
# How to read P&L Charts (part 1)

The question considered in this article might seem too obvious, and one might say that there is nothing to discuss.
But our user support experience tells us that often people who are entirely new in options spent excessive time
on trying to figure out options payoff profiles.
Having a well-developed skill of reading options risk profiles (alternative terms are P&L profiles, payoff function profiles) is essential to successful options trading.

For sure, sooner or later everyone will understand all the details, but we think that with this article we may accelerate this process.

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## P&L of a position in a linear asset. Numbers.

First, we assume stocks, bonds, indexes, commodities, ETFs and even futures are all linear assets.
They all (except futures) have their “own price,” which doesn’t directly (formally) depend on any other asset.
Futures price depends on its underlying asset price in a linear way, thus we also assume futures as a linear instrument.

Assume you have $100 in cash.
You then decide to buy a stock with a current price of $100.
Therefore, your portfolio will consist of 1 share, and you will be glued to computer/smartphone monitoring the price of the stock.
What you are doing is simple and straightforward.
You just observe the price, and since you have only one share, you know that the value of your portfolio entirely coincides with the stock price.
Then you simply compare the current value of the portfolio with your initial investment ($100) to calculate your P&L.

## Putting the numbers on a chart

Now let’s put the example above on a chart. Let’s take a look at figure 1.
The x-axis is the per share price. The y-axis denotes our portfolio P&L
The chart we are going to build shows the relationship between the P&L and the stock price.

![](fig1.png){.thumb}
Figure: Fig. 1, P&L of 1$ price movement up and down

The blue point corresponds to the very moment when we’ve just bought the share.
Price at that moment is $100, and therefore the P&L is zero.

If the price moves from $100 to $101, then our portfolio will be worth $1 more than the initial cash amount; thus, the P&L is $1.
The green dot on figure 1 corresponds to this scenario.
Its coordinates on the plot are $(x;y) = (101;1)$.

On the other hand, if the price goes down to $99, then the P&L will be -$1; the red dot on the figure corresponds to this scenario,
its coordinates are $(99;-1)$.

Similarly, with a bigger price move of let’s say, $2 instead of $1, we can see that On figure 2,
the stock price changes to $102 (green dot) or $98 (red dot).

![](fig2.png){.thumb}
Figure: Fig. 2, P&L of 2$ price movement up and down

Moving onto figure 3, we see that all the points are lying on a straight line.
No matter how much the share price changes, the P&L points on the chart will always be lying on this line.

![](fig3.png){.thumb}
Figure: Fig. 3, All dots are lying on a single line

This means that P&L has a linear relationship with the price.
In teenager math form, this would be $y = Qx$, where $y$ is the P&L of the portfolio, $x$ is the stock price change, $Q$ is the number of shares

The P&L of the portfolio is the number of shares multiplied by the P&L of a single share. Therefore, we can substitute $p - p_{0}$ for $x$,
where $p_{0}$ is the purchase price (for a long position) and $p$ is the current stock price.
We can now rewrite the formula as:

$y = Qx = Q (p - p_{0})$ **(1)**

This equation describes the direct dependence of the portfolio P&L on the share price.

What if we own 2, 3, etc. shares?
The $Q$ in the formula above will be $Q = 2$ or $ 3 $ so $y = 2(p - p_{0}), y = 3(p - p_{0})$ and so on.

On figure 4, we’ve added the line corresponding to a portfolio of 2 shares.
Note the angles between the P&L lines and the x-axis.
The more shares in the portfolio, the bigger angle is, and the faster you earn or lose money.
For 1 share, the portfolio P&L angle is 45 degrees, while for two shares, the angle is 63 degrees.

![](fig4.png){.thumb}
Figure: Fig. 4, Different angles for different position sizes (number of shares in portfolio)

## Changing the open price

In the example above, the stock was bought at $100.
What would the chart look like if the position was purchased at $99?
How do we redraw the P&L line? The line will be the same as before, just shifted to the left by 1, as shown in figure 5.

![](fig5.png){.thumb}
Figure: Fig. 5, Different open prices

## Closing the position

What if the stock price rose to $101 and the holder decided to sell it and close position? What will our chart look like then?

We can think of selling the position as a separate short position and draw them both on the chart (figure 6).
When you buy and sell a security intraday, your broker actually keeps both positions separate.
In effect, you own both the original long and the offsetting short – even though you only see cash.
Only after the trades are settled and cleared, are these positions will be collapsed on your broker’s books.

![](fig6.png){.thumb}
Figure: Fig. 6, Short position

For a short position, the $Q$ in our equation (1) is negative, $Q = -1$.
Thus, the P&L for a short position is $y = -1(p - p_{0})$ and its chart is shown in figure 7.
Since this is a short position, $p_{0}$ represents the sold price and $p$ still represents current price.

The total P&L of the portfolio, green line, is the sum of the red and blue dashed lines on the chart.
Literally we need to sum red and blue lines at each point.
The green line is, therefore, a constant, regardless of how the price changes going forward as the sum is always 1.
The position is closed and we have a $1 profit in cash.

![](fig7.png){.thumb}
Figure: Fig. 7, Total P&L of closed position

The beauty and usefulness of P&L charts are that you can quickly estimate your P&L no matter where price is going.
You see the whole picture in one chart.

Examples considered in this article are simple, but using them, we’ve explained the basic principles of building P&L charts.
Understanding these concepts will be essential when we explain more advanced options concepts in future articles.



