Profit & Loss Diagrams

Options have unique pricing characteristics that are not available using stocks. In the Certificate Course, we show in detail the asymmetrical properties and why they occur, which is one of the big advantages investors can gain from them.

However, you can gain a sense of what it means from what we’ve already covered. If you buy 100 shares of stock for $50 then you will make one dollar for every dollar the stock rises. And you will lose one dollar for every dollar the stock falls. The reason for this is obvious. You’re holding the actual shares so the value will rise and fall with itself.

Now let’s assume you purchased a $50 call for $3 instead. For all stock prices above $50 at expiration, you will make dollar-for-dollar with the stock just as you would if you held the actual shares. However, if the stock price falls below $50 at expiration, you will only lose a maximum of $3. In other words, you participate fully for all stock price increases but do not share in the losses if the stock price falls. This is what we mean when we say that options have an asymmetrical property to their prices.

Because of this, it can be difficult to understand what your profits or losses will be for various strategies, especially if they contain two or more strikes. However, this is easily overcome by using profit and loss diagrams, which are an option investor’s best friend.

There is probably no better way to sum up the advantage of using profit and loss diagrams than with the saying, “A picture is worth a thousand words.” The risks and rewards of any position, no matter how complex, are brought to life by looking at a simple picture.

Even if you’re not familiar with the particular names of strategies, if you can read a profit and loss diagram, you will have a good understanding of what the strategy is trying to accomplish, what the rewards are and, more importantly, where the risks lie.

Constructing Profit and Loss Diagrams
Let’s take a look at how to construct a profit and loss diagram and then we’ll show you how easily they reveal the risks and rewards of various option strategies.

Please understand that the work we are putting into these exercises is not necessary when trading options in the real world. Computer programs will draw the pictures for you and you will not need to create the tables and charts. However, if you run through the calculations by hand while learning, you will understand the pictures much better.

Profit and loss diagrams can be constructed for any asset, not just options. So let’s start with a simple example and create a profit and loss diagram for one of the most basic of all positions, a long stock position.

In order to create any profit and loss diagram, we need two pieces of information. First, we need to know how much our asset in question will be worth at various stock prices. Second, we need to know how much was paid for the asset. With those two pieces of information, we can chart any profit and loss diagram.

Because we need to know what our asset in question is worth at various stock prices, we always start with a table consisting of various stock prices. That’s always the first step. Next, we calculate what the profit and loss would be for our position in question if the stock were at each of those prices.

For instance, assume you purchased stock for $50 per share. To construct the profit and loss table, we’d start with a column of stock prices starting with the $50 purchase price and then extend the range somewhat above and below this center price. For example, we may consider a range of stock prices between $45 and $55 as in the first column of Table 7:

Table 7: Profit and loss table (Long stock)

Next, we list the $50 cost of the asset in the second column. Notice in Table 7 that this cost is fixed. That’s just saying that our cost of the stock does not change as the stock price changes.

To calculate what the profit or loss would be for our asset in question (long stock) for each of the listed stock prices, we just need to take column one minus column two.

For instance, the first row in Table 7 shows a stock price of $45 with a cost of $50. If the stock price is $45, you have a $5 loss since you paid $50 per share. That is the loss that shows in column three.

Naturally, whether the profit/loss column represents a real loss or a “paper loss” depends on whether you actually sell the stock at that moment. If you sell the stock at $45, you have a $5 “realized” loss. If you do not sell it, you have a $5 “unrealized” loss. Either way, if the stock is $45, there is some type of a five-dollar loss facing you and that’s what Table 7 shows.

If you look further down the list, you can see that if the stock price is $50 then you are just breaking even. If you sell the stock at that price, you will have zero gains and zero losses, which is what column three shows. Look further down the list and you can see with the stock at $53, you’d have a $3 profit and so on.

Once our table is constructed, we just need to plot this information on a graph. We will always use the “stock price” column as the horizontal axis (x-axis) and the profit/loss column as the vertical axis (y-axis). This allows us to see how our profitability is affected at various stock prices. Once we do, we get a chart that looks like Figure 4:

Figure 4: Profit and loss diagram (Long stock)

Figure 4 is the profit and loss diagram for a long stock position and is simply a picture of the information in Table 7. (You may also hear of these diagrams referred to by other names such as profit and loss chart, profit and loss curve, profit and loss profile, profit and loss payoff structure but they all refer to the same thing.)

Notice that it is simply a straight line sloping upward to the right. To read the chart, you just select any stock price along the horizontal axis and then trace a vertical line up to (or down to) the profit and loss line. From there you follow it directly to the left axis and that tells you what your profit or loss would be for that particular stock price.

For instance, what would your profit (or loss) be if the stock is $54? All we have to do is trace a straight line from the $54 stock price on the horizontal axis up to our profit and loss line and then over to the vertical axis on the left as shown by the green dashed lines in Figure 5. You can see that we land on a profit of $4:

Figure 5

This tells us that if the stock is $54, you’d have a $4 profit. Likewise, Figure 5 shows that if the stock is trading at $46, you’d have a $4 loss, which is shown by the solid red arrows.

