-of-the-money), it will either move only slightly, or not move at all, when the stock rises by one point.

The delta of this far out-of-the-money call is only 0.04. So theoretically, if XOM moved up by one point, the price of the $95 calls should advance by 4 cents.

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Now, that might seem like a lot in terms of the percentage gain since the theoretical value of this far out-of-the-money option is about 27 cents. (A 4-cent gain would be a 15% gain on a 27-cent call option). But you have to consider the fact that the spread between the bid and ask price can be much larger than the 4-cent gain in the option (so you can still end up with a losing position).

The rule of thumb here is the higher the delta is, the more likely it is the option ends up profitable.

Out-of-the-money options have the lowest delta, while in-the-money options have the highest delta. So you’d want to avoid the out-of-the-money option that has the delta of 0.04 like the plague.

On the other hand, if the stock is trading far above the call option’s strike price — or, said differently, the option is “deep in-the-money” (i.e., the XOM Jan 45 Call, which is 20 points in-the-money with the stock trading at $65), then the call option would likely have a delta of 0.96.

Thus, when the stock moves up one full point, the option will likely move up 96 cents. (Almost point-for-point, aka trading at “parity” with the stock.)

If a call option moved up one full point due to the underlying stock moving up one full point, then the option has a delta of 1.00, and so on.

A put option would work the same way whereas, if XOM moved down one point, a put option that has a delta of -0.70 would move up by 70 cents.

Two Important Notes

1) An option’s delta changes as the price of the stock changes.

This is because the deeper in-the-money that an option becomes (due to the price movement of the underlying stock) the higher the delta becomes. In other words, in the ExxonMobil example, when XOM moves up 5 points from $65 to $70, the delta of the Jan 65 Call would move up from 0.50 to 0.65.

Theoretically, at that point (with XOM at $70), if the stock moved up one point (from $70 to $71) then the call (which now has a delta of 0.65) would increase by 65 cents.

So don’t mistakenly think that if a call option has a delta of 0.50, that the call option would only move up by 5 points if the stock moves up by 10. That is incorrect because, again, the call option’s delta increases as the option moves further above its strike price.

The more the stock advances, the more sensitive the option’s price will be to each one-point movement of the stock. In fact, if ExxonMobil traded up 10 points (from $65 to $75), the Jan 65 Call — which currently has a delta of .50 — would actually advance by approximately $7 (from $5 to $12).

By the time the stock is trading at $75, the delta would move up to about 0.78.

2) An option’s price (and the option’s delta) can be affected by other factors.

In the first part of this series, we are only discussing delta. But the two major factors that impact an option’s price and delta are time decay and a change in volatility of the underlying stock, exchange-traded fund, index, etc.

Replacing Stock With Options vs. Gambling With Options

The reason that so many people shy away from options trading and think that options are so risky is because the option novice tends to be attracted to the lower-priced options, which are the options that are the most difficult to profit from.

This is similar to the situation when people say that they would rather buy a stock that trades at $2 instead of a stock that trades at $20. They make the mistake of ignoring the probability of the stock trading higher. This is a common mistake made by inexperienced investors, and it is one of the absolute WORST ways to approach investing.

The two reasons investors mistakenly think cheap options are better are:

1) If the investor is successful, the win will be greater, percentage-wise.

2) If the investor is wrong, then he or she will have only lost the small amount invested.

But clearly, you can’t argue both. You can’t say the percentage gain is larger and then make the argument for the loss that the absolute number is “all you would lose.”

Sure, the percentage gain might be higher if everything works out. But when the odds of success are low, you wouldn’t feel comfortable putting any real money behind the investment.

Personally, I don’t care if it’s $5 or $500,000. No matter how much money you are putting at risk, the odds of success should be good. If odds favor a loss, why invest even $1?

We must look at our investment portfolio as a business, and not a lottery ticket.

Is Purchasing Out-of-the-Money Options Ever a Good Trade?

More specifically, not if you’re purchasing those options by themselves. However, if you buy them as a hedge, or as part of a multi-leg option position, that’s a different story.

But we are talking about stock replacement here, which just involves buying an option instead of a stock. I’m going to show you how to take less risk than the traditional stockholder.

