Understanding Payoff Charts
Option payoff diagrams are profit and loss charts that show the risk/reward profile of an option or combination of options. As option probability can be complex to understand, P&L graphs give an instant view of the risk/reward for certain trading ideas you might have.
If you've never seen a payoff chart, then below we'll go through two examples of what the P&L looks like for an easy long call option (buying a call) and then a short call option (selling a call).
7 Days of Option Lessons Delivered to your Inbox Show Me More »
Call Option Payoff
Let's look again at the basics of a Call Option. Here is an example;
Underlying: MSFT
Type: Call Option
Exercise Price: $25
Expiry Date: 25th May (30 days until expiration)
The market price of this call option $1.2. Buying the option means you pay this price to the seller. As the option is a call option, exercising the option means you will buy the shares at the exercise price of $25. You would only exercise if it is profitable to do so. But the exercise price alone is not doesn't determine probability.
You also need to consider that you paid something to have the right to exercise; the option premium, in this case $1.20. Therefore, the shares have to be trading at $26.20 for us to break even (Exercise Price of $25 plus the Option Premium of $1.20). If the shares are trading anywhere above $26.20 then we can say the option is profitable. Anywhere below $26.20 and we lose out by the premium - $1.20. So, with a long call we have limited risk (the Option Premium) while at the same time having uncapped profit potential. Let's look at a graph of this concept;
The horizontal line across the graph (the x-axis) represents the price movement of the underlying instrument - in this example, the share price of Microsoft. The vertical axis illustrates our profit/loss. The blue line is our payoff of our option position.
You can see that the vertical distance between the 0 profit line and the blue line is our maximum loss, i.e. the amount we paid for the option. So, anywhere under our break even point of $26.20 means that the option isn't profitable, we will not exercise the option and we will lose any premium we paid ($1.20). Even if the market crashes and the stock goes bankrupt, our maximum loss will still only be the premium we paid.
However, as the shares trade past the $26.20 mark we start making money on the position. If, at expiry, Microsoft shares are trading at $50 then we will make $23.80 per share. How? Because we will exercise our right and have the seller of the option hand over Microsoft shares at a value of $25 (the exercise price). Minus the amount we have already paid for the option ($1.20) and we have a profit per share of $23.80.
Selling a Call Payoff
When we reverse the position and sell a call option, here is the payoff diagram for that.
We have the same format of stock price on the x-axis (horizontal) and P&L on the y-axis (vertical). Because we sold the call, we receive money for the sale, which is the premium. If the shares trade anywhere below $25 then we keep the $1.20 that we received when we sold the call option.
However, if the market rallies then our losses become uncapped as the stock price rises.
Theoretical P&L vs Payoff at Expiration
The above graphs have looked at what option will be worth at the expiration date only. However, you will often see another line inside payoff charts that is usually smooth and referred to as the Theoretical P&L.
This theoretical line graphs what the option is worth today and is calculated from a theoretical pricing model, such as Black and Scholes or Binomial Model. Given the time to expiration, the graph will show how your P&L will change "today" should you have this position vs the axis graphed; usually the stock price.
Here is the same MSFT call option chart now with theoretical P&L added.
The place on the x-axis that represents the current stock price should be where the P&L is zero i.e at the time and stock price of purchase you have not made or lost anything. The payoff line at the same point on this chart is the premium, or price, of the option. (This isn't always the case though regarding the premium for the option and the payoff/P&L line. For certain combinations it can be either the premium or max profit/loss.)
This example was calculated when the option has 30 days until expiration and is worth $1.20. With all other things being equal (time, interest rates, volatility) the smoothed line shows how the P&L will change for each corresponding price movement of the stock as per the axis.
As each day passes, this line will move closer and closer until the point of expiration, which will be the final payoff line.
Combination Payoffs
Outright calls and puts are fairly straight forward to understand when it comes to payoff and P&L. However, payoff charts become very useful when looking at combinations of options i.e. when more than one leg is in the strategy.
Take an option straddle for example. A straddle is a combination of two options; a long call and long put option with the same expiration dates and strike prices. Below is a straddle graph.
Typically when you see combinations charts you will only have the total of all legs plotted. Here, I've plotted each single leg, buy call and buy put, in a lighter color and dashed in the background and then the combination as the darker solid line in the foreground. The P&L line is for the combination.
38 Comments
Jason February 6th, 2012 at 7:50pm
If you sell short an option at $1.20 and the stock goes lower - the direction you intended you would most likely not walk with $120. Within the last 30 days to expiration, even in the money options can take a beating. You may only walk with $20. So, what is the best strategy? Buy to close with 15% profit?
Peter October 30th, 2011 at 6:13am
Hi Steve, if the bond doesn't convert to anything (i.e. convert to a call option on the stock) then the payoff in this example would simply be the stock price plus $500 per year. Unless I have misunderstood?
Steve October 28th, 2011 at 9:34am
Will someone please offer some help?
Draw a final payoff diagram for a stock and a bond, where the bond promises to pay off $500.00 in one year
Peter October 12th, 2011 at 6:43pm
Hi Nancy,
It really depends on your view of the underlying stock. If your view is extremely bullish then you would be more likely to buy deep OTM options as your rate of return on the premium will be greater if the stock does rise as expected compared to the same amount invested in ATM/ITM options.
You can buy deep ITM money options as an alternative to buying the shares outright. Doing this means you can have a large exposure to the stocks' movements without spending as much to buy the shares.
Nancy October 12th, 2011 at 9:06am
I'm struggling with how to arrive at a good strike price for a call. Does one ever choose, for instance, a strike price which is below the current stock price? As the price, goes up, I would still be profitable regardless of the strike price, right? Specifically, I'm looking at AMZN April 225 call. It is currently floating around that number now.
Peter September 5th, 2011 at 5:55pm
Hi Gurko, if the price only reaches $26 then your loss would be less at $1.00 instead of $1.20.
Gurko September 5th, 2011 at 6:08am
Greetings ,
In the first example you said that if the price of the stock is below $26.20 you wouldn't exersize it and you will lose the premium that you paid ($1,20).
What if the price reaches $26 - wouldn't it be more profitable to exersize the option and to lose only $0.2 ?
Could you make that clear to me ?
Peter December 7th, 2010 at 9:09am
What figures do you mean...the payoff charts? They are not currency specific...they are the same no matter what asset/currency the options are traded in.
nic December 7th, 2010 at 7:40am
Hi, I was just wondering how recent these figures are? and do you how i would get hold of the british figures if possible?
Thanks!
Peter October 9th, 2010 at 6:41am
It depends on your broker. Short positions require a margin, rather than just paying out the premium if you were to buy the option. A good guide, however, is to multiply the volume of contracts by the strike price and then multiplied by the contract size, which for US options is 100.
Add a Comment