Short Call vs. Long Call: Comparing Payoff Profiles at Expiration

Imagine you’re at an auction, and you see a beautiful antique vase. You have two options when it comes to call options, which are like agreements related to buying or selling assets, in this case, think of the vase as the underlying asset, like a stock. You can either choose to buy the right to purchase that vase at a specific price, or you can choose to sell someone else the obligation to sell them that vase at a specific price.

Let’s first consider the long call position. This is like buying a ticket that gives you the right, but not the obligation, to buy the vase at a pre-agreed price, let’s say $100, by a certain date. You pay a small fee for this ticket, let’s say $5. This fee is called the premium.

What happens when the auction ends, which we can think of as the expiration date of the option? It all depends on the final auction price of the vase.

If the vase ends up selling for less than $100, say $90, your ticket isn’t very useful. Why would you use your ticket to buy the vase for $100 when you can buy it for $90 in the open market? In this scenario, you simply let your ticket expire worthless. You lose the $5 you paid for the ticket, which is your premium, but that’s all. Your potential loss is limited to the premium you paid.

However, if the vase price skyrockets to, say, $120, your ticket becomes incredibly valuable. You can now use your ticket to buy the vase for $100, and immediately sell it in the market for $120, making a profit of $20, before even considering the initial cost of the ticket. Once we subtract the $5 premium you paid for the ticket, your net profit is $15. And if the vase price goes even higher, your profit potential continues to grow. The higher the vase price at expiration goes above $100, the more profit you make with your long call position. Your potential profit is theoretically unlimited.

Now, let’s switch to the short call position. This is the opposite side of the transaction. Instead of buying a ticket, you are selling a ticket. You are essentially promising to sell the vase to someone at $100 if they choose to exercise their right to buy it by the expiration date. For selling this promise, you receive the premium of $5 upfront.

Again, let’s consider what happens at expiration based on the vase’s final price.

If the vase price at auction is below $100, say $90, the person who bought the ticket from you will not exercise their right to buy. Why would they buy from you at $100 when they can buy it cheaper in the market? In this case, your promise expires unused. You keep the $5 premium you received, and that’s your profit. This is the best-case scenario for a short call position. Your profit is limited to the premium you received.

However, if the vase price rises above $100, say to $120, the person who bought the ticket from you will definitely exercise their right. They will want to buy the vase from you at $100 because they can then sell it for $120 in the open market and make a profit. You are now obligated to sell them the vase for $100. But you don’t own a vase! You now have to go into the market and buy a vase at $120 to fulfill your obligation to sell it for $100. This results in a loss of $20. But remember, you received a $5 premium initially. So your net loss is $20 minus the $5 premium, which is $15.

If the vase price goes even higher, say to $150, your loss gets even bigger. You would have to buy the vase at $150 to sell it for $100, leading to a $50 loss, offset slightly by the $5 premium for a net loss of $45. As the vase price rises, your potential loss on a short call position can become theoretically unlimited.

In summary, at expiration, a long call position profits when the underlying asset’s price is above the strike price, increasing with every dollar the price goes up. The loss is limited to the premium paid. A short call position profits when the underlying asset’s price is below the strike price, with the profit capped at the premium received. However, a short call position incurs losses when the underlying asset’s price rises above the strike price, and these losses can increase significantly as the price goes higher. The payoff profiles are mirror images of each other, illustrating the fundamental difference between holding the right versus having the obligation in options trading.