Call Options: Gains & Losses

First, let's display our graphs again:

Figure 1: Gain or Loss when buying a call option

Figure 2: Gain or Loss when writing a covered call option

Figure 3: Gain or Loss when writing an uncovered call option

where:
S = Stock price at expiration of the option
C = Call strike price
O = Option price ... or premium
P = the current Price of the stock (when the option was bought or written).

Here's our real live example, for Merck:

Suppose we buy the oct 60 for \$5 5/8 = \$5.625 and we sell covered oct 65 for \$1 3/4 = \$1.75 ; the gain/loss chart would look like so:

Buy oct 60 and Write oct 65

Observations:

1. The green guy is the gain/loss curve for buying and the blue is for writing and the red graph is (would-you-believe) the total Gain (which is, of course, the sum of the other two guys).
2. The breaks occur (always) at the strike prices which are identified by the big dots on the horizontal axis. The right one also happens to be the current stock price of \$65 which is why I hi-lited it with a red centre.
3. The Gain curve has two (count 'em!) two breaks, one at each of the strike price breaks.
4. The shape of the Gain curve is characteristic of a buy and sell where the buy is at the lower strike price ... which reminds me, here's the situation if the buy is at the higher strike:

Buy oct 65 and Write (covered) oct 60

Uh ... did I mention that the gains/losses illustrated on the charts are for one contract, not for one share ... and since a contract is 100 shares we multiplied everything by ... well, you get the idea.
About the Total Gain chart (when writing a covered call), we make some
Observations:
• Buy at the lower strike: the slope doubles between strike prices (because the two 45 degree slopes add together).
• Sell (covered) at the lower strike: the slope is zero between strike prices (because both slopes are zero).
• Outside the two strike prices, the Gain graph is always increasing ... at 45 degrees to the horizontal.

If we refer to Figures 1, 2 and 3, above, we can put some general values in the Total Gain chart when selling (covered) at the lower strike price ... or buying at the lower strike price or even selling uncovered (but at the higher strike price):

Buy ... and Write a covered call at a lower strike price

Buy ... and Write a covered call at a higher strike price

Buy ... and Write an UNcovered call at a higher strike price

Buy ... and Write an UNcovered call at a lower strike price

where C(s) and C(b) are the strike prices for selling and buying.

Notice (from the last two charts) that both Gains and Losses are limited if we buy a call and write an uncovered call.

We might have anticipated this, because, for tiny stock prices, both buy and sell charts are horizontal (hence, so is the sum) and for huge stock prices the buy chart goes UP at 45 degrees and the sell chart goes DOWN at 45 degrees (hence the sum is again horizontal, the slopes cancelling out). We'll be doing more of this in the next part, that is: adding positive and negative slopes to get horizontal graphs (limiting gains or losses)
... and adding positive slopes to get steeper slopes
... and adding ... well, wait for it ...

Excuse my using sometimes writing or sometimes selling ... like ... randomly choosing one or mebbe t'other ... or mebbe saying uncovered then mebbe naked ... then mebbe ...

Let's play.
Look at the various gain charts below. We want to shift the buy and sell (covered) and sell (uncovered) charts up and down or maybe left and right (by choosing appropriate strike prices and option premiums) so that the gain looks appetizing ...

Remember these charts:

Go To PART 3

buying     writing covered     writing naked     gains