**Online Trading Academy Article of the Week**

*by Russ Allen, Online Trading Academy Instructor*

When trading options, we are dealing with an instrument that is much more mathematical than other things like stocks and futures. Those are “*single-dimension*” instruments. Their prices go up, and they go down. Options have three dimensions. They are moved by changes in the underlying stock. But in addition, they change due to time and volatility. Visualizing the options profit picture is therefore more challenging.

Fortunately though, we have a powerful tool to help us with this. This is the option payoff diagram, also sometimes called the risk graph. This tool helps us to visualize how the value of an option position would change in response to all three of these influences. This is is an invaluable aid in creating profitable positions. In fact, that task is pretty nearly impossible without it.

Here’s how it works. First, let’s look at a payoff diagram for a simple stock position. Below is the diagram for the stock of Apple.

Figure 1 – Payoff diagram for AAPL stock – long position

Across the bottom of the chart is the scale showing different stock prices for AAPL. Today AAPL closed at $100.61 per share. The vertical red line marks this price.

The vertical scale, labeled on the left as “*Theo Value P&L,*” is the profit or loss on a 100-share stock position, assuming that you bought it at the present price.

The blue diagonal line plots profit or loss at any stock position. The blue line crosses the red line where Stock Price equals the current price of $100.61, and the value for theoretical profit or loss is zero. This indicates that today, tomorrow or at any other time, if the stock price stays at our cost, we would have zero profit or loss.

As we move away from that intersection toward the right, we are moving to higher stock prices. At those higher prices, our profits rise as well, so the blue line slopes up. For every dollar AAPL moves above our cost, we make $100 on our hundred shares. And if AAPL’s stock price goes down (leftward on the graph), we have a loss of $100 for every dollar (the blue line goes down to lower P&L values).

A line that slopes in this direction (upward to the right) is said to have *positive slope*. On payoff graphs, positive slope means that higher stock prices lead to higher profits – in other words, a bullish trade.

Until we get accustomed to it, one odd thing about this chart is that price is read left to right, instead of up and down. Another is that time is completely absent from the chart. This is not a *record* of what *has happened* to price over time. It is a *projection* of what *will* happen to *profit*, at any price, regardless of time.

To help further with visualizing in this way, look at the chart below. It is also a payoff graph for AAPL stock, but this time for a short position. If we were to sell the stock short, we would make money if it went down, and lose money if it went up.

Figure 2 – Payoff diagram for AAPL stock – short position

Now the blue line slopes in the opposite direction – downward as stock prices increase from left to right. This is called negative slope. It indicates that higher prices (rightward movement) lead to lower profits (lower P&L values on the vertical scale). In other words, negative slope indicates a bearish trade.

These are the simplest possible payoff diagrams. The slope is one to one, either positive or negative, over the whole chart. One dollar price change leads to one dollar difference in P&L, per share.

Now let’s look at the payoff diagram for a call option. Let’s say that we were to purchase a call option that gives us the right to buy 100 shares of AAPL at a fixed price of $100 per share, good for three months. As of now, such options are available for $5.30 per share ($530 for a 100-share contract).

Here is the diagram for that $100 November call. It shows the profit or loss as of a particular moment in time – the moment when these options expire on November 21.

Figure 3 – Payoff diagram for AAPL $100 call option purchased for $5.30

Now the blue line is not just a straight diagonal line. On the left side of our $100 strike price, the blue line is flat, at a P&L value of minus $530. This means that if AAPL is below $100 when the call options expire, we would lose the entire $530 cost of the option.

If AAPL is above $100, then the right to buy it at that price represents a discount to market value. Since there will be no time left for market value to change any further, the call at that point will be worth exactly the amount of discount that it provides. In other words, the call will be worth exactly the amount by which the price of AAPL exceeds $100. If AAPL is $106, then the call will be worth $6, and so on. There is no limit to the amount of profit that could be made, since there is no limit to how high the price of AAPL could go. So the line continues up and to the right to infinity.

Notice that the blue line crosses the zero P&L level where the stock price equals $105.30. This is because AAPL would have to be above the $100 strike price by at least our $5.30 cost for us to make any money.

So a quick glance at this graph tells us several things:

*This is a bullish trade.*The positive slope indicates that.*The trade has limited risk.*The lowest point on the graph is at a loss of $530. Since the graph is flat and does not go any lower, that is our maximum loss.*The trade has unlimited profit.*Since the line slopes up and runs off the chart, there is no limit to potential profit.*The break-even price is $105.30.*We can see this because the blue P&L line crosses zero at this stock price.

All of this is instantly visible from the graph. If we add in our opinion as to where we believe price will be in the next three months, then we have a powerful tool for visualizing our profits.

This chart can do even more for us than we’ve described so far. Like any power tool, it doesn’t do the job by itself. It can make possible tasks that we could not otherwise attempt. It also requires a skilled operator to get its maximum benefit. A proper education, like that provided in our classes, is the key to getting the most out of the power tools available to us.