First, you should understand that an out-of-the-money call option is an option that has a higher strike price than the current price of the stock. (With put options, it’s the opposite. With puts, the out-of-the-money options are those with a strike price that is lower than the stock price. But we’ll stick with call options in our examples.)

Below you can see eight call options listed. The strike prices are circled in red. The stock is trading at $65.70. The call options that are highlighted in yellow are the out-of-the-money options. You can also see these are the cheaper options, and they get cheaper with higher strike prices.

The option that is the least likely to advance is the Jan 85 Call (at the bottom), and the option that is the most likely to advance is the Jan 50 Call (which is 15.7 points in-the-money).

Many option traders lose money trading out-of-the-money options because they are overly confident in their prediction.

For example, they may think a stock will trade from $65 to $80 in a given period of time. But, most of the time, markets and stocks trade plus one or minus one standard deviation from the mean.

That is why time decay tends to be a factor that new, out-of-the-money option, traders learn about very quickly (and painfully).

An out-of-the-money option’s delta will trend toward zero as time passes. And remember, the lower the delta is, the less the price of the option will be impacted by the movement in the stock.

Therefore, the underlying stock can trade much higher over time, but the call option with a very low delta could still trade lower, even to zero, even though the stock traded higher.

I’m sure many of the people reading this have bought an out-of-the-money call option because they thought the stock was going to advance, and they were right because the stock advanced, but disappointed because the call options traded lower anyway. That’s because they bought the wrong call option. At the same time, other call options traded higher with the stock.

Trading With a Low Delta

Suppose XOM is trading at $80, and a trader is looking to buy call options because he is looking for a move of one point from $80 to $81.

If the trader were to buy the Oct 85 Call (which is 5 points out-of-the-money), the trader would pay $2.35 for the call option.

This call option has a delta of 0.37. That means that if XOM traded from $80 to 81, (all other factors being equal — such as ZERO time decay — so we assume that the stock moved the very same day), you could assume that the Oct 85 Call options would move approximately 37 cents higher.

The Argument for Buying Low Delta Options

If you bought the option at $2.35 and sold it 37 cents higher (within a day or two) at $2.72, then you would realize a fast 15.74% return on our money. Not bad.

If you have $7,050, you could buy 30 call options (representing 3,000 shares), and you would make $1,110 within a day or two.

If you got lucky, and you underestimated XOM’s upside move, and it happened to trade to $95 (instead of $81), then you would make a killing (more than $30,000 on your $7,050 investment).

However, before you start mentally spending those profits … STOP IT!

I can see the greed seeping out of your ears right now. A wise man once told me that the traders who make the HUGE profits like that are the same ones that take LOTS of big losses.

Remember, the low-delta options are the out-of-the-money options, and it’s very likely that they don’t end up profitable.

The Argument Against Buying Low Delta Options

I usually don’t like to buy an option with a low delta unless I am covering (hedging) myself against a significant stock movement/loss. (Such is the case when using a protective put.)

There are two main reasons why, and both reasons spell a higher risk with lower delta. The first is one that most people understand; the second is what many people overlook.

1) The lower the delta, the more extrinsic value your option contract consists of.

Extrinsic value (aka, time value) is what is left over after calculating intrinsic value. Extrinsic value is affected by time decay.

Intrinsic value is the amount by which your option is in-the-money. Intrinsic value is NOT affected by time decay.

If I own a Schering-Plough ( SGP) Jan 20 Call, with the stock trading at $22.50, then my call option is $2.50 in-the-money.

If that SGP Jan 20 Call is trading at $3, then $2.50 of that $3 is intrinsic value, and the remaining 50 cents is extrinsic value and is exposed to time decay. (Keep in mind that these are not recommendations. They are examples to illustrate the power of delta.)

Remember: The extrinsic value (or time value) portion of an option is at the mercy of the clock. Time decay has zero effect on the intrinsic value portion of my options premium. That’s why we like to trade in-the-money options that have minimal extrinsic value.

Notice in the table above that the percentage of the value of the option contract, that is, extrinsic value, increases as the delta decreases. So, the lower the delta, the more extrinsic value exists. And that extrinsic value is at the mercy of time decay.

