# Stock Options - Building Profit and Loss Diagrams to Support Trading Strategies

Updated on July 28, 2016 Philip retired from investment banking to write. To date he has written 9 books on trading forex, 3 short stories, and one poetry book.

## Introduction

In this article, you will learn to draw basic profit and loss diagrams of option strategies. It is important that you master the skill of drawing these diagrams for several reasons. Understanding potential benefit and potential risk is an important first step in determining whether a particular strategy is appropriate in a specific situation.

The diagrams illustrate the important risk/reward elements of a particular strategy, including the profit potential, the maximum theoretical risk, the break-even point at expiration and how various market scenarios will affect the ultimate outcome of the strategy.

The ability to draw strategy profit and loss diagrams also demonstrates a true understanding of a particular strategy, and it is an excellent method of communicating the advantages and disadvantages of a strategy to a colleague, manager, customer or risk controller.

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## The Steps for Building a Profit and Loss Diagram

We will start with the pay-off diagram of a long stock position; that is what is the potential profit or loss if you owned 100 shares of ABC stock. There are seven steps to constructing the profit and loss diagram.

Step 1: Construct a profit and loss grid for the diagram. The vertical axis is for profit and loss, and the horizontal axis contains a range of prices for the underlying instrument.

Step 2, describe the transaction completely. In the case of an option, it is not enough to say "buy a call," as this does not provide sufficient information to calculate profit and loss at various outcomes. Rather, "buy a \$60-strike call for 3 ½ per share" does provide all you need. We assume in this example that one share of stock is purchased for \$50 without transaction costs.

## Steps 3 and 4

Step 3 - Pick a specific price for the underlying. Let’s try this out. Choose a stock price. If we assume that we bought the stock at \$50 a share, calculating the profit or loss is simple. We just subtract \$50 from our selected price. For example, if we choose \$53, the profit is \$3.

Step 4 - Choose the price and profit we would like to see displayed. Since the grid has a range of prices from \$45 to \$55, we will pick a price within that range.

## Step 5

Now let's choose the prices and profits we would like to see displayed. Again since the grid has a range of prices from \$45 to \$55, we will pick a series of prices within that range.

## Constructing a Call Option profit and Loss Diagram

We have just completed a Profit and Loss Diagram!! This diagram indicates the potential profit, the potential risk and the break-even stock price.

Potential profit -- theoretically unlimited if the stock prices rises

Potential risk -- \$50 per share if the stock price falls to -0-

Break-even stock price -- \$50, in this case equal to the purchase price

Step 1 - We are going to construct a profit and loss grid using the same methodology We will use the same profit and loss grid that we used for the long stock example described above. Note that the option strike price -- in this case \$50 -- is in the centre of the horizontal line on the grid.

Step 2 - We will describe the transaction completely. We will buy a \$50 call for \$3.

Remember everything is described on a “per-share” basis. Therefore, this description means that the right to buy one share of stock at \$50 (a \$50-strike call) has been purchased for \$3 per share. In the real world, of course, options cover 100 shares, and a \$50 Call on 100 shares would cost \$300 (not including commissions) which is \$3 per share.

Step 3 - Pick a specific price for the underlying stock on the expiration date.

As an example, let’s pick \$55. This means that time has passed since we purchased our \$50 Call for \$3 (per share), and the stock price has fluctuated during that time period. It is now the expiration date, and the stock price is \$55 per share.

Step 4 - Determine the option’s value. Notice! We have not been asked for a profit or loss calculation. we have been asked for the option’s value. With the stock at \$55, at expiration, the \$50 Call is in-the-money and has intrinsic value of \$5. Therefore, the option’s value is \$5.

Step 5 - Calculate the profit or loss. Now we have been asked for the profit or loss. Do we know what the profit or loss is? Remember, initially, we purchased a \$50 call for \$3 and now, with a stock price of \$55 on the option’s expiration date, the call has a value of \$5. The call which was purchased for \$3, has a \$5 value at the expiration date therefore as our cost is \$3 this results in a profit of \$2.

Step 6 - Let's now plot this on our profit and loss diagram.

Now, lets calculate a second point on the diagram. With a stock price of \$46 at expiration, what is the profit/loss on the long call position? The \$50 call which was purchased for \$3 has no value at expiration as our option expired out-of-the-money. Therefore the transaction resulted in a \$3 loss for us. The cost of buying the call option. Let us now plot this on the diagram as shown below.

Now we will go through and calculate several other points on this graph. It should now be apparent that the result is the same at any price below \$50 because the \$50-strike Call expires worthless, and the result is always a \$3 loss which is he cost (premium we paid) of the call option.

## Long and Short Call

There you have it! The completed long call diagram! This diagram depicts the “risk profile” of the long call strategy.

(1) risk limited to the premium paid ( in this case, \$3 per share).

(2) unlimited profit potential if the underlying stock price rises.

(3) a break-even stock price of \$53 at expiration.

The purpose of this type of exercise is to get people comfortable with understanding the profit or loss outcome of various option strategies. When they are comfortable with profit and loss results, it will be easier to select a strategy based on a given forecast. This is what happens when you buy a 50 call for 3 dollars a share.

There are a total of four basic option positions. we have looked at the long call position in detail. However, the procedure for deriving the short call, long put and short put positions are identical to that which you just completed for the long stock and the long call. Here are the remaining three option positions. We should look in particular at the pay-off in the event of rising and falling prices as well as the potential risk.

The next option position is the short call where we have sold a \$50 call at \$3. Here we sold a call to a buyer and we will receive the \$3 premium on the call.

The risk profile of the short call is:

(1) unlimited risk (if stock price rises).

(2) profit potential limited to premium received (in this case \$3 per share).

(3) a break-even stock price of \$53 at expiration.

The profit and loss diagram for this position is below.

## Long Put

We can apply the same technique to create the pay-off diagrams for puts. In this example, we buy a \$50 put for \$2.

“Risk profile” of the long put strategy:

(1) risk limited to the premium paid (in this case \$2).

(2) profit potential similar to short stock from the break-even point.

(3) a break-even stock price of \$48 at expiration.

The profit and loss diagram below shows the long put option position.

## Short Put

Below is the profit and loss pay-off at expiration for the short put strategy. Again, it is a \$50 put sold for \$2.

“Risk profile” of the short put strategy:

(1) potential risk is equal to a long stock position below the break-even point.

(2) profit potential is limited to the premium received.

(3) a break-even stock price at expiration of \$48.

What have we learned? First, we have been introduced to drawing profit and loss diagrams of basic option strategies. Second, we learned that profit and loss diagrams present a “risk profile” which reveals three things about strategies.

Risk Profile of Options:

(1) profit potential (which can be limited or unlimited)

(2) potential risk (which can also be limited or unlimited)

(3) the break-even stock price at expiration (strike price plus premium or strike price minus premium)

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• AUTHOR

Philip Cooper

6 years ago from Olney

Glad it was of help. Thanks for dropping by.

• Old Poolman

6 years ago

This was awesome information. I am just getting my feet wet in the equity options game, and there is a bunch to learn. So far, I have learned a few expensive lessons. This hub should go far in getting me on the right track.

Thanks for sharing.

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