Call Options: an Introduction

We peek at the CBOE website, looking at the CALL options for Merck Inc. the top part of which looks like:

The "call" options are in the left column, "put" options (which we'll talk about later) are in the right column, the current stock price is \$65 and the situation is as of September 30.
Here we see MRK Oct 60 CALL options trading; the asking price is \$5 5/8 (or \$5.625). We won't worry about the funny (MRK JL-E) except to note that this symbol for the option has MRK embedded (as you might expect, cuz that's the stock symbol) and the terminal letter E just means it's trading at the Chicago Board of Options Exchange (as well as at other exchanges identified by letters A, P, etc.) and the JL is their fancy way of saying it's an October call and it's the \$60 one. (You'll notice that the Oct 65 call has the funny letters JM, with J meaning October and M meaning \$65.)

If we buy this option for \$5 5/8 we have purchased the right to buy the stock for \$60, any time before the third Friday in October. (We don't have to buy the stock, but we could if it were worth our while. In other words, we have the right, but not the obligation. Indeed, we could also sell our option before it expires rather than using it to purchase Merck stock.)

If we do exercise our option, from whom do we buy the stock (for \$60/share)? From the person who sold the option!

Of course, the stock is now trading at \$65 so buying it at \$60 sounds great - but we had to pay \$5 5/8 for this right, so the stock would actually have to increase in price to something greater than \$60 + \$5 5/8 = \$65 5/8 before we could make any money! Nevertheless, if the stock exceeded \$60 by any amount, we'd exercise our option, buy the stock and immediately sell it; that way we'd at least make something. Of course, if the stock fell to below \$60 we'd just let our option expire, worthless ... losing all of the \$5 5/8 which we paid for the option.

Uh ... one other thing. One doesn't buy the right to purchase a single share but rather blocks of 100 shares. That's called one contract, so it'd cost us 100(\$5 5/8) = \$562.50 for this 100-share contract (since \$5 5/8 = \$5.625). However, we'll just work with single shares (and we'll multiply everything in sight by 100 when we're finished).

Okay, under what circumstances do we make money on this option?

If, by that third Friday in October, the Stock attains a price of \$S, then we have two cases (depending upon whether we exercise our option ... or we don't):

1. \$S < \$60
2. \$S > \$60
• As we've already noted, we'd lose our \$5 5/8 in the first case. (Why would we buy the stock for \$60 when it's selling in the market for less than \$60? So, we'd just let our option expire ... and we've lost our \$5 5/8.)
• In the second case, we'd exercise our option (buying the stock for \$60) then we'd sell it for \$S, making (S - 60) on this transaction ... but it's cost us \$5.625 for the option so our gain would be S - 60 - 5.625 per share so, for one contract, that'd mean 100(S - 60 - 5.375). In case you haven't noticed, this could be NEGATIVE (so our gain could be negative in this second case).
• In the best-of-all-worlds, the stock price will exceed \$65.625 and this gain is POSITIVE.

Maybe we should put it this way:
Let \$C be the Call strike price. In the above example, it's \$60. (Did I mention that it's called the strike price?)
Let the cost of the Option be \$O. (In the above example, that's the \$5.625 per share.)
Let the Stock price (on that third Friday expiration date) be \$S.

In the first case mentioned above (where S < C), our gain is negative, namely -O; we lose the cost of our option.
In the next case our gain is S - C - O (which is positive only when S > C + O).
How about if we combine these two magic formulas? Our gain is either {0} - O or {S - C} - O so it's always

 {the MAXIMUM of (S - C) and 0} - O

(Uh ... did I mention that 0 is zero whereas O is the letter which represents the Option price?)

Anyway, we'll make this our first magic formula:
Magic formula 1:
 Call Option Gain (BUYING) = MAX{S - C,0} - O
where
S = Stock price at expiration of the option
C = Call strike price
O = Option price ... or premium
and, because we'll be using this later,
P = the current stock Price

Of course, when you buy a call option, the numbers C and O are then fixed. (For our Merck example, C = \$60 and O = \$5 5/8.) As time progresses (toward the expiration date of the option), the stock price S will indoubtedly change from its current value of P. Your gain (or loss!) will look like this:

showing possible locations of the current stock price \$P

where your gain is -\$O when S < C and it increases as S increases, eventually becoming POSITIVE when S > C + O.

