Option Payoffs and Profits Illustrated

I have a friend who opened up an options account yesterday, I’ll call this friend Ron. Ron said the broker just gave him access to it but Ron did not know what a call and a put were… This is kind of concerning and could be crushing to his portfolio if he were to use it and not understand what is actually being executed. I thought I’d do an options primer, to at least get your mind going.

What is an option? An option is a type of derivative, because the option derives its value from some underlying security. It is an option, purchased today, to either buy or sell a stock, at a particular price (referred to as the Strike Price), at a predetermined date. A Call option is an option to buy at a particular price at a predetermined date were as a Put option is an option to sell at a particular price at a predetermined date. For this option to buy or sell in the future one must pay a premium today to have that right.

Let’s do some Call hunting. Let’s look at the company Paycom, symbol PAYC. This is what I’m seeing the morning of 2/12/21, on Yahoo Finance:

If we click on the options button we see what is referred to as the options chain:

This is where one can see call options on Paycom expiring on February 19th. The rows correspond to different strike prices. If we go down we can see a contract for a strike price of 420:

Let’s get into someone’s headspace that would be thinking about purchasing this. Since Paycom is currently sitting at around 409 to buy this call would mean that someone is bullish on the price of Paycom stock over the next week. Why is that? Would someone want the option to buy it at $420 if they thought it was going to go down to $350 by the end of next week? No. What if they thought it was going up to $440 though? In a week, if the $440 mark comes to fruition, the contract would be worth effectively the amount of buying the stock for $420 and selling for the market price of $440, with a payoff of $20. The profit realized on a call is [max(0, price at expiry – strike price) – premium to enter the contract]. One should theoretically be subtracting the future value of the premium, with interest, but I’m going to disregard that since we’re just looking over a week. Let’s look at the possible payoffs and profits from buying this call option:

The option is worthless below $420. If in a week the price of Paycom is above $420 the payoff is the price minus $420. The profit is then the payoff minus the premium, $5 in this case. It should be noted that the upside is theoretically boundless for purchasing a call. One can see on the right chart, profit in orange, that for the profit to be non negative the price of Paycom in a week must hit $425. If you look at this chart below you may see some of the allure of options (may lose your whole premium as the option expires or make off like a bandit):

What affects an option’s price?

  • The time to expiration
  • The perceived volatility of the underlying asset
  • The current price of the underlying asset
  • The strike price
  • The risk free interest rate

Let’s now look at purchasing a $420 put, the right to sell the stock for $420 in a week:

In a put’s case the upside comes from when the stock goes down in value. At a level of $409 currently we would say this option is “in the money” because if the price didn’t move at all for another week the payoff would be positive, 420 – 409 = 11 (you’d have the right to sell the stock at 420 when it’s only 409), but the profit would be 11 – 16 = -5 (profit once again shown in orange on the right graph). The stock would have to get down to $404 for the put value to breakeven [max(420-404,0)-16]. To contrast with a call’s possible profits, a put’s upside is capped by the strike price minus the premium. This would happen if the stock went to 0.

What if you didn’t really think strongly one way or the other but you thought the price was going to move a real lot (highly technical term I know), maybe after a news announcement for example. One could buy both a call and a put, or more commonly known as a straddle. Below is a call and a put at a strike of $410 (closer to our market price of 409), once again with payoffs in blue and profits in orange. One would need the price to drop to $393 or get above $427 to make a profit:

Hopefully this gives people a glimpse into options! I lost a lot of money buying Groupon calls as a youngen so do your homework and manage your expectations. One thing I have done which is a relatively conservative way to use options is selling calls on stocks which I already own (aka covered calls), but that may be a post for another time:) And if you found this useful please subscribe:)

One thought on “Option Payoffs and Profits Illustrated

Leave a Reply