Options and futures: payoffs, break-evens and hedging
Options and futures are contracts whose value comes from the price of something else, such as a share or a barrel of oil. This lesson explains calls, puts and futures in plain terms, shows their payoffs at expiry with a calculator for buyers and sellers, compares the size of a real oil futures contract with a standard stock option, and works through a simple hedge. It is an explanation of how the payoffs work and not advice to trade.
- Level
- Beginner
- Reading time
- About 26 minutes
- Know this first
- Diversification
By the end you will be able to:
- explain what a call, a put and a futures contract give each side
- calculate the payoff and break-even of a call or put
- explain why an option seller's risk differs from a buyer's
- use contract size to turn a price move into a money amount
- work through a simple futures hedge and say what it gives up
Contracts whose value comes from something else
Stocks and bonds are claims on a company. Options and futures are different: they are contracts whose value depends on the price of something else, such as a share or a barrel of oil. They are called derivatives, because their value is derived from an underlying price. They are used for two opposite purposes. The US Commodity Futures Trading Commission describes hedgers as people who trade futures to reduce the risk of financial loss from price changes, and speculators as those who attempt to profit from price changes.
The SEC warns that with options it is possible to lose all of your initial investment, and sometimes more, and the CFTC warns that many individuals lose all of their money in futures and can be required to pay more than they invested initially. This lesson is about understanding the payoffs, not a recommendation to trade. The lessons before it covered risk and return and diversification, and derivatives are the main tool for reshaping risk precisely.
Options: the right, not the duty
The SEC's introduction to options defines a call option as a contract that gives the buyer the right to buy shares of an underlying stock at the strike price, and a put option as a contract that gives the buyer the right to sell shares at the strike price. The seller, also called the writer, must sell the shares if the buyer exercises a call, and must buy them if the buyer exercises a put. The buyer pays a premium up front to the seller, and the SEC notes that it is non-refundable. An option contract generally represents 100 shares of the underlying stock and it has an expiration date.
A call is in the money if the strike price is below the actual stock price, and a put is in the money if the strike price is above it. The buyer risks the entire premium. The SEC adds that option writers may carry an even higher level of risk, since certain types of options can expose writers to unlimited potential losses.
Futures: an obligation fixed in advance
The CFTC describes a commodity futures contract as an agreement to buy or sell a particular commodity at a future date. Unlike an option, it is an obligation for both sides. Most contracts contemplate delivery of the actual commodity, though some allow cash settlement instead. Accounts are adjusted at the close of every trading day to reflect the day's current market value, so gains and losses are paid as they happen.
The buyer of a futures contract gains if the price rises above the agreed price and loses if it falls. The seller is the mirror image. The payoff therefore runs in a straight line, with no premium and no floor.
At expiry, per share (or per unit for a future), the payoffs are:
Payoffs on an invented share
An invented share trades at $100. Calls and puts both have a strike price of $100, and a future is agreed at $100. Set the share price at expiry and the premium per share. The left page shows what the buyers of the options make or lose. The right page shows the sellers of the options, and the buyer and seller of a future. All figures are in dollars per share, so multiply by 100 for a standard contract. At the starting settings the share ends at $112 and the premium is $5.
At 112 the call is in the money and pays $12 a share, so after the premium of $5 its buyer gains $7 and its seller loses $7. The put expires worthless: its buyer loses the premium of $5 and its seller keeps it. A futures contract opened at 100 gains $12 a unit for the buyer and loses the same for the seller.
Four experiments. First, at the starting settings the call buyer gains $7 a share, which is $700 on a 100-share contract, while the put buyer loses the whole $5 premium. The call seller loses the same $7 that the buyer gains, because an option is a zero-sum bet between the two. Second, set the price to 103. The call is in the money and pays $3, but that does not cover the $5 premium, so the buyer still loses $2. A call needs the price to pass the break-even of 105, not just the strike. Third, set the price to 60. The put buyer gains $35 and the call buyer loses only $5, the most it can ever lose. Fourth, set the price to 140. The call buyer gains $35, and the call seller loses $35 after keeping $5, a loss that would keep growing if the price rose further. The buyer's loss is capped, and the seller's is not. The future has no such cap in either direction: the buyer gains $40 and the seller loses $40.
Two real contracts: oil futures and a stock option
The contract size turns a small price move into a large sum of money. The table compares the CME Group's WTI crude oil futures contract with the standard US stock option described by the SEC. The value of a $1 move is the contract size times $1.
| One contract | WTI crude oil futures (CME) | Standard US stock option (SEC) |
|---|---|---|
| What it is based on | Crude oil | A stock |
| Contract size | 1,000 barrels | Generally 100 shares |
| Value of a $1 move in the quoted price | $1,000 | $100 |
| Value of the smallest price move | $10 ($0.01 × 1,000 barrels) | Not covered in the source |
| Obligation or right | Obligation for both sides | Right for the buyer, obligation for the seller |
| What the buyer can lose | More than the initial investment is possible | The premium paid |
| Delivery | Physical delivery at Cushing, Oklahoma, per the CME fact card | Buyer chooses whether to exercise |
A move of one dollar in the oil price is worth $1,000 on one futures contract, and a move of one dollar in the quoted option premium is worth $100 on one option contract. The SEC bulletin's own example makes the second point: a premium of $2.20 means a cost of $220 for the contract. Contract size is the reason that small positions in derivatives can produce large gains or losses.
