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The Invaluable Understanding of "Delta" Part III

By Chris Rowe May 16, 2007 Facebook Logo Twitter Logo Email Logo LinkedIn Logo

For those of you who don’t know (shame on you,) for the last two weeks (Thursdays,) we have been talking about understanding “Delta”.

We have been talking about it, not so much as a tool or a calculation, but more as a concept.  The goal is for you to have a clear understanding of the reasons option prices change the way that they do.

I am going to keep it that way, because it is most important to understand the concept, and if you sit here and try to figure out how to actually calculate delta on your own or what the calculation is, you would really be missing the forest for the trees.   How options react when they are a certain distance away from their strike price is what is important here.

By understanding the concept of delta, we understand why it pays to buy in-the-money options as opposed to (the cheaper) out-of-the-money options.

For instance, check out Cisco Systems (Nasdaq: CSCO) call options below. 

The 2008 January 20 call options (yellow) are 6.28 "in-the-money."  Said differently, they have 6.28 of intrinsic value.  (CSCO at $26.28 - $20.00 strike price = $6.28 intrinsic value.) 

These January 20 calls are trading at $7.20, so the cost of the option only includes 92 cents of extrinsic value (option price or "premium" - intrinsic value = extrinsic value.)

($7.20 - $6.28 = $0.92 extrinsic value)

Now we know (assuming that Cisco's stock price remained the same,) that out of the option's price of $7.20, only $0.92 is exposed to time decay, and the remaining $6.28 will only change based on the movement in the stock's price, and not due to time decay.

Now look at the 2008 January 27.50 calls (red,) which are trading at $2.10.  Since the stock is NOT trading above this 27.50 strike price, we know that these call options are not in-the-money, but they are out-of-the-money (by $1.22.)  We know that they therefore have zero intrinsic value, and we now that 100% of the price of the option ($2.10) is extrinsic value.  So 100% of this call option is at the mercy of time decay.


The effect of Cisco Systems change today.



(This assumes that all other variables do not change.)

You can see that the call options that are deeper in-the-money (which have the higher deltas) gain the most when the stock moves higher.  At the same time, they lose less in value when the stock moves down, than they gain when the stock moves up, and obviously they lose less than the stock does when it moves lower.

By now, you probably understand why the lower the delta is, the more aggressive the option is at that point.  If your goal was not to replace the stock's performance with an option, but instead to speculate on an option, then you would be focused on the actual percentage gain or loss on the option itself.  The option with the higher strike price gives us the highest percentage gain possible. At the same time,  the likelihood of making money is smaller, and if the stock doesn't do what you want, you are likely to lose much more, if not all of the amount committed to the trade.

So we know that if our crystal ball was working well, and the stock did in fact move up 5 points on the same or next day, then the far out of the money call is the best bet (with the highest percentage return.)  But guess what... We don't always know exactly what will happen the same or next day do we?  In fact, never know for sure what will happen.

Some people even think of the delta as being the probability of the option being in-the-money at expiration.  (Delta of 20 indicating that there is a 20% chance of the option being in-the-money at expiration.)

I still think that it's smarter to buy the in-the-money option (which has the higher delta) even if your focus is solely to speculate on the option itself.  But today we're talking about the option's price in relation to the underlying stock.

The two considerations here are the effect of time decay, and the effect of price fluctuation.The chart above assumes that the stock moved today, so time decay is eliminated from the example.  But you can see that even though time didn't pass, the extrinsic value did decrease when the stock moved higher. This is the other way that the extrinsic value disappears.  (And this is one reason why I don't like to refer to the extrinsic value as "time value" as many people do.)

Our Goal:

What we want to do when buying calls in place of the stock is we want to buy the call option that comes as close as possible to mimicking the gains in Cisco's stock. (If the option traded in parity with the stock - for example: CSCO trades up 5 causing the option to also trade up 5 - then the option would have the highest possible delta of 1.00.  The deeper in-the-money the option is, the higher the delta is, the closer the option's price comes to mimicking the stock's price.)

You can see above that the call options with the lower strike price (which have the higher delta) gain more, point wise, when Cisco moves higher, than the call options with the higher strike price (which have the low delta.)  You can also see that the call options with the lower strike price (which have the higher delta) lose less, point wise, than Cisco's stock.  

