September 19th, 2014
by Russ Allen, Online Trading Academy Instructor
Our example so far has been about a covered call position on the stock of Apple, Inc. It involved a stock purchase at $102.39, together with the sale of a September $105 call at $1.41.
Here is the payoff graph for that position, showing its profit or loss on expiration of the call:
This graph shows a black line plotted for profit and loss at expiration. Two price levels are marked. The red vertical line is at the purchase price of the Apple stock at $102.39. If you were to start from the point where the red line crosses the black line, and trace straight to the left to the P&L axis, you would find that the P&L value at that point is at $141. If Apple were to be unchanged until the option expired, this position would have a profit of $141, equal to the amount received for the call option.
The gold vertical line is positioned at the position's break-even point. This is at the purchase price of $102.39, minus the $1.41 reduction in cost represented by the proceeds from selling the call. This is $102.39 - $1.41 - $100.98.
Also note that for any price of Apple above $105, this position makes its maximum profit. At $105 or anywhere above, we will be forced to sell the Apple stock, which cost us $102.29, at $105.00. The maximum profit amount is therefore the difference between the call strike price of $105 and the stock purchase price of $102.39, or $2.61; plus the $141 received for the call. Together these total $4.02 per share, or $402 for the 100 shares. This is the P&L value that lines up with the horizontal part of the black P&L plot, from a price of $105 onward.
Now let's add something new. All of the above profit figures were as of a specific moment in time - the option's expiration. But the position's profit would not suddenly jump to its final value at the moment of expiration. It would approach that final value gradually, as time passes.
The P&L diagram can help us to see the effect of time passing, as well as that of price changing.
How can a graph with only two dimensions - in this case profit (vertical) and price (horizontal) - show us the effect of a third variable, such as time? We indicated earlier that the P&L plot is as of a single moment in time.
We can accomplish this by plotting an additional line on the chart. This extra line can be as of an earlier time - for example, today. Then by looking at the two separate lines, we can see the effect of time passing.
Here is the same chart as above, but with an extra magenta line added. The magenta line represents profit or loss on this covered call position at any Apple price today.
The blue and magenta lines above are the profit and loss plots, or P&L plots.
Besides the P&L plots, this graph also has stock price marker lines. These are the vertical lines at Apple prices of $100.98 and $102.39, as before. I've also added a marker line at the $105 call strike price.
The table under the graph in the diagram above has a "Theo P&L" column. This shows the profit or loss that this position would have at expiration (lines labeled Plot 1 in blue) or today (lines labeled Plot 2 in magenta), at the stock price indicated in the "Stock Price" column. These stock prices correspond to the prices where the marker lines are located.
The $105 call which we sold short has time value now, but will have none at expiration (no time left equals no time value). As each day passes, the chances of Apple's moving above $105 in the time remaining grow dimmer; so the call option sheds some of its time value day by day. When we re-draw the magenta line tomorrow, it will be a little higher than it is today, approaching the blue line. Eventually the magenta line will merge with the blue line along its entire length.
Note that at each point where the vertical marker lines cross the P&L plots now, the magenta line is lower than the blue line. This indicates that at any of these Apple prices, the position shows a lower profit today (magenta) than it will at expiration (blue). In fact there is no price of Apple at which the profit today would be greater than at expiration.
There are, however, prices at which the P&L today would be the same as at expiration. Notice that the magenta and blue lines coincide below Apple prices around $95, and above prices around $115. This is because at these price levels, the $105 call would have zero time value today. There would therefore be no difference between the position's profit or loss today vs that at expiration.
At very low Apple prices, the $105 call would simply have no value at all, even though it had time remaining. If Apple were below around $95 now, with nine trading days remaining until expiration, there is about zero probability of its reaching $105. So the option would be worthless. In that case we would have a loss on the Apple stock we own. But that loss would be $141 less than it would have been if we had not sold the call.
At very high Apple prices, the call would have a great deal of value, but none of it would be time value. If Apple were at $115 today, the $105 call would represent a $10 discount compared to that $115 market value, and so the option would have $10 worth of intrinsic value per share. However, having gotten to $115, there would be virtually no chance that Apple would drop back below the $105 strike by expiration. Since the remaining nine days of time would not change the fact that this option was in the money, the option would have zero time value in this case also. A lot of intrinsic value, representing the $10 discount to market value, but no time value. So the blue and magenta plots show identical P&L values at very high or low Apple prices.
Any option has time value only if the underlying stock could move to the strike within the option's remaining life. That is, if there is any chance of the option's switching from out of the money to in, or in the money to out, the option has time value. But if the stock is so far away from the strike, either above or below it, that it could not get back to that strike by expiration, then the option will have no time value. The option will in that case have a price equal to its intrinsic value (if in the money); or zero (if out of the money).
With the addition of the magenta "P&L today" line, we can now see at a glance some additional items of information:
- This position is short time value. In any case where our profit later would be more than it is today, at the same stock price, we have sold time value and therefore are short time value. This is depicted by the position of the magenta "P&L today" line being below the blue "P&L at expiration" line.
- If Apple hit our $105 maximum profit price today, we would not make our maximum profit today. In the table, note that the last line indicates that at $105 today, our profit would be only $155.90. This is because our short call would have a lot of time value if its strike price were reached with nine days left to run. All of that time value will eventually run out, but we would have to wait until expiration for that to happen, if Apple were static at $105. That difference - $402 maximum profit at $105 at expiration, vs only $155.90 now, indicates that the $105 call would have time value equal to the difference, or ($402 - $156 = $246). In fact the vertical difference between the blue and magenta lines at any point is the amount of time value the option would have today, if the stock price were at that point.
- The amount of time value in the option changes at a given moment as the stock price changes, separately from the change in time value due to the passage of time. This is apparent because the distance between the blue and magenta lines is different at different prices. The closer the stock price is to the $105 strike price, the greater the difference. As the stock price moves toward the strike price, the option gains time value; and as the stock price moves away, it loses time value. This is another way of saying that options with strike prices nearest the stock price have the greatest time value at any particular moment.
Knowing which of the huge number of option opportunities is likely to work best in a given situation is a key to option profits. A thorough education, like that offered in our classes at Online Trading Academy, is required to know how to locate and sort through the possibilities. Once we are armed with the right approach, the P&L graph gives the kind of info we need to select and fine-tune our option positions.