Using a future to hedge
Hedging means taking a position that offsets a risk the business already has. Take an invented company that will need to buy 5,000 barrels of oil in three months. If the price rises, its costs rise. To lock the price today, it buys five futures contracts, each for 1,000 barrels, at $70 a barrel. Suppose the price rises to $80. The company pays $50,000 more for the oil, but the futures gain 5 × 1,000 × $10 = $50,000, which offsets it. If the price instead fell to $60, the oil would cost $50,000 less, but the futures would lose the same amount. The hedge removes the gain as well as the loss. Options can hedge too: buying a call caps the cost at the strike plus the premium and keeps the benefit if the price falls, and the premium is the price of that flexibility. Prices here are invented, and a real hedge also has to deal with differences between the contract and the exact oil bought.
What the payoff picture leaves out
- Only the end of the contract. The figures are the payoff at expiry. Before then an option has a market value that depends on time left and volatility, which the SEC notes in its discussion of the premium.
- The premium is given. Where it comes from is a separate subject, option pricing.
- One price and one strike. Real markets list many strikes and expiry dates, and each has its own premium.
- Costs are ignored. Commissions, margin requirements and taxes are left out.
- Early exercise and delivery details are skipped. Contracts differ on when they can be exercised and how they settle.
- This is education, not a strategy. Nothing here suggests that any position is suitable for anyone.
Common mistakes
Forgetting the premium
An option can be in the money and still lose, as the 103 experiment shows. Compare the price with the break-even, not the strike.
Treating an option and a future as the same thing
The buyer of an option has the right to act, and the buyer of a future has the obligation.
Thinking sellers of options have limited risk
The seller's gain is capped at the premium, but a seller of a call can face large losses if the price keeps rising.
Ignoring the contract size
A standard option covers 100 shares and an oil future 1,000 barrels. A small quoted move is a large amount of money.
Assuming a hedge only helps
A future hedge locks in a price. It gives up the gain from a favourable move.
Try it yourself
1. A call has a strike of $50 and a premium of $3 a share. The stock ends at $58. What does the buyer make on one 100-share contract?
Show the working
The call pays 58 − 50 = $8 a share. After the $3 premium the gain is $5 a share, or $500 on 100 shares.
2. The same stock ends at $49. What does the buyer make or lose?
Show the working
The call is out of the money and expires worthless. The buyer loses the premium: 3 × 100 = $300. That is the most the buyer could lose.
3. A put has a strike of $80 and a premium of $4. What is its break-even price?
Show the working
The put pays only if the price is below 80, and it must pay back the $4 premium, so the break-even is 80 − 4 = $76.
4. A trader buys one WTI futures contract (1,000 barrels) at $70.00 and the price rises to $72.50. What is the gain?
Show the working
The gain is 72.50 − 70.00 = $2.50 a barrel, so 2.50 × 1,000 = $2,500. If the price had fallen by $2.50, the loss would have been the same size.
5. A company that must buy 5,000 barrels hedges with five futures contracts bought at $70, and the price rises to $80. How much do the futures gain, and what does that do to the hedge?
Show the working
Gain = 5 × 1,000 × (80 − 70) = $50,000. The oil costs 5,000 × $10 = $50,000 more, so the gain exactly offsets the higher cost, and the company's effective price stays at about $70 a barrel.
Where this is used
- An airline, a refiner or a farmer uses futures to lock in the price of fuel, oil or grain.
- An investor holding a stock buys a put to limit a possible fall, at the cost of the premium.
- A fund uses index futures to adjust its market exposure quickly.
- An analyst reads a company's notes on derivatives to see how it manages commodity or currency risk.
Key terms
- Derivative
- A contract whose value depends on the price of an underlying asset.
- Call option
- A contract giving the buyer the right to buy the underlying at the strike price.
- Put option
- A contract giving the buyer the right to sell the underlying at the strike price.
- Strike price
- The price at which the option holder can buy or sell the underlying.
- Premium
- The price paid up front by the buyer of an option to the seller.
- In the money
- A call is in the money if the strike is below the stock price, and a put if the strike is above it.
- Futures contract
- An agreement to buy or sell an asset at a set price on a future date.
- Hedger
- Someone who uses a contract to reduce an existing price risk.
- Speculator
- Someone who takes a position to profit from price changes.
Questions people ask
Why would anyone sell an option?
To receive the premium. In return the seller accepts the obligation to buy or sell if the buyer exercises, and a seller can lose more than the premium.
Can I lose more than I invest?
Buying an option risks the premium. The SEC says writers can face unlimited losses on certain options, and the CFTC says futures traders can be required to pay more than they invested.
Is a derivative the same as gambling?
The payoff of a derivative is the same whether it is used to hedge or to speculate. What differs is whether the holder has an offsetting exposure.
How is the premium decided?
The SEC says it depends on the stock price relative to the strike, the time until expiration and the stock's price volatility. Pricing models are a separate subject.
Sources and review
- US Securities and Exchange Commission, Investor.gov, An introduction to options, for the definitions of call and put options, strike price, premium, expiration date, in the money, the 100-share contract and the risks to buyers and writers.
- US Commodity Futures Trading Commission, Basics of futures trading, for the definition of a futures contract, hedgers and speculators, daily adjustment of accounts, delivery and cash settlement, and the risk of losing more than the initial investment.
- CME Group, Light sweet crude oil (WTI) futures and options fact card, for the contract size of 1,000 barrels, the minimum price fluctuation of $0.01 per barrel and delivery at Cushing, Oklahoma.
How the numbers were checked: the option and futures payoffs, break-evens and the hedge were recomputed in plain code, and the calculator, which runs separately, was compared with that code for every combination of settings it allows. The contract sizes come from the sources above, and the $1 move values are the contract size multiplied by $1. The share, its premiums and the hedging company are invented for teaching.