CFA Program — Derivatives

36 free practice questions with full explanations.

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Question 1

Which of the following would most likely increase the value of a call option, all else equal?

A) A decrease in the underlying asset's price volatility
B) An increase in the underlying asset's price volatility
C) A decrease in the time remaining until expiration
D) An increase in the strike price

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Correct answer: B) An increase in the underlying asset's price volatility

Higher volatility in the underlying asset increases the probability of the option finishing deep in the money, increasing the value of both call and put options, all else equal.

Question 2

An investor buys a call option on a stock with a strike price of $50. If the stock price at expiration is $60, what is the option's intrinsic value (ignoring the premium paid)?

A) $0
B) $10
C) $50
D) $60

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Correct answer: B) $10

A call option's intrinsic value at expiration equals max(0, Stock Price - Strike Price) = max(0, 60 - 50) = $10.

Question 3

An investor buys a put option on a stock with a strike price of $40. If the stock price at expiration is $55, what is the option's intrinsic value?

A) $0
B) $15
C) $40
D) $55

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Correct answer: A) $0

A put option's intrinsic value equals max(0, Strike Price - Stock Price) = max(0, 40 - 55) = max(0, -15) = $0, since the put is out of the money.

Question 4

Which of the following best describes a forward contract?

A) A standardized, exchange-traded agreement with daily settlement
B) A customized, privately negotiated agreement between two parties to buy/sell an asset at a future date for a price agreed today
C) A contract that provides the right, but not the obligation, to buy an asset
D) A contract that can only be used for equity securities

Show answer & explanation

Correct answer: B) A customized, privately negotiated agreement between two parties to buy/sell an asset at a future date for a price agreed today

A forward contract is a customized, over-the-counter agreement between two parties, in contrast to a futures contract, which is standardized and exchange-traded with daily mark-to-market settlement.

Question 5

The writer (seller) of a call option has:

A) The right, but not the obligation, to buy the underlying asset
B) The right, but not the obligation, to sell the underlying asset
C) The obligation to sell the underlying asset if the option is exercised by the holder
D) No obligation of any kind

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Correct answer: C) The obligation to sell the underlying asset if the option is exercised by the holder

The option holder (buyer) has the right to exercise; the option writer (seller) has the corresponding obligation -- for a call option, the writer must sell (deliver) the underlying asset at the strike price if the holder chooses to exercise.

Question 6

A swap contract most commonly involves:

A) A one-time exchange of a single fixed payment
B) An exchange of a series of cash flows between two parties over time, such as fixed-for-floating interest payments
C) The purchase of a single share of stock
D) A guarantee against default with no cash flow exchange

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Correct answer: B) An exchange of a series of cash flows between two parties over time, such as fixed-for-floating interest payments

A swap is an agreement between two parties to exchange a series of cash flows over time, with an interest rate swap (fixed-for-floating) being a common example.

Question 7

Which of the following best describes a "forward rate agreement" (FRA)?

A) A contract requiring physical delivery of a commodity.
B) An over-the-counter contract in which two parties agree to exchange interest payments based on a notional amount and a specified interest rate, for a future period, without exchanging the notional principal itself.
C) A standardized, exchange-traded futures contract on a stock index.
D) A type of common equity security.

Show answer & explanation

Correct answer: B) An over-the-counter contract in which two parties agree to exchange interest payments based on a notional amount and a specified interest rate, for a future period, without exchanging the notional principal itself.

A forward rate agreement is an OTC derivative in which counterparties agree on an interest rate to apply to a notional principal amount for a specified future period, settling in cash based on the difference between the agreed rate and the actual reference rate at settlement, without exchanging the notional itself.

Question 8

The seller (writer) of a call option receives which of the following in exchange for taking on the obligation to sell the underlying asset if exercised?

A) The option premium, paid upfront by the buyer.
B) A guaranteed profit regardless of the underlying price movement.
C) Ownership of the underlying asset immediately.
D) Nothing -- the seller receives no compensation.

Show answer & explanation

Correct answer: A) The option premium, paid upfront by the buyer.