Notice that the horizontal axis intersects the vertical axis at zero, which is our breakeven point. In Figure 5, you can see that if the stock is $50 then you are just breaking even.

Anytime a profit and loss line intersects the horizontal axis that represents a breakeven point. (For some option strategies, there will be more than one break even point.) Breakeven points are critical since they identify points where you will head into profit loss territory for the next up or down move in the stock.

Figure 5 shows graphically what we’ve already determined at the beginning of this section. That is, if you pay $50 for the stock, you will make one dollar if the stock rises to $51, two dollars if it is $52, etc. Likewise, it shows that you lose one dollar if it falls to $49, two dollars if it falls to $48, etc. In other words, if you own stock, you make dollar-for-dollar as the stock price rises and lose dollar-for-dollar as the stock price falls.

Now take a look at a side-by-side comparison between Table 7 and Figure 5:

Even though they are two different ways of expressing the same information, the picture is easier to follow. It is much harder to visualize the profit and loss behavior by looking at the table.

Now, if you are familiar with graphing, you may have figured out that the information in the table would plot as a straight line. However, as we move to the asymmetrical payoffs of options and add more complex strategies, the table will be impossible to follow in your head. A picture becomes a much easier way of understanding how your profit or losses will be affected with changes in the underlying stock and that’s why you need to understand profit and loss diagrams. 

Let’s take the next step and try a little harder problem by creating a profit and loss diagram for a $50 call option that we purchased for $5.

To create the profit and loss chart, we must create a table and that always starts with a column of stock prices. However, when dealing in options, we pick the stock prices based on the strike price of the option (or options) rather than the purchase price as we did for the long stock example. Because we’re trying to figure out the profit and loss diagram for a $50 call, we would create a column of stock prices starting at $50 and then select a few stock prices above and below $50 such as shown in the first column of Table 8:

Table 8: Profit and loss table (Long $50 call)

Notice that our stock prices are in five-dollar increments rather than one-dollar increments we used for the previous long stock example. In actuality, it doesn’t matter which increments you use since all methods produce the same picture. But in order to keep the tables small, we generally count by five-dollar increments when dealing in options.

The second column in Table 8 shows what the $50 call will be worth at expiration. It’s important to understand that when drawing profit and loss diagrams for options, we are drawing them at expiration of the option. This is one of the motivations for understanding the third pricing principle we discussed in the previous section. That is, all options are with zero or their intrinsic value at expiration.

For example, we know that if the stock is $35 at expiration, the $50 call expires worthless. In fact, the $50 call will expire worthless for all stock prices at $50 or lower. However, if the stock is $55, the $50 call would be worth exactly $5 at expiration. If the stock is $60 at expiration, the $50 call is worth $10 and so on.

The third column in Table 8 shows us the cost of the call, which we assumed was $5 for this example. If this were a real-life example, we may just use the $5 premium for the option or we may be more realistic and include commissions. Either decision will not change the shape of the profit and loss diagram but it would change the profit or loss values.

Whether you decide to include commissions or not, the cost you come up with does not change as the stock’s price changes. That’s why the third column in Table 8 is the same answer ($5) for the entire column.

Now we have our two necessary pieces of information to draw the profit and loss diagram: (1) We know the value of the $50 call at various stock prices by looking at column two and (2) We know the cost of the $50 call by looking at column three. Now we just need to figure out what our profit or loss will be for the various stock prices in the table.

We figure out the profit or loss just as any business would by taking “revenues minus costs.” Look at the first row of Table 8. If the stock closed at $35 at option expiration, your revenues would be zero from the sale of the option since it is worthless (shown in column two). Because you paid $5 for the option (shown in column three), you’d have a $5 loss with the stock at $35. This same reasoning is used to complete the table for each stock price. The formula for the profit/loss column is simply Column 2 - Column 3.

Once we have the necessary pieces of information, all we have to do is plot the profit/loss column against the stock prices (red columns in Table 8) and we get the following profit and loss diagram shown in Figure 6:

Figure 6: Profit and loss diagram (Long $50 call)

We read this profit and loss diagram in the same way as we did for the long stock profit and loss diagram. For instance, how much would we make or lose if the stock closed at $60 at expiration? We just need to find $60 on the horizontal axis and draw a line to the profit and loss curve. From that point, we just look directly to the left axis to find the answer, which is $5, as shown by the dashed arrows in Figure 7:

Figure 7: Profit and loss diagram (Long $50 call)

We can check the answer by hand. If the stock were $60 at expiration, the $50 call would be worth exactly $10. Because we paid $5 for it, our profit must be $5. Hopefully you are convinced that it is much easier to look at the picture to arrive at this answer rather than going through all of the steps by hand.

While it is easy to determine the profits or losses at various stock prices, the advantages of profit and loss diagrams do not stop there. More importantly, we can immediately get valuable insights about the strategy.

For instance, the picture tells us that a long call is a bullish asset since it makes money as the stock price rises. Further, there is no limit to the amount of money that could be made since the chart continues to rise with increasing stock prices. We can also tell that there is a defined, limited loss. No matter how far below $50 the stock may be at expiration, the maximum loss is $5. We can also see that the strategy needs the underlying stock price to be $55 at expiration in order to break even (since that is the point where the profit and loss curve crosses zero.)

