Calls and Puts

Why this matters

Options are a complicated product that's marketed to ordinary investors. A brokerage app may offer them beside shares, a tap away. They aren't the same kind of thing. A share is a piece of a company that can be held for decades. An option is a contract between two people about a share, with a date after which it no longer exists. This track is about how these contracts work and how they go wrong. It isn't a trading course, and nothing in it is a recommendation to use them. Options: A First Look introduced the vocabulary. This lesson builds the whole structure, starting from the fact that every option has two sides.

A right, sold by someone

An option is the right to buy or sell a specified amount of an underlying interest, such as a company's shares, at a fixed price, by exercising the option before a specified expiration date.¹ Options are derivatives: they take their value from the price of that underlying asset.² There are two types.²

• A call gives its buyer the right, and no obligation, to buy shares at the fixed price.
• A put gives its buyer the right, and no obligation, to sell shares at the fixed price.

The fixed price is the strike price, also called the exercise price. For most options on shares, one contract covers 100 shares.¹

A right that one person holds is an obligation that another has accepted. The buyer of an option, called the holder, pays a price called the premium. The seller, called the writer, receives it, and in exchange accepts the obligation to buy or sell if the holder chooses to exercise.¹² When that happens, the writer is said to be assigned.

The words long and short here mean holder and writer.¹ Notice that "short a put" is a position that profits when the shares rise, so short doesn't mean betting on a fall. It means having sold the contract.

Buying a call

The examples in this track use STU Corp, a fictional company whose shares trade at $50. All the prices are hypothetical.

Dana buys one call on STU with a strike price of $55, expiring in three months, for a premium of $2 a share. The contract covers 100 shares, so it costs $200. At expiration, the call is worth whatever the right to buy at $55 is worth: nothing if STU is at or below $55, and the difference if it's above.

STU at expiration	Call is worth	Less premium paid	Buyer's result
$45	$0	$200	−$200
$55	$0	$200	−$200
$57	($57 − $55) × 100 = $200	$200	$0
$60	($60 − $55) × 100 = $500	$200	+$300
$70	($70 − $55) × 100 = $1,500	$200	+$1,300

The most Dana can lose is the $200 premium. That loss is total, and it happens at every price up to $55, including prices where STU has risen. The break-even is the strike plus the premium, $57. Above that, each further dollar on the share price adds $100.

Selling that call

Someone sold Dana the call. Suppose it was Ravi, who doesn't own any STU shares. A call sold without owning the shares is called uncovered, or naked. Ravi received $200. If Dana exercises, Ravi has to deliver 100 shares at $55, buying them at the market price to do it.

STU at expiration	Premium received	Cost of meeting the obligation	Seller's result
$45	$200	$0	+$200
$55	$200	$0	+$200
$57	$200	$200	$0
$60	$200	$500	−$300
$70	$200	$1,500	−$1,300

Every row is Dana's result with the sign reversed. The most Ravi can make is the $200. What he can lose depends on how high STU goes, and a share price has no ceiling, so the maximum loss on an uncovered call is theoretically unlimited.²

Buying and selling a put

A put is the same contract turned over. Dana buys one put on STU with a strike of $45 for $1.50 a share, $150 in all. It gives her the right to sell 100 shares at $45. That's worth nothing if STU is at or above $45, and the difference if it's below.

STU at expiration	Put is worth	Buyer's result	Seller's result
$60	$0	−$150	+$150
$45	$0	−$150	+$150
$43.50	$150	$0	$0
$40	$500	+$350	−$350
$30	$1,500	+$1,350	−$1,350
$0	$4,500	+$4,350	−$4,350

The put buyer's break-even is the strike minus the premium, $43.50. The put seller keeps the premium unless STU falls below $45, and then has to buy shares at $45 that are worth less. A share can't fall below zero, so the seller's worst case is large and known: $4,350 here.