For example, the extrinsic value of the Jan 17.50 Call (with the highest delta of 0.97) only accounts for 5.7% of the entire value of the option. This means that only 5.7% of the value can be lost due to time passing. Any other loss in the option would have to do with the actual stock moving lower.

Twenty percent of the Jan 20 Call is extrinsic value and is therefore at the mercy of time decay. The other two options have 100% extrinsic value.

Now, just about every options trader understands that time decay occurs as time passes, and most are familiar with what a time decay curve looks like.

The deterioration of the extrinsic value portion of the call option’s value accelerates, especially in the last 90 days before expiration.

By purchasing an option that has a high delta, I can significantly reduce the effect that time decay has on my option’s value (or premium).

2) Starting with a high delta reduces your loss when the stock moves in the wrong direction.

This is what an alarming number of option traders either don’t understand, or only have a slight understanding of.

Remember how I said that the delta of a stock option changes as the stock fluctuates? For example, in the table above, you see that the delta of the Jan 20 Call (which is 2.5 points in-the-money) is 0.84. It has such a high delta because it is 2.5 points in-the-money.

But if SGP traded down to $21, the Jan 20 Call would only be one point in-the-money. Thus, the delta would change from 0.84 to 0.69.

This is a good thing if you are the owner of that call option. It means that as SGP stock trades lower, the call option actually loses less in value (dollar-wise) than the stock!

In other words, you stand to lose a lot less by owning the call option. This is especially true when you are talking about an option that has an expiration day farther out than 90 days. (Remember, 90 days before expiration is when the extrinsic value decay tends to speed up.)

NOTE: When you buy an option strictly for the upside (and you aren’t using it for hedging purposes), you should always give yourself extra time for it to work. Try to buy it with an expiration month that is at least 90 days after the time that you wish to sell it.

Think about that for a second.

This is the part that many newer option traders tend to overlook, and it’s one of the most important considerations when using beginner, intermediate or advanced option strategies.

Buy More Delta, Lose Less if Trade Goes South

When you buy options with a high delta (which are deep in-the-money) and the stock trades lower, your option loses less value than the stock does!

So, you put up less capital (and, therefore, ultimately risk less capital), and the call option holder will actually lose less value when the stock trades down a few points. If SGP traded from $22.50 down 3 points to $19.50, the Jan 20 Call is likely to lose only about $2.30 in value.

So, why even bother trading stock? What if the stock drops by 10 points? You’d only lose a maximum of $3 that you committed to the option as opposed to the $10 that the stockholders lost!

There’s more to this, and it gets even better. So go on to Part II of this series where you’ll learn how to Turn Your Deltas Into Dollars.

Chris Rowe is the Chief Investment Officer for Tycoon Publishing’s The Trend Rider. To learn more about him, read his bio.

Definitions for Delta
ˈdɛl tə Delta

Here are all the possible meanings and translations of the word Delta.

Princeton’s WordNet (4.00 / 4 votes) Rate this definition:

a low triangular area of alluvial deposits where a river divides before entering a larger body of water

“the Mississippi River delta”; “the Nile delta”

an object shaped like an equilateral triangle

the 4th letter of the Greek alphabet

Wiktionary (4.40 / 5 votes) Rate this definition:

The fourth letter of the modern Greek alphabet u0394, u03B4.

A landform at the mouth of a river where it empties into a body of water.

The letter D in the ICAO spelling alphabet, which assigns words to letters of the alphabet.

u03B4 In the IPA, the symbol that represents the voiced dental fricative, the hard th in the English word father; frequently represented by the Icelandic eth (ð).

The symbol u0394.

A small but noticeable effect, compare with epsilon.

This will slow the main code path down, but only by delta.

The set of differences between two versions of a file.

When you update the file, the system will only save the deltas.

The angle subtended at the center of a circular arc.

A municipality in British Columbia, Canada

Origin: From its location near the delta of the

Webster Dictionary (0.00 / 0 votes) Rate this definition:

a tract of land shaped like the letter delta (/), especially when the land is alluvial and inclosed between two or more mouths of a river; as, the delta of the Ganges, of the Nile, or of the Mississippi

Origin: [Gr. de`lta, the name of the fourth letter of the Greek alphabet (the capital form of which is , Eng. D), from the Phnician name of the corresponding letter. The Greeks called the alluvial deposit at the mouth of the Nile, from its shape, the Delta of the Nile.]