Even if you do not understand a particular strategy, a quick glance at its profit and loss diagram immediately shows what the trader would like to have happen to the stock price.

Notice that the profit and loss diagram for a long call looks more like a “hockey stick” rather than the straight line we saw for a long stock position. This is because the holder of a long call can only lose the purchase price no matter how low the stock’s price may fall below the strike price. This is a graphical representation of the asymmetrical payoff structure of options. The call holder participates for all price increases but does not lose for all drops in the price.

If the stock is $50 or lower at expiration, the long call holder loses a maximum of five dollars and that’s why the curve flattens out for all stock prices below $50. Anytime you see a “flat” segment (running parallel to the horizontal axis) of a profit and loss diagram, it tells you any stock price changes over that range have no additional effect on your profit or loss at expiration.

The profit and loss curve shows that long calls allow traders and investors a way to participate dollar-for-dollar as the stock price rises but not lose dollar-for-dollar if the stock price falls. In other words, long calls provide traders and investors with some downside protection.

Characteristics of Profit and Loss Diagrams
There are three important characteristics that are common to all profit and loss diagrams:

  • A “bend” will occur at every strike price
  • There will be a portion above and below zero
  • The curve will cross zero at one or more points (the break even point)

Let’s go through each of these in a little more detail. First, all profit and loss diagrams will “bend” at the strike of each option(s). In Figure 7, the $50 call bends upward at the $50 strike but that will not always be the case. Depending on the option, whether it is long or short, and how it is paired with other assets, the profit and loss diagram may bend up, down, or even sideways. But you can always be sure that it will bend at every strike price involved in the strategy.

The second characteristic of all profit and loss diagrams is that every one will have a portion of the diagram that falls above and below zero. The reason is simple. Every strategy has a potential reward and that is the portion that is represented in the chart as the area above zero. If there is a reward then there must be a potential risk in attempting to gain that reward and that is the portion that lies below zero. This is important to understand because it will help you to decide if a particular strategy has a risk-reward ratio suitable for your tastes.

Train your eye to see the profit areas (area above zero as shown in green below) as well as the loss areas (area below zero as shown in red) and at which stock prices those occur:

Figure 7: (Reproduced)

The third characteristic is that all profit and loss diagrams will have at least one break even point. This follows from the fact that if a portion of the profit and loss diagram must lie above and below zero then it follows that the diagram must cross zero at some point.

The point where it crosses the zero on the horizontal axis is the break even point. In Figure 7, our long $50 call purchased for $5 crosses zero at a stock price of $55. This tells us that if the stock closes at $55 at expiration, we will have no profit and no loss (not counting commissions). If the stock is $55, the $50 call can be sold for $5. Because we paid $5, we break even on the trade.

The break even point for a call position (long or short) is found by adding the strike price and the premium. In this example, $50 strike + $5 premium = $55 break even and that’s exactly what the chart is showing us. Remember, every profit and loss diagram will have at least one break even point. Figure 8 highlights these three important characteristics:

Figure 8: Main Characteristics of Profit and Loss Diagrams

Okay, let’s finish this section with one final example to really show the power of profit and loss diagrams. We’re going to name an advanced strategy that you’ve probably never heard of and one that we’re not even going to discuss in this course. That strategy is called the Short Iron Condor. This particular example will be constructed by selling the $55 put and $60 call. Next, we will buy the $50 put and $65 call. We will assume that these transactions bring in a $3 credit to the account.

Now for the hard part. Can you tell if this is a bullish or bearish strategy? What are the maximum gains and losses? Where will the strategy break even? You can see these questions are nearly impossible to answer without the visual aid of a profit and loss diagram. Figure 9 shows the profit and loss diagram for this short iron condor:

Figure 9: Short Iron Condor

Now that you have a picture, you should readily see the answers. You can see that the strategy outlined in this example can make a maximum of $3, which occurs if the stock price is between $55 and $60 at expiration. The maximum loss is $2 and that occurs if the stock’s price is below $50 or above $65 at expiration.

This strategy is not looking for big price moves in either direction. Instead, it needs the stock to stay relatively quiet between $55 and $60. It is not bullish or bearish – it is a neutral strategy. This strategy has two break even points. The first is at $52 and the second is at $63. Even though the ideal situation is to have the stock close between $55 and $60, it can actually close between $52 and $63 at expiration and still be profitable. Below $52 and above $63 we start to head into losing territory.

Notice how much we could tell about a strategy that we knew nothing about just by looking at its profit and loss chart. They are invaluable tools for learning strategies and assessing the risks and rewards of any position. As you start trading options, computer software will draw these charts for you. The important thing is that you know how to read them.

In fact, most programs will even draw profit and loss diagrams prior to expiration. This requires the aid of an option pricing model to help with theoretical calculations (that’s why we draw them at expiration by hand). The pictures will change but the way you read them is the same. If you take the time to work with profit and loss diagrams, you will have a much better understanding if a particular strategy really is right for you. 

                               Next Section: Hedging

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