All four, side by side

• Switch between "Buy a call" and "Sell a call, uncovered". The line flips top to bottom around zero.
• Raise the premium and watch the buyer's break-even move further away.
• Look at where each line is flat. That's where the option expires worthless, and it's the buyer's whole loss and the seller's whole gain.

Three things the tables show

What one side gains, the other loses

At expiration, the buyer's result and the seller's result add up to zero at every price. An option contract creates no wealth. It moves it between two people, depending on what the share price does. After commissions and the gap between buying and selling prices, the two together come out slightly behind.

The risks are lopsided

The buyer's loss is capped at the premium, and the buyer has all, or nearly all, of the possible gain. The seller's gain is capped at the premium, and the seller carries the possible loss. That's the reason for the difference in language. The purchaser of an option has a right and no obligation. The seller has an obligation, and has to meet it if assigned.²

Lopsided doesn't mean unfair. The premium is the price of the lopsidedness, set so that buyers are willing to pay it and sellers are willing to take it. With options like the ones above, a buyer loses a small amount in most outcomes and wins a large one in a few. A seller wins a small amount in most outcomes and loses a large one in a few. Which of those is the better deal depends on the premium, and Strike, Expiration, and Premium starts on what goes into it.

The option runs out

Every row in the tables is labelled "at expiration" because an option has one. A share that falls can be held until it recovers. An option that's below its break-even on its expiration date is finished: a contract expires worthless when the share price is below a call's strike or above a put's.² Being right about a company and wrong about the timing loses the whole premium. Dana's $55 call loses $200 if STU reaches $70 a week after it expires.

Who's on the other side

Dana doesn't know Ravi, and doesn't need to trust him. Listed options have standardized terms, and options with the same terms are identical, which is why they can be bought and sold on a market like shares. The Options Clearing Corporation and its member firms stand between the two sides: the firms guarantee that writers will perform, and post collateral to back that up.¹ If Dana exercises, she doesn't have to find Ravi. The system assigns the obligation to a writer, and it's met.

Standardization also means a position doesn't have to be held to expiration. A holder can sell an identical option, or a writer can buy one, in what's called a closing transaction, which cancels the position. Holders often realize their gains or losses that way in place of exercising.¹

Why anyone uses them

The same four positions serve three different purposes, and the rest of this module takes them up.

• Leverage. A buyer controls 100 shares for a premium that's small beside their value.² Above $55, Dana's $200 call gains as much for each dollar on the share price as 100 shares costing $5,000 would. Leverage is also why her loss at $55 was 100% while a shareholder had gained 10%.
• Protection. Someone who owns shares can buy a put as insurance against a fall. Covered Calls and Protective Puts covers this.
• Income. Someone can sell options to collect premiums, accepting the obligation. Whether the premium is adequate pay for the risk is the whole question.

Key takeaways

• A call is the right to buy at the strike price. A put is the right to sell at it. One contract usually covers 100 shares.
• The buyer pays the premium and has a right. The seller receives it and has an obligation.
• A call buyer breaks even at strike plus premium, and a put buyer at strike minus premium.
• A buyer can lose only the premium. A seller's loss can be many times the premium, and has no limit for an uncovered call.
• At expiration, the buyer's gain is exactly the seller's loss.
• An option expires. Being right too late pays nothing.

Check your understanding

An investor buys one put with a strike price of $80 for a premium of $3 a share. At expiration the shares are at $72. What's the result?

1. A loss of $300, since the shares fell and the put was the wrong bet.
2. A gain of $500: the put is worth $800 and cost $300.
3. A gain of $800, since the shares are $8 below the strike price.

Which of these positions has a possible loss with no upper limit?

1. Buying a call, since the share price could fall all the way to zero.
2. Selling a put, since the seller has to buy the shares if assigned.
3. Selling a call without owning the shares, since prices have no ceiling.

What's next

Each example here fixed three things in advance: the strike, the expiration date, and the premium. Strike, Expiration, and Premium looks at how those terms are set and how they relate to one another.