In exchange for accepting the obligation to sell the underlying asset at the strike price if the buyer exercises, the call option seller (writer) receives the option premium upfront from the buyer.

Question 9

Which of the following best describes the payoff to the holder of a long forward contract at expiration?

A) A fixed payoff regardless of the underlying asset's price.
B) Always zero, since forward contracts have no payoff.
C) The premium originally paid for the contract.
D) The difference between the spot price of the underlying asset at expiration and the original forward price.

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Correct answer: D) The difference between the spot price of the underlying asset at expiration and the original forward price.

The payoff to a long forward position at expiration equals the spot price of the underlying asset at that time minus the forward price agreed upon at initiation, reflecting the gain or loss from having locked in that forward price.

Question 10

A "collar" options strategy typically combines which of the following, applied to an existing long stock position?

A) Selling both a call and a put at the same strike price.
B) Buying two calls at different strike prices with no puts involved.
C) Buying a protective put and selling a covered call, often structured so the premiums roughly offset.
D) Buying both a call and a put at the same strike price.

Show answer & explanation

Correct answer: C) Buying a protective put and selling a covered call, often structured so the premiums roughly offset.

A collar strategy combines a protective put (bought, providing downside protection) with a covered call (sold, generating premium income that helps offset the put's cost), applied to an existing long stock position, capping both potential losses and potential gains within a defined range.

Question 11

Which of the following best describes counterparty risk in a derivatives contract?

A) The risk that a derivative contract will expire early.
B) The risk that the other party to the contract will fail to fulfill their contractual obligations.
C) The risk that the underlying asset's price will never change.
D) The risk exclusively associated with exchange-traded futures, never OTC derivatives.

Show answer & explanation

Correct answer: B) The risk that the other party to the contract will fail to fulfill their contractual obligations.

Counterparty risk refers to the possibility that the other party to a derivatives contract will default on or fail to fulfill their obligations. This risk is generally higher in OTC derivatives (like forwards and swaps) than in exchange-traded derivatives (like futures), which benefit from clearinghouse guarantees.

Question 12

A commodity producer wants to lock in a selling price for a future harvest to hedge against the risk of falling prices. Which position would most directly achieve this?

A) Selling (shorting) a futures contract on the commodity.
B) Buying (going long) a futures contract on the commodity.
C) Buying a call option on an unrelated commodity.
D) Taking no position at all.

Show answer & explanation

Correct answer: A) Selling (shorting) a futures contract on the commodity.

A producer wanting to lock in a selling price to hedge against falling prices would sell (take a short position in) futures contracts, since a short futures position gains value as prices fall, offsetting the lower revenue the producer would receive from selling the physical commodity at the lower market price.

Question 13

A futures contract's "initial margin" requirement refers to:

A) The minimum amount of funds a trader must deposit to open a futures position, serving as a performance bond.
B) The full notional value of the underlying asset.
C) A one-time fee paid to the exchange with no ongoing purpose.
D) The maximum profit a trader can earn on the position.

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Correct answer: A) The minimum amount of funds a trader must deposit to open a futures position, serving as a performance bond.

Initial margin is the minimum deposit required to open a futures position, acting as a performance bond to help ensure the trader can cover potential losses; this is distinct from the (typically lower) maintenance margin required to keep the position open.

Question 14

Which of the following best describes the buyer of a put option's maximum potential loss?

A) Twice the premium paid for the option.
B) The premium paid for the put option, and no more.
C) Unlimited, since the underlying price could theoretically rise without limit.
D) The full strike price of the option.

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Correct answer: B) The premium paid for the put option, and no more.

A put option buyer's maximum loss is limited to the premium paid, since the buyer is never obligated to exercise an option that has become worthless (would simply let it expire unexercised rather than take on any further loss).

Question 15

Which of the following best describes the concept of "intrinsic value" for an option?

A) The value the option would have if exercised immediately, equal to the favorable difference (if any) between the underlying price and the strike price.
B) The total premium paid for the option.
C) A value that is always zero for any option.
D) The value attributable solely to the passage of time.

Show answer & explanation

Correct answer: A) The value the option would have if exercised immediately, equal to the favorable difference (if any) between the underlying price and the strike price.