Freebase (2.50 / 2 votes) Rate this definition:

Delta is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician letter dalet . Letters that come from delta include Latin D and Cyrillic Д. A river delta is so named because its shape approximates the upper-case letter delta.

Chambers 20th Century Dictionary (4.00 / 1 vote) Rate this definition:

del′ta, n. the fourth letter of the Greek alphabet, the capital form of which is Δ : a tract of land of like shape formed at the mouth of a river.—n. Deltaficā′tion , the process of forming a delta.—adj. Del′toid , of the form of the Greek Δ : triangular.—Delta metal, a hard alloy of copper, zinc, and iron—the three metals symbolised by the triangular shape; Deltoid muscle, the large triangular muscle of the shoulder. [Gr.,—Heb. daleth, a tent-door.]

The Nuttall Encyclopedia (1.00 / 1 vote) Rate this definition:

the signature of D. Macbeth Moir in Blackwood’s Magazine.

The New Hacker’s Dictionary (5.00 / 1 vote) Rate this definition:

1. [techspeak] A quantitative change, especially a small or incremental one (this use is general in physics and engineering). “I just doubled the speed of my program!” “What was the delta on program size?” “About 30 percent.” (He doubled the speed of his program, but increased its size by only 30 percent.) 2. [Unix] A diff, especially a diff stored under the set of version-control tools called SCCS (Source Code Control System) or RCS (Revision Control System). 3. n. A small quantity, but not as small as epsilon. The jargon usage of delta and epsilon stems from the traditional use of these letters in mathematics for very small numerical quantities, particularly in ‘epsilon-delta’ proofs in limit theory (as in the differential calculus). The term delta is often used, once epsilon has been mentioned, to mean a quantity that is slightly bigger than epsilon but still very small. “The cost isn’t epsilon, but it’s delta” means that the cost isn’t totally negligible, but it is nevertheless very small. Common constructions include within delta of —, within epsilon of —: that is, ‘close to’ and ‘even closer to’.

Dictionary of Military and Associated Terms (5.00 / 1 vote) Rate this definition:

This condition applies in the immediate area where a terrorist attack has occurred or when intelligence has been received that terrorist action against a specific location or person is imminent. Normally, this FPCON is declared as a localized condition. FPCON DELTA measures are not intended to be sustained for substantial periods. See also antiterrorism; force protection.

Dictionary of Nautical Terms (3.00 / 3 votes) Rate this definition:

A name given by the Greeks to the alluvial tract inclosed between the bifurcating branches of the Nile and the sea-line. It is well known that rivers which deposit great quantities of matter, do also very often separate into two or more branches, previous to their discharge into the sea; thus forming triangular spaces, aptly called deltas from their resemblance to the Greek letter Δ. All deltas appear by their section to be formed of matter totally different from that of the adjacent country. They are the creation of the rivers themselves, which, having brought down with their floods vast quantities of mud and sand from the upper lands, deposit them in the lowest place, the sea; at whose margin, the current which has hitherto impelled them ceasing, they are deposited by the mere action of gravity. This is particularly illustrated on the western coast of Africa by the shoals off the Rio Grande, Rio Nunez, and others. The coast, as well as the embouchures of the rivers, exhibit a deposit of deep mud, and yet far at sea banks of clean siliceous sand arise.

What Is Delta?

Expertise: Investment Banking | Private Equity

Delta is a term used in trading to compare the change in price of a derivative compared to the change in price of the underlying asset. Delta is one of the 5 technical risk ratios and is sometimes known as the ‘hedging ratio’.

Delta is used to calculate risk and whether a position is suitably hedged or not. An example of delta is as follows:

  • A call option on oil has a delta of 1.2
  • This means that for every $1 that the price of oil increases, the value of the call option will increase by $1.2

If an investor holds options as a means of hedging and they have a low delta , then the movement in option value will not offset any losses they experience on the underlying asset and therefore they are likely to be underhedged.

With options, as they near their expiry date their delta will tend to 1 (call) or -1 (put).

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