# Archimedes Finance

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## Creating a map when buying options

Lesson in Course: Derivatives and options (expert, 9min )

I want to start taking the first steps in buying options. How do I make a plan? Before we put any of our money at risk, we should understand all our possible outcomes. When will we make money? Or what situations will result in us losing money?

For options, we can create a visual map to help us answer these questions. This visual map is called a payoff diagram. A payoff diagram is a graphical representation of when the options are in-the-money, at-the-money, and out-of-the-money compared to the price of the underlying stock.

### KEY TAKEAWAYS:

The three takeaways for this lesson are:

• Learn how to visually interpret the risk of an option
• Understand the difference between a value diagram and a profit diagram
• Be able to recognize the diagrams between buying a call or put option

Visually seeing the possible gains and losses of an option position will help us avoid situations where we are caught unprepared. Let's start by watching a quick 3-minute video starting with buying a basic call option.

## Understanding payoff diagrams

Pay off diagram can come in two flavors. A value diagram will tell us the moneyness of our options, or if they are in-the-money, at-the-money or out-of-the-money. While that's could be helpful, a profit diagram will show us when we actually make money. Let's jump into understanding the difference between the two.

### Value diagram

The value diagram for an option contract is a visual representation of the intrinsic value of the call at maturity compared to the underlying stock price.

Call option diagrams and put options diagrams differ in how they look since a put is betting on a drop in stock price and a call is betting on a rise in stock price. We can see above that as the stock price increases, call options become more valuable. When the stock price decreases, put options become more valuable.

We'll use an example to help us understand the graphs. Let's assume Verizon (\$VZ) is trading at \$50 a share. We ended up paying \$10 in premiums for an at-the-money call option with the strike price of \$50.

The minimum value of the graph is always \$0.  Since our strike price is \$50 in our example, the call option is only in the money if the underlying stock is above \$50. As the option becomes in-the-money, the value of the options increases on a dollar-per-dollar basis. For example, when \$VZ is at \$51 per share, our option has an intrinsic value of \$1 and at \$52 per share, our option is worth \$2...etc. Let's look at the same put option.

The put value diagram is in light red and is overlayed on top of the call value diagram. Since we are betting against the stock, our option is in-the-money as long as the price of \$VZ is below the strike price of \$50. The option increases in value on a dollar-per-dollar basis after the underlying stock drops below \$50 a share. For example, when the underlying is at \$49 per share, our option is worth \$1 and at \$48 per share, our option is worth \$2...etc.

For value diagrams, at-the-money is right when the option value goes above \$0 for the first time. In-the-money options have a slope and positive value. Out-of-the-money options just sit on the X-axis.

### Profit diagram

The profit diagram for a call option is a visual representation of the profit and loss at maturity relative to the underlying stock price.

The profit diagram is a bit different than the value diagram since it includes the cost we paid for our option premium. In both cases above, we actually start in the negative. The negative amount is the same as the cost we paid for the options. Let's step through the Verizon example again.

The call option example above shows when the stock is at \$50 we have a loss of \$10. The call option is at-the-mone and we would never exercise the option even though we paid \$10. It's not until the underlying stock is at \$60 are we at our break-even point (strike price + premium per share). And beyond \$60, we are profitable on a dollar-per-dollar basis.

The profit diagram for a put option, like the call option, shows that we have a loss of \$10 in premiums paid when our option is at-the-money. The break-even point is shown where the light red line crosses the X-axis and is below our strike price and can be calculated as (strike price - premium per share). We have to be in-the-money the same amount as the premiums we paid to break even. When \$VZ is below \$40, our graph turns positive and we are profitable on a dollar-per-dollar basis.

## Understanding what's at risk

The maximum loss for our option is always going to be our premium paid. We can go as far left or right on the profit diagrams above, and the most we'll lose is -\$10.

A call option gives us the right but not the obligation to buy the underlying stock at the strike. So even if VZ's price dropped all the way to \$0, we can choose to walk away and forgo exercise. Likewise, we can choose to not exercise our put option and sell our stock at the strike price if the market gives us a better price. Understanding this will help us avoid unfortunate situations. We shouldn't buy options contracts if we can't afford to lose the premiums paid.

A helpful trick for us to identify a call option diagram right away is to imitate a phone with our fingers.

While value diagrams are helpful for us to get a grasp of when the option is in-the-money, profit diagrams are preferred for us to really understand when we make money and how much we have at risk. Being comfortable reading profit diagrams will be essential for the complex options strategies that use multiple calls and puts such as a collar, iron condor, and different types of spreads.

For each of these profit diagrams, it's important to identify the maximum loss, break-even point, and when the option pays out on a dollar-per-dollar basis. Do we feel confident doing that today?

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