# Modelling a naked call position

## Small intro about how-tos

We often hear the rebuke that our documentation is much too dry and much too technical.
With this blog we’re going to breath in some personality into our public material.
We’ll do this by examining some concrete use examples and describing how to solve them using our software.
All posts of this kind will be registered in the [how-to](https://optionworkshop.net/blog/tags/how-to/) category,
so it will be easy to filter them.

:::cut:::

## Preconditions

Below we describe how to play with some **very basic options positions modelling**.
We assume that the user has already setup the software with at least one datasource.
We’ve created several videos describing integration with external systems, if you’re interested,
you can find them [here](http://optionworkshop.net/videos/).

## Modelling a single position

One options trading mentor had a very simple reply to the question “How to start trading options”:

> _– Just buy a call and see what will happen_

So you want to follow this advice, but without opening a real position.
Maybe even without having a real account.
It means that all you need is to create a virtual position at the current market price
and with the desired number of contracts and then monitor it as the market changes.

### Adding an account

This step is optional, because in most cases after connecting OptionWorkshop to some datasource it will pull trading accounts
and automatically add them to the list.
But if, for example, the user connected the software to IQ Feed – a pure market data source,
without execution – then it’ll be necessary to create an account.
Another reason to create a virtual (test, modelling) account is just to separate modelling options positions from real ones.

![](optionsworkshop_2016-05-03_02-42-581-150x140.png)
Figure: Add new account button above accounts list

![](optionsworkshop_2016-05-03_02-51-32-150x150.png)
Figure: Add new account dialog

To add virtual account in the **Positions** form press the cross button above the accounts list.
The form for entering a new account name appears, there we have to fill in the **Name** field as shown on the second form.
Now press Ok and see that account was added and appears in the list.

![](optionsworkshop_2016-05-03_02-59-00-150x150.png)
Figure: New Account, without strategies yet

## Strategy

![](optionsworkshop_2016-05-22_22-19-37.png)
Figure: Fig. 2, Add new strategy dialog

Now let’s add a strategy.
Press the button with a cross icon that’s above the strategies list (see Fig. 2), that will bring the form on the lift.
The **Account** field will be pre-filled out if before clicking the add strategy button you’ve selected an account in the list.
The only thing you’ll need to do is to select a base asset and type in the new strategy name.
Remember that the name must be unique within an account and base asset subportfolio.
When the form has been filled out, press **Ok**. The new strategy will be added.

![](optionsworkshop_2016-05-22_22-25-12-150x150.png)
Figure: New strategy added

In the next post we will talk about strategies in more details, for now let’s just consider that our strategy is just a subportfolio,
in which we place some positions.

## Position

There are three ways to add a modelling position into strategy and the aim of this post is to describe them all:

1. The “Add position” button;
2. Drag&drop instrument from the options desk to the positions table;
3. Drag&drop instrument from the instrument tree to the positions table.

### “Add position” button

![](optionsworkshop_2016-05-22_23-54-43.png)
Figure: “Add position” button

Above the positions table there is a button with a cross icon, showed on the picture on the left.
Clicking this button brings the “Add a new position” form and users only need to fill in the form fields,
which are the instrument, the position price and the quantity.
Remember, the quantity can be negative, that means the position will be a short position.

### “Drag&drop” from options desk

This is the most convenient way to add new positions.

![](2016-05-26_16-21-52.png)
Figure: Drag&drop option from options desk to positions table

From the options desk you can drag&drop any option into the positions table,
and this action will also open the “Add new position” dialog. Dragging the left (green) part of a row will add a call,
the right (red) – will add a put.

Note, that “Add new position” will be prefilled as much as possible: account, instrument, strategy and price
will all have predifined values when the form opens.
The price field will be prefilled with a value depending on which cell you started dragging from.
If we start dragging the “bid” cell, then the price will be taken from the bid.

### “Drag&drop” from instruments tree

![](optionsworkshop_2016-05-26_16-30-50.png)
Figure: Drag&drop instrument from instruments tree

Simply drag the instrument from the instruments tree onto the positions table. It works exactly the same as the previous two methods.

## Chart

![](optionsworkshop_2016-05-26_16-37-56.png)

Now that the position is added, we can build a risk profile and visualize the greeks.
The **Chart** button above the positions table opens a new window with all the strategy parameter graphs.

![](optionsworkshop_2016-05-26_16-43-29-150x150.png)
Figure: Call P&L and greeks chart

![](optionsworkshop_2016-05-26_16-44-20-150x150.png)
Figure: Call P&L chart

![](optionsworkshop_2016-05-26_16-44-58-150x150.png)
Figure: Call gamma chart

![](optionsworkshop_2016-05-26_16-44-42-150x150.png)
Figure: Call delta chart

![](optionsworkshop_2016-05-26_16-41-37-150x150.png)
Figure: Call P&L and greeks chart



Managing accounts
=================

New short video about managing real and virtual accounts.

![](https://www.youtube.com/watch?v=14clydxob-o)

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Integration with CQG Continuum
==============================

Watch one of our recent videos, this time it’s about setting up a connection with [CQG Continuum](http://www.continuumtradingsolutions.com/).

![](https://www.youtube.com/watch?v=cXi8TYKR6s0)

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Blog #how-to

How to read P&L Charts (part 1)

Modelling a naked call position

Managing accounts

Integration with CQG Continuum

Last thing