Back

Creating a map when selling options

Lesson in Course: Derivatives and options (advanced, 6min)

I can understand and read the payoff diagrams when I buy call and put options. What about when I sell options?

Eureka!

What it's about: Making sense of pay-off diagrams when selling a put or call option.

Why it's important: Visually, we can see when we make or lose money as an option writer and how much is at stake.

Key takeaway: The maximum possible profit is capped at the initial price received for the option. The maximum possible loss is unlimited in some cases.

Selling option contracts is synonymous with shorting option contracts. We should become comfortable with using the descriptors "selling" and "short" interchangeably as most options traders do so. We already know that short call and put options expose us to additional risk compared to just buying calls and puts. The risk is harder to understand if we can't see it visually. Let's learn how to make sense of the pay-off diagrams for short calls and puts. 

The inverse relationship

Instead of starting from scratch, we can lean on the knowledge we've gained from understanding pay-off diagrams for buying options.

Options are considered zero-sum 

Added together, the gains and losses between option holders and sellers equal 0.

An investor's loss is another investor's gain

Let's revisit the concept that an options contract represents an exchange of value between two different investors. Within this contract, for every single dollar in value received by one investor, the other is losing the same amount. Understanding this inverse relationship helps us to be able to construct payoff diagrams for selling options. 

Inverting long call and put diagrams

To create payoff diagrams for selling options, we would simply just invert the purchase diagrams vertically.

 

Let's watch a quick video breaking this concept down.

Khan Academy
https://www.youtube.com/watch?v=TdW3LdN5SJw

Understanding payoff diagrams for short positions

The value diagram for a short position is not very helpful since we aren't holders of the option. Value diagrams help us see the intrinsic value and as option writers, we don't get a choice to exercise the options. In reality, we are hoping the intrinsic value stays below $0 so we can pocket the premiums.

We want to look at the profit diagram for short positions
Short call profit diagram

For example, if we sold a $50 strike call option on a stock for $10 in premiums, we can expect the profit diagram to look like the red-lined graph below.

We make money (the premium collected) as the seller until the stock is at $60 (premium + strike), the break-even point for the call. After the break-even point, the call option is now in-the-money for the holder of the option and we face the risk of being assigned. Every additional dollar that the option moves in-the-money results in a dollar loss for us. We want the stock to stay below break-even when we short a call. 

 

For a short put, the concept works very similarly. Let's watch another short video.

Khan Academy
https://www.youtube.com/watch?v=WFuLVSz6n8M

Recall that break-even for a put is calculated differently and has to be lower than the strike price since a put option bets against the stock price. 

Short put profit diagram

The put break-even is the strike value subtracted by the premium or $40 in the example.

As the put writer, we make money by collecting the premium as long as the put option stays out-of-the-money, or above the break-even at $40. If the stock price drops below $40, we will have losses and be at risk of assignment.

 

Actionable ideas

An easy way to identify short profit diagrams is when we see one that is capped in height. For short calls and puts, the most we can stand to make is the premium collected for selling those options. The limited profit is what makes the graph vertically short. The graph also shows us that shorting options can expose us to a lot of downside risk, or the risk to lose our money. In the diagrams above, while the maximum gains are capped, the losses can be great. We'll cover the risk profile of short option positions in more detail in future lessons.