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
benjamin October 9th, 2010 at 2:48am
i am looking to short uncovered options. i will be short selling 5-7 option contracts. how much $$$ would i need in my account?
Peter June 9th, 2010 at 12:37am
Hi Dolf, the question Carter asks is in relation to a naked call, not a covered call - they have different payoff profiles. Sure, a covered call's losses is technically limited to the stock price going to zero. Not unlimited - but a lot.
With a covered call, you're short a call option. Once the stock trades below the strike the holder of the option won't exercise, so you just lose the premium and the option value goes to zero. However, you are still long stock, which will lose value as the price drops - not unlimited, sure, but all the way to zero.
As the stock rallies past the strike, yes, you would be called out and have to sell the stock at the strike price offsetting the long position already held in the stock making the profit realized the premium already received for selling it. This is why a coverved call is a bullish strategy as you want the market to rally so you are called away and give up the stock.
Dolfandave June 8th, 2010 at 1:46pm
Peter, As Carter mentione (two years ago:) in the first post below there is some question to "unlimited" losses. Yes if this is a naked call. I have been studying covered calls in my trek to learn options trading and if it were a covered call I personally don't view it as an unlimited loss. If I buy an OTM option as I understand this is the best technique w/ covered calls, then I will make the premium paid to me for writing the call plus the difference between the purchase price of my stock and the strike price. I don't think this is a bad deal nor would I really cry about it if I got called out in this situation. I wouldn't necessarily buy back the same security if I got called out. Your thoughts?
joel April 8th, 2010 at 1:54pm
thanks guys i was struggling to understand the pay offs now it has become easy
Peter June 11th, 2009 at 12:03pm
Hi Henry,
Hard to say exactly, but the following article points to the CBOE saying 10% of options are actually exercised:
http://www.protraderdigest.com/articles/20081025_7
Mmm, I've never heard of this happening. If the option is very close to expiration and a company is bidding up the options above their intrinsic value, market makers would arb them out by selling the options and hedging with the stock.
henry June 9th, 2009 at 9:10am
Hi, silly question im sure...
but what ratio (about) are options actually exercised and go through to trade? Im guessing people get it wrong more than right and therefore it is extremely common to not exercise the trade.
Secondly, are there companies out there that buy up your options once they have alot of intrinsic value very near to expiration and you dont have the liquidity/cash to exercise the trade (hence why you would sell it). I hope that makes sense. Thanks
Peter May 21st, 2009 at 6:37am
Hi Rajeev,
Your clearer decides who the counterparty is if you decide exercise your option. The person on the other side will be a holder of a short call option.
About your second question...if you bought the option and then sold it 3 months later, you no longer have a position. You would only be obliged to sell shares if you were short the call option and the buyer exercised the option.
Rajeev May 20th, 2009 at 9:52pm
This is very useful After going through the whole thing, I have a question. If I decide to exercise the call option, who is the other side, who is going to sell the stock. On the same thought, if I bought the call option for 1.20, sold it for 2.00 3 months later, at the time of maturity, if the buyer decides to exercise the right, am I supposed to provide the shares or the whoever wrote the call option originally.
Peter May 5th, 2009 at 7:32pm
Hi Tom,
It depends on the specifications of the options, but generally, yes. In the US exchange traded options have a "multiplier" or "contract size" of 100, so the price is multiplied by 100. However, in Australia the multiplier is 1,000. So it depends on the exchange where the options are traded.
Tom May 5th, 2009 at 10:59am
Sorry for the very basic question, but if you're buying an option priced at $1.20 as in the above example, are you physically paying $1.20, or is it multiplied by 100, i.e. $120?
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