In the above showed the payoff graph for a regular stock position – a hundred shares of Apple Computer. The rest ikof this article was written at a later time. Updating that to the price as of this writing, this is what that chart looks like:

*Option Payoff diagram – AAPL stock*

This graph is just a 45-degree line, a slope of one in one (one dollar “*rise*” in profit per one dollar “*run*” in the stock price). The red vertical line is at today’s close of $102.39. If we look to the left from the intersection of that line with the P/L plot (the dark green line), we see that that intersection is at a “*Theo Value P/L*” value of $0.00. This makes sense. If we bought AAPL at the current price of $102.39 then we would have zero profit if it stayed there. We’d have positive P&L if it went up, and we would lose if it went down.

Next, let’s look at the chart of a *call* option on AAPL, instead of the stock itself. As of today, we could buy a 105 September Call option for $1.41 per share ($141 per 100-share contract). Anyone who owns one of these calls has the right to buy 100 shares of AAPL at $105 per share, at any time before the options expire at 4:00 PM EDT on Friday, September 19. If we bought one of those calls *instead of the stock*, then our profit picture would look like this:

*Option Payoff diagram – Long AAPL Sep 105 Call*

Unlike the case with the stock position, this one has a horizontal section. It stretches from a stock price of zero (off the chart to the left) all the way to $105. That horizontal line is at a P&L value of -$141 (on the left scale). This indicates that the maximum loss on that position is the amount paid for the option – $141. If AAPL doesn’t exceed our $105 strike, and we hang on until expiration, that will be the amount of our loss.

Above $105 (prices further right on the chart), the P/L curve ascends. If AAPL is higher than $105 when this option expires, then the option will have some value, and we as owners of the call will not lose our full $141 investment. If AAPL exceeds the $105 strike price by the amount needed to pay back our $141 investment, then we break even. The gold vertical line at that stock price (strike price plus option premium, $105 + $1.41 = $106.41) crosses the green P/L line where that green line’s value is zero.

If we are fortunate enough to see AAPL climb higher than $105, then we begin to make money. And the higher it goes, the more we make, with no limit.

This particular option could potentially pay off many times more than our $141 investment. BUT – AAPL has to move a lot in a short time to make that happen. If it doesn’t get a move on, we stand to lose money. True, that’s only $141 at worst, and that is a lot less than the cost of 100 shares of stock. Still that $141 is 100% of our investment.

Buying this specific option is therefore a very speculative trade. We’re betting on a big move. If it doesn’t happen, we lose.

So who wins? If we did lose our $141, to whom would it go? The answer is that it would go to the seller of the call option. We paid that person $141 when we bought the call. In return, they were obligated to sell us AAPL at $105 whenever we wanted, up until expiration. Since we never exercised that option, their obligation disappears when the option expires, and they pocket the money.

So let’s look at the other side of this trade. Here is the profit picture from the call seller’s point of view:

*Option Payoff diagram – Short AAPL Sep 105 Call*

Compare this diagram to the previous one. Note that it is the exact mirror image, if the graph is rotated around the horizontal axis. The horizontal line, at a P/L value of +$141, now indicates the option seller’s maximum profit. He took in $141, and he hopes to retain it. If AAPL stays below $105, he will do just that.

On the other hand, the P&L plot extends down to infinity at the right side of the graph. This reflects the fact that the call seller’s loss in unlimited – the literal mirror image of the option *buyer’s* unlimited potential profit.

The gold vertical line at $106.41 still crosses the P/L plot at a value of $0.00 on the left axis. But here the P/L curve slopes downward. This illustrates the fact that if an option buyer makes any money, the option seller loses that same amount. This is true at any price of the underlying asset at expiration. What one side gains, the other side loses. This is the definition of a *zero-sum game*. The sum of the wins and losses is zero.

Now let’s take another step. What if the person who *sold* the call option (as in the above diagram) also bought AAPL’s stock at its current value of $102.39 (the first diagram)? The combination of the long stock and the short call is referred to as a *covered call*. This combined position would have a diagram of its own, which would look like this:

*Option Payoff diagram – Long 100 shares AAPL at $102.39, Short AAPL Sep 105 Cal @ $1.41*

The profit or loss on this covered call position, at any stock price, is the combination of the profit or loss on the stock, and the profit or loss on the short call. Notice these points about this combined position:

- The break-even price – where the dark green line crosses zero on the left scale – is now at a price that is lower than the current stock price. That break-even point is now at $100.98 (gold line). By selling the call in addition to owning the stock, the investor has reduced his cost by the $141 call premium.
- If AAPL now stands still, the stock owner’s profit is positive – in fact he makes $141.
- This improvement in his immediate P/L picture has come at a cost. His profit is no longer unlimited. Because he is obligated to sell the AAPL stock at $105, he can never make more than ($105 – $102.39 = $2.61) on the stock; this amount, in addition to the $1.41 that he received for the call, is his maximum profit. This is shown by the horizontal line at a P/L value of ($261 + $141 = $402).

By combining the diagrams of these two separate positions, we can now see what the combined net profit would be at any stock price. This is a tremendous help in visualizing our potential profits and losses. There is still more that these diagrams can tell us, and we’ll review that in future articles.

Knowing how to interpret these diagrams, and manipulate them to take into account our educated forecasts for future prices, is an essential skill. A proper trading education is essential to being profitable in options, or any other kind of trading. That kind of education is available in our on-location or online classes. Contact your local center for details, or go to www.tradingacademy.com.