# Option Trading Strategies Using P&L Diagrams

## Why Use Profit and Loss Diagrams

In this hub we will look at and draw basic profit and loss diagrams of option strategies. It is important that we understand these diagrams for several reasons.

Understanding potential benefit and potential risk is an important first step in determining whether a particular option 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 option 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.

## Diagram 1 - Long Stock

## Diagram 2 - Long Stock

## The Long Stock

We will start with the payoff of a long stock position; that is what is the potential profit or loss if you owned 100 shares of ABC stock at $50 a share. There are seven steps to constructing the P/L diagram. Each step is notated on the P&L 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.

**Step 3**: Pick a
specific price for the underlying. Let’s assume that the market price is $53. Put
an X on the grid in the appropriate place as in diagram 1.

**Step 4**: Determine
the option's value. This will be either the option's intrinsic value if the
underlying price chosen is in-the-money or zero if the underlying price is
out-of-the-money. For the long stock
position, there is no option value.

**Step 5**: Plot all the
profit and loss points on the grid and place an X as in diagram 2.

**Step 6**: Calculate
the profit or loss, which is simply the difference between revenue and
cost. For the long stock, this would be
the profit or loss you would earn if you sold the stock at the current market
rate of $53.

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 – maximum $50 per share if the stock price falls to $0

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

## Diagram 3

## Diagram 4

## The Long Call

Now we are going to construct a profit and loss diagram for a long call option.

**Step 1**: We will
use the same profit and loss grid that we used for the long stock example above. Note that the option strike price, in this
case $50, is in the centre of the horizontal line on the grid.

**Step 2**: Describe
the opening transaction completely. In this, your first option strategy, we
“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 one lot of 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! You have __not__ been asked for a profit or loss
calculation. You have been asked for the option’s __value__. With the stock at $55, at expiration, the $50
Call is in-the-money and has an intrinsic value of $5. Therefore, __the
option’s value is $5__.

**Step 5**: Calculate
the profit or loss. Now you have been asked for the profit or loss. Do you 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.

**Step 6**: Plot the
profit or loss on the grid (Diagram 3). With the stock at $55, the result is a
$2 profit. Now let's plot another point
on the grid. With a stock price of $46 at expiration, what is the profit/loss
on the long call position? Well the 50 call, purchased for $3, has a $0 value
at expiration and, therefore, resulted in a $3 loss as we can see. Upon reflection,
it should be apparent that the result is the same at any price below $50: the
$50 strike Call expires worthless and the result is a $3 loss which is the
amount of premium we paid.

Now we can plot all the profit and loss points on the grid (Diagram 4).

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 exercise was to get you comfortable with understanding the profit or loss outcome of various option strategies. When you 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.

## Short Call

## Long Put

## Short Put

## Other Risk Profiles

We have just covered the risk profile for a long stock and a long call and step by step constructed the profit and loss (pay off) diagrams. Now we will look at the risk profiles for the long put, the short call and the short put.

Now we will derive the remaining 3 basic options positions. The procedure for deriving the short call, long put and short put positions are identical to that which we have just completed for the long stock and the long call. Please take a few moments to study these diagrams. You should look in particular at the payoff in the event of rising and falling prices as well as the potential risk.

**Risk profile** of the **short call** strategy: (Diagram 5)

The risk profile of the short call (the seller of a call option who has the obligation to sell the call if the buyer decides to exercise his right) is exactly opposite that of the long call.

(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.

**Risk profile** of the **long put** strategy: (Diagram 6)

(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.

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

**Risk profile** of the **short put** strategy: (Diagram 7)

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

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

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

Conversely, this is the P/L pay off at expiration for the short put strategy. Again, it is a 50 put sold for $2.

Let’s summarize this section. 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 reveal 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)

In the next article we will go one further step and discuss the role options play in equity portfolio management.