Oh, by the way, if the strike price C is greater than the current stock price P, we say that the option is out of the money. (That's the leftmost location of the green \$P dot.) It's "out of the money" because, if the call is exercised immediately, there would be a loss on the transaction. Buy at \$C, sell at \$P, you lose.

If the strike price C is less than the current stock price P, we say that the option is in the money. Buy at \$C, sell at \$P, you're in the money on that transaction, right? ... and that's the rightmost location of the green \$P dot.

One other thing: When we bought our call option, the stock was trading at \$P. It is always true that C + O > P. If this were NOT the case, I'd run out and pay \$O for the option, immediately exercise it (hence buy the stock for \$C so I've now invested \$(C+O)), then I'd sell immediately for the market price of \$P making an instant profit of \$(P - C - O) ... and I'm not that lucky (and neither is anybuddy else). Come to think of it, maybe we should promote this result to:
Magic formula 0:
 Universal Truth: = C + O > P
Sorry for putting the formula numbers out of sequence ...

Okay, how about if we SELL a call option ... or should I say we WRITE a call option? (That's option-speak. You don't SELL, you WRITE!?) Again we have the four numbers:
S = Stock price at expiration of the option
C = Call strike price
O = Option price ... or premium
P = the Price of the stock when we wrote the option.

Here, we're assuming we actually OWN the stock (though, as we'll see, we could write calls even if we didn't own any stock; that would be called (is that a pun?) an uncovered or ... uh ... a naked write). For now, we'll just deal with covered calls.

When writing a call, we actually receive the option premium, O, so we're in the money already! If the Stock price exceeds the strike price, C, then whoever buys our option will undoubtedly exercise the option and we'd have to sell the shares at \$C. However, we've already made \$O by selling ... and \$C - \$P from the increase in the stock price (from the price we paid, \$P, to the price we received, \$C). Our total gain is \$O + \$C - \$P
Can this be negative?
No, 'cause we saw that C + O > P.
(That's Magic Formula 0 ... which explains why we elevated this result to a magic formula).

What if the Stock price fell dramatically, say S < C? Then no buyer of our option would exercise the option; why'd they buy from us at \$C when they can buy the stock on the market for less, namely \$S? So we keep the stock, but it's now worth \$S instead of the \$P we paid, so may lose here, but any loss is compensated for, in part, by the premium of \$O which we received. In fact, we won't actually lose until the Stock price falls by \$O. \$Our net gain is then:
Option_Price + Change_in_Stock_Price = \$O + \$S - \$P.

Let's compare the two formulas:

 S > C: (our stock is called away at \$C) Gain = \$O + \$C - \$P S < C: (we keep the stock, now worth \$S) Gain = \$O + \$S - \$P

Which brings us to our next magic formula:

Magic formula 2:
 Covered Call Option Gain (WRITING) = MIN{S,C} + O - P

and, of course:

the picture for WRITING a covered call option:

showing possible locations of the current stock price \$P

compared to the picture for BUYING a call option

Observations:

