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The Invaluable Understanding of "Delta", Part I

By Chris Rowe May 2, 2007 Facebook Logo Twitter Logo Email Logo LinkedIn Logo

Happy Thursday, Tycoons!

Given the current market environment, and since our readership has grown so much over the last six months, I thought that it would be a good idea for me to "recycle" this three-part series that I wrote last year because of its high level of importance.  If you remember reading it, then it's still a good idea to review it.

Even if you don't trade options, you should read it.  Why?  Because today the market is breaking highs, and stocks are WAY overbought.  Now the bulls are in control, and they may be in control for a long time (or may not), so the fact that we are "overbought" doesn't necessarily mean that it's time to sell (on the contrary, we shouldn't fight the trend), but it means that we are in high-risk territory and should act accordingly.

Therefore, you may want to consider options, as they can significantly reduce your risk to this market.  You can trade in your overpriced stock for some call options ... but you MUST know which option to buy, or else you might actually be increasing your risk.

Doing something like this is not really complex, so don't be intimidated.  Just remember the two most important things:

1) If you sell your stock and buy call options to replace it, then buy "in-the-money" call options.

2) Only buy one call option for every 100 shares of stock that you own.  In other words, if you have 100 shares of Merrill Lynch, and want to sell it at $91.23, you will have $9,123.00.  You should buy only 1 call option (which represents 100 shares.)  If you buy the October 80 call and pay $14.00/contract (a $1,400.00 investment,) then you should put the remaining $7,723.00 in a very safe interest bearing security such as treasuries.

This three-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).

It will also give you a crystal clear understanding of what I said in the second half of last week's article, "What To Do When You're Bullish/Neutral."  In it, I explained why you will have, by far, the highest profit and probability of success (when selling covered calls) if you always sell the call with the closest strike price (to open) and almost always sell the call with the closest expiration day (to open).


Most stockbrokers and money managers have no real concept of what I’m about to talk about, so if you are one of them, then pay close attention.  If you understand options, you can bring your production WAY up.


The “delta” of an option measures how much the option changes in price when the underlying security moves one point.

For example:

Let’s say that Exxon Mobil (NYSE: XOM) is trading at $80.00/share, and the October 80 call is selling for $4.80.  (Because XOM’s stock price is the same as this option’s strike price,  this option is “at-the-money”.)

When XOM rises one point to $81.00, the January 80 call should then sell for $5.40.  Thus, the option only increases by 60 cents when the stock rises by one full point.  This option is said to have a delta of 0.60.

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.

Hint:  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, XOM October 95 call which is 15 points out-of-the-money,) it will either move only slightly, or not move at all even if the stock rises by one point.

The delta of the this FAR out-of-the-money call is only .0792, so theoretically, if XOM moved up by one point, the call options should only trade from $4.80 to $4.8792 (but options trade in increments of 5 cents, so assume it would move to either $4.85 or $4.90.)

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" (ex. XOM October 60 call which is 20 points in-the-money,) then the call option would likely have a delta of 0.97.

Thus, when the stock moves up one full point, the option will likely move up 97 cents.  (Almost parity.)

If a call option moved up one full point due to a 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 which has a delta of 0.70 would move up by 70 cents.


1)  An option’s delta changes as the price of the stock changes because the deeper in-the-money that an option becomes (due to the price movement of the underlying stock,) the higher the delta becomes.  So don't mistakenly think 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.

2)  Today we are only discussing delta.  But an option’s price (or the option's delta) can be affected by other factors.  The following factors determine an option’s price (or contribute to the delta):

   1. Time Decay (which we have discussed several times in the past)

   2. Delta

   3. Historical volatility (If the underlying stock becomes super volatile, the option may become more expensive, all things considered, than when the same underlying stock was not volatile.)

   4. Implied volatility (If traders are anticipating a big move in the stock, then the options may become more expensive because they are more attractive to speculators.)

   5. The risk-free interest rate

   6. Dividends that the underlying stock pays.


The reason that so many people shy away from options trading and think that they are so risky has to do with the same misconception that some people have when they say that they would rather buy a stock which trades at $2.00 instead of a stock which trades at $20.00.  Their reasoning is that either they can buy more shares of the stock at $2.00, or that IF it increases by a point it's a larger percentage gain.

Basically they let greed get the better of them, while failing to consider the actual odds of the trade itself working out.  These people tend to make the mistake of focusing on the share amount, rather than the dollar amount invested compared to the dollar amount received when it comes time to sell – while at the same time factoring in the assumed risk of the trade/investment.

I would rather use $80,000.00 to buy 1,000 shares of Exxon Mobil than use $80,000.00 to buy 8,000,000 shares of some bulletin board stock trading at $0.10.

Because it trades at 10 cents doesn’t mean I can necessarily make more money with it, because it can trade down to 1 penny and if it did, then I’d lose $72,000.00.

Sure, if the bulletin board 10-cent stock traded from 10 to 40 cents, then I would make 300% on my money.  But I would never feel comfortable enough to put that kind of money into such a crap-shoot like that.

I would never put a meaningful amount of money into an option that was way out-of-the-money, either.

Here’s a similar scenario:

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

For Example: They may think that a stock will trade from $80 to $100 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.  So 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.

TRADING WITH (what I consider to be) A LOW DELTA

Suppose Exxon Mobil (NYSE: XOM) were trading at $80.00, and a trader was looking to buy Exxon Mobil options because he was looking for a move of one point from $80.00 to $81.00.

If the trader were to buy the October 85 call (which is five 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 October 85 call options would move approximately 37 cents higher.


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

If I have $7,050.00, I could buy 30 call options (representing 3,000 shares,) and I would make $1,110.00 within a day or two.

If I got lucky, and I underestimated XOM’s upside move, and it happened to trade to $95.00 (instead of $81,) then I would make a killing (over $30,000.00 on my $7,050.00.)

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 huge losses.


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

If I own a Schering Plough (NYSE: SGP) January 20 call, and the stock is trading at $22.50, then my call option is $2.50 in-the-money.  If that January 20 call option is trading at $3.00, then $2.50 (out of that $3.00) is intrinsic value, and the remaining 50 cents is extrinsic value and is exposed to time decay.

(Remember, this is an old article...)

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.

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

For example: the extrinsic value of the January 17.5 (with the highest delta of 0.97) only accounts for 5.7% of the entire value of the option.  That 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.

20% of the January 20 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 options value (or the options premium.)

   2)  Starting with a high delta reduces your loss when the stock moves lower.

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 January 20 (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 $21.00, the January 20 call option 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 which has an expiration day further 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 which 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.

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 Schering Plough traded from $22.50 down three points to $19.50, the January $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 $3.00 that you committed to the option as opposed to the $10.00 that the stock holders lost!

... There's more to this, and it gets even better.

Tune in next Thursday, and I will give you PART TWO of  "Advanced Options Made Simple "where you are sure to add invaluable weapons to your arsenal that even your broker can't comprehend.

Don't forget to click on the link below to rate this article and to leave comments!

Until next Thursday,

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