Intrinsic value represents the immediate exercise value of an option -- for a call, the amount by which the underlying price exceeds the strike price (if positive); for a put, the amount by which the strike exceeds the underlying price (if positive). It excludes time value, the other component of an option's total premium.

Question 16

A company enters into an interest rate swap to convert its existing floating-rate debt into effectively fixed-rate debt. In this swap, the company would:

A) Receive a payment only if interest rates fall to zero.
B) Pay a fixed rate and receive a floating rate from the swap counterparty.
C) Pay a floating rate and receive a fixed rate from the swap counterparty.
D) Exchange only principal amounts, with no interest payments involved.

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Correct answer: B) Pay a fixed rate and receive a floating rate from the swap counterparty.

To convert floating-rate debt into effectively fixed-rate debt, the company would enter a swap in which it pays a fixed rate to the counterparty and receives a floating rate, which offsets the floating payments owed on its underlying debt, leaving a net fixed obligation.

Question 17

Which of the following best describes "basis risk" in a hedging context?

A) A risk that applies only to hedges using physical commodities.
B) The risk that a company will pay too much in brokerage commissions.
C) The risk that the price of the hedging instrument (such as a futures contract) does not move perfectly in tandem with the price of the asset being hedged.
D) The risk that a hedge will always perfectly offset the underlying exposure.

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Correct answer: C) The risk that the price of the hedging instrument (such as a futures contract) does not move perfectly in tandem with the price of the asset being hedged.

Basis risk arises when the hedging instrument and the underlying exposure being hedged do not move in perfect lockstep (for example, hedging jet fuel exposure with crude oil futures), meaning the hedge may not perfectly offset changes in the value of the exposure being hedged.

Question 18

Which of the following best describes a "strangle" options strategy?

A) Buying only a single call option with no put involved.
B) Buying a call and a put with identical strike prices.
C) A strategy that can only be executed using futures contracts, never options.
D) Simultaneously buying (or selling) a call and a put on the same underlying asset with the same expiration but different strike prices.

Show answer & explanation

Correct answer: D) Simultaneously buying (or selling) a call and a put on the same underlying asset with the same expiration but different strike prices.

A strangle involves simultaneously holding a call and a put on the same underlying asset with the same expiration date but different (typically both out-of-the-money) strike prices, profiting from large price movements in either direction (if long) or from low volatility (if short), similar in spirit to a straddle but with different strikes.

Question 19

A European call option has a strike price of $50. The current stock price is $45. The option is:

A) In-the-money
B) At-the-money
C) Out-of-the-money
D) Deep in-the-money

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Correct answer: C) Out-of-the-money

A call option is out-of-the-money when the stock price ($45) is below the strike price ($50). Exercising would result in buying stock above market value, so it would not be exercised.

Question 20

According to put-call parity, the price of a European put option equals:

A) C + PV(X) − S
B) C − S + PV(X)
C) S − C + PV(X)
D) C + S − PV(X)

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Correct answer: A) C + PV(X) − S

Put-call parity: P = C + PV(X) − S, where C is call price, PV(X) is present value of strike price, and S is current stock price. This relationship holds for European options on non-dividend-paying stocks.

Question 21

An investor enters a long forward contract to buy 100 shares at $50 in 6 months. At expiration the stock trades at $55. The investor's profit/loss is:

A) Loss of $500
B) Profit of $500
C) Profit of $5,000
D) Breakeven

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Correct answer: B) Profit of $500

At expiration, the investor buys at $50 (forward price) and can sell at $55 (spot). Profit = ($55 − $50) × 100 = $500.

Question 22

A company enters a pay-fixed, receive-floating interest rate swap. It will benefit when:

A) Fixed rates rise above the swap rate
B) Floating rates rise above the fixed swap rate
C) The yield curve flattens
D) Credit spreads narrow

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Correct answer: B) Floating rates rise above the fixed swap rate

In a pay-fixed, receive-floating swap, the company pays a fixed rate and receives the floating rate. It benefits when the floating rate received exceeds the fixed rate paid.

Question 23

All else equal, which of the following increases the value of a call option?