This assumes that the move happened today.  This would remain the case for the next several months. 

If you want to benefit from this feature, you should trade the options that have at least 3 months left before the expiration day.  If you hold the Cisco options for a few months, and you realize that expiration day will be in 3 months, then what you should do is sell the calls that you own, and buy the calls with an expiration day that's further out.  This way you can keep the feature of the call options gaining more and losing less.

Here it's easy to see one of the benefits of owning call option's that are in-the-money. 

But what about the time factor?  Well we already know that anything that's out of the money would be worthless at expiration

If Cisco traded flat until expiration, January 30 call and the 27.50 call, which are out-of-the-money, would lose all value.  The January 25 call would be at $1.68 (the in-the-money amount, aka. intrinsic value.)  Our January 20 however, which only had 92 cents of extrinsic value would be at $6.28 (again, the intrinsic value of $6.28 is not affected by time decay.)

We've covered the impact on the Cisco options if the stock moved today.  We've covered what would happen if the stock didn't move at all until expiration.  But what would happen to the options in 6 months from now if the stock moved 5 points higher, 5 points lower, or traded at the same price that it's at today ($26.28?)


The options above illustrate the impact of Cisco's stock price on the options assuming that there is only 66 calendar days left before expiration.

See the difference?

This is why I prefer to sell out of the option position at least 3 months before the expiration day.  If you want to benefit from the reduced risk of the stock trading lower, you should play it this way too.  You will see at the bottom of this article why I like to be out before the last 3 months.

A great way to really grasp the concept is by understanding the other variables’ concepts because the other variables are what determine the amount of extrinsic value is reflected in the options premium (price.)  For now, we will focus basically on the impact that the other variables have on the extrinsic value.

Remember: Intrinsic value is the amount that an option is in-the-money.  Extrinsic value is the rest.

Let's use another example.  Let’s say that we were looking at JP Morgan when it was at $47.50, and that it was early November.

If the March 45 call options were trading at $4.00, then how much of that $4.00 was “intrinsic value” (which is only affected by price fluctuation,) and how much of that $4.00 was “extrinsic value”, aka “time value” which was affected by all of the other factors such as:

a) Time remaining
b) Volatility
c) The risk-free interest rate
d) Dividends that the stock pays.

Well, the option was in-the-money by 2.5 points, so 2.5 out of the 4.00 is intrinsic, and the rest (1.5) was extrinsic.

That 1.5 extrinsic value was assigned to this particular JP Morgan call option based on the factors mentioned above.  Those factors are also what affects the measurement called “delta”.  The delta is not a factor. The delta is the conclusion or a result of the varying factors mentioned above. 

With JPM trading at $47.50, the delta of the JPM March 45 call happened to be 0.748.  But that delta of any particular option will change as any of the other factors change.  The other factors are constantly changing, and those varying factors are what affect the extrinsic value of an options premium (price).

That is why when you learn about how option-pricing works, as the educator explains each individual factor to you, you will see that they will always say “all other things being equal”.  

After watching options trade for a while you will start to understand that:

- An option contract with a lot of time remaining has a delta that changes rather moderately as the underlying stock moves from out-of-the-money to in-the-money.

- On the flip side, a short-term option’s delta will change dramatically as the underlying stock moves from out-of-the-money to in-the-money.  

For the option that has a week left until expiration (very short-term,) the option’s delta rises to nearly 1.00 very quickly when it moves in-the-money.  The option’s delta drops to zero very quickly when the option moves out-of-the-money.

If you don’t grasp this immediately, then don’t be intimidated or make this more complicated than it really is.

First, stop and think about what you just read above, and then remember that delta is just a measure of how much the option’s premium (price) changes when the stock changes in price by one point. 

So, if you understand extrinsic value, you will have a good understanding of why a short-term option’s price change is much more dramatic when the stock moves around the option's strike price.  (Answer: it’s because there is much less extrinsic value right before expiration.)

The other variables (volatility, time left and interest rates) are what affect the amount of extrinsic value in a particular option’s price.  But if there is only a week before expiration, then there will be very little extrinsic value in that option’s premium regardless of the variables mentioned.

Extrinsic value is just the extra fluff in an option’s price after the intrinsic value is calculated.