• BUYING a call option? There is limited loss* if the stock goes down and unlimited gain if the stock goes up.
• WRITING a covered call? There can be large losses if the stock goes down and limited gain if the stock goes up.
• Expecting a bull market for this stock? BUY a call.
• Expecting a bear market for this stock? WRITE a call, collect the option premium \$O and pray the stock doesn't fall by much more than \$O (hence cushion the blow when the stock goes down).
• Note that, in the chart for writing a call, the point \$(P - O) lies the the left of the point \$C.
Q: How can we be sure of this?
A: Magic Formula 0!
• Changing the \$Option price (or premium) shifts the broken-line graph (for buying) up or down (but the "break" occurs at the same place ... ALWAYS AT \$C !).
• Changing the \$Call strike price shifts the broken-line graph (for buying) left or right (and the "break" moves left or right). (This does NOT apply for writing (covered), 'cause the stock Price is involved!)
• The broken lines are either horizontal or they're at 45 degrees to the horizontal.
(That's important; we gotta remember this!)
• The TOTAL gain, from writing (covered) and buying a call, is the sum of the two gains
... though we may buy at one strike price and sell ... uh, write, at another ... and the option premiums may be different.
* This limited loss phraseology is prevalent terminology among those who speak in glowing terms about options
... but wait'll y'all git to PART 5.!
For our Merck example, for the oct 60 call which we could sell for \$5 5/8, our maximum gain would be \$C + \$O - \$P = \$60 + \$5.625 - \$65 = \$.625 per share ... no matter how high the stock might move in the future. If that doesn't sound too exciting -- it's about a 1% gain -- remember that, for the Merck example, the date was Sept 30 (see the CBOE table, above) and the option expires on the third Friday of October and that's only a couple of weeks into the future and now 1% doesn't sound that bad, right?

If we were to look at options which expire several months into the future, the option premium, O, would increase and so would our maximum gain. In fact, for call options with a \$60 strike price (and sold ... uh, written on Sept 30), the premium would probably look something like this:

Umm ... did I might mention that options aren't available in every month of the year ... but that's another story.
And how do I know the trading prices for these options ... months into the future? I used Black-Scholes ... aah, but that, too, is another story.

Now, let's consider the scarier:
Writing an uncovered call.

Here we sell (or write) an oct 60 call option contract (which means we agree to sell 100 shares of stock for \$60 per share anytime the buyer wants to exercise her option ... so long as it's before the third Friday in October, when the option expires) except that we don't even own any stock!

Should the stock price \$S rise dramatically (to \$100/share?) and the buyer of our call exercises it, we must run out and buy 100 shares of stock (for \$100/share!) and sell it to her for \$60/share. Mamma mia! Scary!

The good news is: if the stock price drops below \$60 (to \$5\$?) no buyer will exercise it and ask to buy our stock for \$60 (when it's available for \$5!) ... so we just pocket the option premium. Since we don't actually own any stock we don't lose any value in our stock portfolio. Neato!

So what does the gain/loss chart look like? As usual there are two cases:

1. \$S < \$60     where we just keep the option premium \$O
2. \$S > \$60     where we buy stock at \$S and sell it for \$60, losing on this transaction ... but we've already pocketed the premium \$O so our net gain/loss is \$60 - \$S + \$O
We make this another:
Magic formula 3:
 Uncovered Call Option Gain (writing) = O + MIN{C - S,0}
where, as usual
S = Stock price at expiration of the option
C = Call strike price
O = Option price ... or premium
P = the stock Price when the option was written

Notice that \$P is (almost) irrelevant; we didn't actually buy any stock at this \$Price (although \$P does influence the Call strike price and the Option premium).

Now, the picture:

showing possible locations of the current stock price \$P

and some
Observations:
• You lose if the \$Stock price exceeds \$C + \$O.
• You lose big time if the stock REALLY takes off. Indeed, there is no limit to your losses!!
• With uncovered calls (that's what we're talkin' about here) you could lose your shirt. (Is that why they call them naked calls?)
• Changing the Option premium shifts the writing (uncovered) graph up and down. Changing the Call option strike price shifts it left and right ... just as it did for buying. In other words, in each case we need only know C and O in order to determine these graphs!
 Writing (covered) is the only case where we actually buy stock ... so we need to know the stock Price before we can draw the graph. Indeed, the graph changes significantly when P (hence O) changes:

As you might expect, certain combinations of writing (covered) or writing (uncovered) calls and buying options may be a good strategy. We'll stick a bunch of these broken-line graphs together to see what gains we can come up with ... in PART 2.

 P.S. Did I mention that I ain't no options guru? I read me a coupla books, attended a seminar, surfed the Net fer option bumpf, bought a CALL or two, made a few bucks, lost a few bucks ... then stuck what I larned here, so y'all kin git a taste ...

buying     writing covered     writing naked     gains