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).
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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
Peter April 13th, 2009 at 7:01am
Hi Chuck,
It depends on the exchange. For example, in the US there is no charge for exercise and assignment for US stock options, however, in Australia and Europe you will be charged commissions.
This was taken from the Interactive Brokers website under Fees and Commissions:
IB Commissions
Chuck April 11th, 2009 at 5:04pm
If you intend to exercise your in the money call option and sell the stock immediately to realize your profit, would you also incur two stock trade fees as well as the original option purchase fee ? Are option trading fees similar to stock trading fees ?
Peter April 9th, 2009 at 7:42am
The last trading day for April 09 options in the US is Friday the 17th. CBOE shows the 18th (Saturday) as the expiration date but Yahoo! is currently showing 17th when checking MSFT options. I couldn't see the 11th mentioned. I would say that's what it comes down to..."technically" they expire on the Saturday following the third Friday of the expiration month. But really Friday is the last trading day...i.e. you cannot get out of the option by trading it on a Saturday.
Jack April 8th, 2009 at 1:39pm
april contracts on scottrade expire on 4/18. april contracts on yahoo financial expire on 4/11. I don't understand.
Admin October 9th, 2008 at 4:52am
Hi Queenie,
Sorry...don't fully understand your question.
You will know the Microsoft is trading at $50 because of the price in the open market.
Queenie October 6th, 2008 at 7:44am
"If, at expiry, Microsoft shares are trading at $50 then we will make $23.80 per share."
How would you know the shares are trading at $50 and will will make &23.80 per share.
Admin October 3rd, 2008 at 8:43pm
Hi Carter,
When you sell a call option you are obliged to sell stock to the option buyer if s/he decides to exercise. Once the stock trades upwards past the strike price the buyer will certainly exercise the option as it is now ?in-the-money?. At this point you are effectively short the stock at the strike price of $25. Your losses have no limit and will continue to increase as the stock rallies. For example, if the stock is trading at $40 at expiration, you will be exercised and have to sell stock at $25 and buy them back on the open market at $40 for a $15 loss per contract.
Make sense?
carter October 3rd, 2008 at 6:57pm
Why would our options be unlimited if the market rallies in the last example? Wouldn't we only lose the price of the contract, as in the other scenario, if the stock doesn't go above $26.20?
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