With JPM at $47.50, if I had wanted to use the JP Morgan March 45 calls to actually buy JP Morgan at 45, then I could have sold it immediately at the then current price of 47.5, and made 2.5.  That’s why the call option was trading at a minimum of 2.5 (the intrinsic value.) 

But, since it was trading at 4.00, we know that there was an additional 1.50 in that price that we had to pay for the option.  For that extra 1.5, we were buying time.  (Time value/extrinsic value.)  That 1.5 is that extra “fluff” that I’m referring to.

If there were only one week left, there would be less fluff.

Now lot's say that JP Morgan was trading at $45.00.

Let’s compare the effect on the delta of the November vs. March options as they moved to 1-2 points in-the-money, then at-the-money, and 1-2 points out-of-the-money.

JP Morgan's Stock Price November 45’s Delta March 45's Delta
$43.00 (when the 45 call is 2 pts. out-of-the-$) 0.07 0.33
$44.00 (when the 45 call is 1 pt. out-of-the-$) 0.25 0.44
$45.00 (when the 45 call is at-the-money) 0.54 0.56
$46.00 (when the 45 call is 1 pt. in-the-money) 0.80 0.67
$47.00 (when the 45 call is 2 pts. In-the-money) 0.97 0.76

As you can see, the short-term options' deltas change dramatically when compared to the longer term options. 

The amount of extrinsic value factored into the price of such a short-term option (2 weeks before expiration) is significantly low or nearly cut out of the equation, especially once the option is in-the-money. 

If JP Morgan had been at:

$43.00 the November 45 would have traded at about $0.05  -  $0.05 extrinsic value
$44.00 the November 45 would have traded at about $0.20  -  $0.20 extrinsic value
$45.00 the November 45 would have traded at about $0.55  -  $0.55 extrinsic value
$46.00 the November 45 would have traded at about $1.25  -  $0.25 extrinsic value
$47.00 the November 45 would have traded at about $2.15  -  $0.15 extrinsic value

If JP Morgan had been at:

$43.00 the March 45 would have traded at about $1.30  -  $1.30 extrinsic value
$44.00 the March 45 would have traded at about $1.75  -  $1.75 extrinsic value
$45.00 the March 45 would have traded at about $2.25  -  $2.25 extrinsic value
$46.00 the March 45 would have traded at about $2.90  -  $1.90 extrinsic value
$47.00 the March 45 would have traded at about $3.50  -  $1.50 extrinsic value

A SIDE NOTE: Did you notice that the option with the most extrinsic value is always the option which is at-the-money?  So if you were the seller of the option, in order to collect a premium in the case of a covered call, you would be taking the most advantage of time decay by selling the at-the-moneys.

The deterioration of extrinsic value known as time decay comes into play mostly in the last three months remaining on the life of the option contract.

I will help you understand why this is true.  During the last three months of an option's life is when the decay of extrinsic value (time value) increases at an accelerating pace. 

Here's a good example, along with a chart which illustrates what happens to the extrinsic value portion of a call option: 

I once bought a call option (a long time ago,) which gave me the right to buy IBM at $100.00.

I think that the option had about three months of time left before expiration.

When the stock was at $101.50, the IBM 100 call was $1.50 in-the-money. The call option was trading at $4.00. So, out of the $4.00 premium that the call option was trading at, the remaining $2.50 was extrinsic value. 

If you study the time decay chart below, you will see the way that the decay of extrinsic/time value (aka "time decay") accelerates.  All options will react differently since all of the variables change depending on the specific option's situation.  But you get a basic understanding with this chart. 

Notice that the time value portion of the option only loses 10% (from 100% to 90%) of value in the period with 9-6 months left, the period with 6-3 months left loses 30 more percentage points (from 90% down to 60%,) and the remaining 60% of the extrinsic value portion of the price is clobbered in the last 3 months.

Again, remember that the red part that loses value is the extrinsic value, and you can see that the green part is the intrinsic and is not affected by time decay.

Do yourself a favor and stare at this for a LONG time.  That alone will actually make you a better options trader.

I hope that I have kept someone from making a terrible mistake.  I hope that I have caused someone to make smarter options decisions.  I hope that I have demystified the price action of options with respect to time decay and delta.  And I hope that you understand why options can be used to REDUCE risk and increase leverage at the same time. 

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