A) Decrease in the volatility of the underlying
B) Decrease in the time to expiration
C) Increase in the risk-free rate
D) Increase in the exercise price

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Correct answer: C) Increase in the risk-free rate

Higher risk-free rates increase call option value (the present value of the exercise price decreases, making it less costly to acquire the stock). Volatility and time to expiration positively affect call value; higher strike price reduces it.

Question 24

Which derivative strategy is most appropriate for an investor who holds a stock and wants to limit downside risk while retaining upside potential?

A) Short a call option on the stock (covered call)
B) Buy a put option on the stock (protective put)
C) Enter a short forward on the stock
D) Short a put option on the stock

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Correct answer: B) Buy a put option on the stock (protective put)

A protective put combines a long stock position with a long put option, providing a floor on losses (downside protection) while preserving unlimited upside potential. A covered call caps the upside.

Question 25

The buyer of a call option has the right, but not the obligation, to:

A) Force the option seller to exercise the option.
B) Receive dividends from the underlying asset automatically.
C) Buy the underlying asset at the strike price, on or before expiration (depending on option style).
D) Sell the underlying asset at the strike price.

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Correct answer: C) Buy the underlying asset at the strike price, on or before expiration (depending on option style).

A call option gives its buyer (the holder) the right, but not the obligation, to purchase the underlying asset at the strike price, exercising this right if and when it is advantageous to do so.

Question 26

An investor buys a call option with a strike price of $50 for a premium of $3. At expiration, the underlying stock is trading at $58. The investor's profit on this position is closest to:

A) -$3
B) $5
C) $8
D) $3

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Correct answer: B) $5

Payoff at expiration = max(Spot - Strike, 0) = max(58-50, 0) = $8. Profit = Payoff - Premium paid = 8 - 3 = $5.

Question 27

The seller (writer) of a put option has the obligation to:

A) Buy the underlying asset at the strike price if the buyer chooses to exercise the option.
B) Sell the underlying asset at the strike price if the buyer chooses to exercise.
C) Exercise the option whenever they choose.
D) Receive an unlimited profit if the underlying asset price falls to zero.

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Correct answer: A) Buy the underlying asset at the strike price if the buyer chooses to exercise the option.

A put option gives its buyer the right to sell the underlying asset at the strike price; correspondingly, the put seller (writer) has the obligation to buy the underlying asset at the strike price if the buyer chooses to exercise.

Question 28

A forward contract, compared to a futures contract, is best described as:

A) A standardized contract traded on an organized exchange with daily mark-to-market settlement.
B) A type of common stock.
C) An agreement that never involves any counterparty risk.
D) A customized, privately negotiated agreement between two parties, typically not traded on an exchange.

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Correct answer: D) A customized, privately negotiated agreement between two parties, typically not traded on an exchange.

A forward contract is a private, customized agreement between two counterparties (traded over-the-counter), unlike a futures contract, which is standardized and traded on an exchange with daily mark-to-market settlement and reduced counterparty risk via a clearinghouse.

Question 29

An investor holding a long position in a stock purchases a put option on that same stock as a hedge. This strategy is best described as:

A) A naked call, which exposes the investor to unlimited risk.
B) A strategy with no relationship between the stock and option positions.
C) A protective put, which limits downside risk on the stock while preserving upside potential (minus the premium paid).
D) A covered call, which caps the investor's upside.

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Correct answer: C) A protective put, which limits downside risk on the stock while preserving upside potential (minus the premium paid).

Buying a put option to hedge an existing long stock position is known as a protective put strategy: it limits downside risk (the put gains value if the stock falls) while the investor retains upside potential in the stock, at the cost of the premium paid for the put.

Question 30

Which of the following factors, all else equal, generally increases the value of a call option?

A) A decrease in the price of the underlying asset.
B) An increase in the volatility of the underlying asset.
C) An increase in the option's strike price.
D) A decrease in time remaining until expiration.

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Correct answer: B) An increase in the volatility of the underlying asset.

Higher volatility of the underlying asset increases the probability of larger favorable price movements, increasing the value of both call and put options, all else equal, since option payoffs are asymmetric (limited downside, unlimited or large upside potential for the buyer).

