Calls and puts are the two basic kinds of option. A call gains when a stock rises. A put gains when it falls. We compare them on one made-up stock, Harbour Co, priced at $100 today. Each contract costs $5 a share.
Every price here is an assumption we chose. All figures are per share, on the contract's final day (the expiry), before commissions and tax. A $130 finish pays the call buyer a $25 profit. A $70 finish pays the put buyer the same.
What is the difference between calls and puts? A call gives its buyer the right to buy a stock at a fixed price by a set date. A put gives its buyer the right to sell at that price. A call gains when the stock rises, while a put gains when it falls.
In our example, a call buyer needs the stock above $105 to profit. A put buyer needs it below $95.
Each buyer can lose at most the $5 premium, the price paid for the contract. The call buyer's gain has no upper limit. The put buyer's gain stops at $95, if the stock falls to zero.
The seller takes the other side of each contract. The seller's gain is at most the $5 premium. The call seller's loss has no upper limit. The put seller's loss stops at $95.
What is a call option?
An option is a contract tied to another asset, called the underlying. Here the underlying is one share of Harbour Co, which we assume trades at $100 today.
A call option gives its buyer the right, but not the obligation, to buy the underlying at a fixed price. That price is the strike. The contract ends on a set date, the expiry. The buyer pays a price up front for the contract, called the premium.
Our call has a strike of $100 and a premium of $5. If Harbour Co ends above $100 at expiry, the call is worth the gap between the stock price and $100. If it ends at $100 or below, the call is worth nothing. The buyer loses the $5.
Our explainer on what an option is covers the basics. This article sets the call and the put side by side.
What is a put option?
A put option gives its buyer the right, but not the obligation, to sell the underlying at the strike. It is the call turned around.
Our put also has a strike of $100 and a premium of $5. If Harbour Co ends below $100 at expiry, the put is worth the gap between $100 and the stock price. If it ends at $100 or above, the put is worth nothing. The buyer loses the $5.
We set both premiums at $5 so the two shapes are easy to compare.
How do call and put payoffs compare at expiry?
The payoff is what the contract is worth at expiry. The profit is the payoff minus the premium. Break-even is the ending stock price at which the profit is exactly zero.
The call breaks even at $105: the strike of $100 plus the $5 premium. The stock has to rise 5% from $100 before the call buyer is ahead. The put breaks even at $95: the strike less the $5 premium. The stock has to fall 5% before the put buyer is ahead.
Chart 1 plots the profit per share for both buyers across ending prices from $50 to $150.
Source: YX Insights
The call line is flat at a $5 loss up to $100, then climbs one dollar for every dollar the stock rises. The put line is the reverse. It climbs one dollar for every dollar the stock falls below $100, then flattens at a $5 loss above it.
The table gives the same figures at ten ending prices.
Harbour Co price at expiry | Call buyer | Put buyer | Call seller | Put seller |
|---|---|---|---|---|
$0 | −$5 | $95 | $5 | −$95 |
$50 | −$5 | $45 | $5 | −$45 |
$70 | −$5 | $25 | $5 | −$25 |
$90 | −$5 | $5 | $5 | −$5 |
$95 | −$5 | $0 | $5 | $0 |
$100 | −$5 | −$5 | $5 | $5 |
$105 | $0 | −$5 | $0 | $5 |
$110 | $5 | −$5 | −$5 | $5 |
$130 | $25 | −$5 | −$25 | $5 |
$150 | $45 | −$5 | −$45 | $5 |
Profit per share, strike $100, premium $5 for both contracts, before commissions and tax. Source: YX Insights
At $130 the call buyer makes $25. At $70 the put buyer makes $25. Each contract is worth $30 at that price. After the $5 premium, each gain is $25, five times the amount paid.
What can a call or put buyer lose and gain?
Each buyer can lose at most the premium. For both contracts in our example, that is $5 a share.
The call loses it at every ending price of $100 or below. The put loses it at every ending price of $100 or above. Neither buyer can lose more than $5, at any ending price.
The upside differs. The call buyer's profit has no upper limit, because a stock price has no ceiling. At $150 the profit is $45. At $200 it is $95.
The put buyer's profit has a ceiling, because a stock price cannot fall below zero. The most the put can earn is $95, if Harbour Co falls to zero.
What does the seller of a call or a put risk?
Every contract has a seller, also called the writer. The seller collects the premium and takes the other side. If the buyer's contract is worth $30 at expiry, the seller owes $30.
The seller's profit is the buyer's profit with the sign flipped, so the two always sum to zero. Chart 2 shows the seller's side.
Source: YX Insights
The call seller keeps the full $5 premium if Harbour Co ends at $100 or below. Between $100 and $105 it keeps part of the premium. At $105 it keeps none.
Above $105 the loss grows without limit. At $150 it is $45 a share. At $200 it is $95.
The put seller keeps the full $5 premium if Harbour Co ends at $100 or above. Between $95 and $100 it keeps part of the premium. At $95 it keeps none. Below $95 the loss grows until the stock reaches zero, where it is $95 a share.
The seller's best case is a $5 gain in both cases. The buyer's best case is far larger.
Where does each position make a profit?
Chart 3 shows which ending prices, between $50 and $150, leave each position in profit.
Source: YX Insights
The call buyer profits above $105, a $45 span. The put buyer profits below $95, a $45 span. The call seller profits below $105, a $55 span. The put seller profits above $95, a $55 span.
The buyer's span is narrower because the stock must first cover the premium. The seller's span is wider, but the loss outside it is larger. The put seller can lose up to $95 a share. The call seller's loss has no upper limit.
Which one wins: a call or a put?
Neither wins on its own. The two contracts pay in opposite directions, so the stock's move decides which side of each trade is ahead.
If Harbour Co rises 30% to $130, the call buyer makes $25 and the put buyer loses $5. If it falls 30% to $70, the put buyer makes $25 and the call buyer loses $5. If it stays at $100, both buyers lose $5.
A third choice is to buy both. That costs $10 a share, so the stock must end above $110 or below $90 for the pair to profit.
What does this example leave out?
Our charts show each contract at expiry only. Before expiry, the time left and the stock's volatility also affect a contract's price. Our explainer on volatility covers the second idea.
The example uses one strike and one premium. It ignores commissions and tax.
Real contracts come in many strikes and expiry dates, each with its own premium. Our guide to what a futures contract is covers a related contract that obliges both sides.
A call gains when the stock ends above the strike plus the premium, while a put gains when it ends below the strike minus the premium. The buyer risks the premium, while the seller takes on the larger exposure.
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Common questions about calls vs puts
What is the difference between a call and a put?
A call gives its buyer the right to buy a stock at a fixed price, the strike, by a set date. A put gives the right to sell at the strike. In our example, a call profits when the stock ends above $105, while a put profits when it ends below $95.
Can you lose more than you pay for a call or put?
A buyer cannot lose more than the premium paid, which is $5 a share in our example. A seller can. Selling the call, the loss grows without limit as the stock rises. Selling the put, the loss reaches $95 a share if the stock falls to zero.
Is a call or a put riskier?
For the buyer, neither is riskier, because both lose at most the $5 premium. For the seller, the call is riskier in our example. Its loss has no upper limit, while the put seller's loss stops at $95 a share, the strike less the premium.
The premium is the price the buyer pays the seller for the contract. In our example it is $5 a share for both the call and the put. The buyer loses the premium if the contract expires worthless. It also sets the break-even, the ending price where the profit is zero. That is $105 for the call and $95 for the put.
DISCLAIMER: This article is intended for educational purposes only. Any information or analysis in this note does not constitute an offer to sell or a solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice, nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.