Question 31

An investor purchases a call option with a strike price of $75 for a premium of $6. At expiration, the underlying stock is trading at $90. The investor's profit on this position is closest to:

A) $15
B) $6
C) $9
D) $21

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Correct answer: C) $9

The call option's payoff at expiration = max(Stock price - Strike price, 0) = max(90-75, 0) = $15. Subtracting the $6 premium originally paid, the investor's net profit is 15-6 = $9.

Question 32

A domestic importer will owe a foreign supplier a fixed amount of foreign currency in 90 days and wants to eliminate the risk that the foreign currency will appreciate against the domestic currency before payment is due. Which position would most directly hedge this risk?

A) Entering into a long forward contract to buy the foreign currency at a fixed exchange rate for delivery in 90 days.
B) Entering into a short forward contract to sell the foreign currency.
C) Taking no position, since exchange rates are guaranteed not to change over such a short period.
D) Purchasing a call option on the domestic currency, denominated in the domestic currency.

Show answer & explanation

Correct answer: A) Entering into a long forward contract to buy the foreign currency at a fixed exchange rate for delivery in 90 days.

An importer who will need to buy foreign currency in the future to make a payment is exposed to the risk that the foreign currency appreciates (making the payment more expensive in domestic currency terms). Entering a long forward contract to buy the foreign currency at a fixed rate today locks in the exchange rate for the future payment, eliminating this currency risk.

Question 33

A non-dividend-paying stock currently trades at $40. The risk-free rate is 4% annually, and a futures contract on the stock expires in 6 months. Using the cost-of-carry model (with no storage costs or dividends), the theoretical futures price is closest to:

A) $40.00
B) $41.60
C) $38.46
D) $40.79

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Correct answer: D) $40.79

Using the cost-of-carry model, F = S x (1+r)^T = 40 x (1.04)^0.5 = 40 x 1.0198 = approximately $40.79, reflecting the cost of carrying (financing) the underlying stock position over the 6-month period until the futures contract expires.

Question 34

In a one-period binomial option pricing model, the value of an option today is determined primarily by:

A) Simply averaging the option's payoff in the up-state and down-state, with no discounting or adjustment for probabilities.
B) The option seller's personal opinion about likely future stock price movements.
C) Constructing a replicating portfolio of the underlying stock and a risk-free bond that produces the same payoffs as the option in both the up-state and down-state, then using risk-neutral probabilities to discount the option's expected payoff back to the present at the risk-free rate.
D) The historical average return of the underlying stock over the past decade.

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Correct answer: C) Constructing a replicating portfolio of the underlying stock and a risk-free bond that produces the same payoffs as the option in both the up-state and down-state, then using risk-neutral probabilities to discount the option's expected payoff back to the present at the risk-free rate.

The binomial model prices an option by constructing a replicating portfolio (a combination of the underlying stock and risk-free borrowing/lending) that exactly matches the option's payoffs in each possible future state, then uses risk-neutral probabilities (not actual real-world probabilities) to calculate the option's expected payoff, which is discounted back to the present at the risk-free rate to arrive at the no-arbitrage option value.

Question 35

A one-year European call option on a stock with a strike price of $50 trades at $4. The underlying stock currently trades at $50, and the one-year risk-free rate is 5%. Using put-call parity, the price of a one-year European put option with the same strike price is closest to:

A) $4.00
B) $1.62
C) $6.50
D) $0.00

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Correct answer: B) $1.62

Put-call parity states: Call price + PV(Strike price) = Put price + Stock price. Solving for the put: Put = Call + PV(Strike) - Stock = 4 + [50/1.05] - 50 = 4+47.62-50 = approximately $1.62.

Question 36

An investor purchases a put option with a strike price of $80 for a premium of $4. At expiration, the underlying stock is trading at $68. The investor's profit on this position is closest to:

A) $8
B) $12
C) $4
D) $-4

Show answer & explanation

Correct answer: A) $8

The put option's payoff at expiration = max(Strike price - Stock price, 0) = max(80-68, 0) = $12. Subtracting the $4 premium originally paid, the investor's net profit is 12-4 = $8.

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