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CFA Level I Derivatives Practice Questions

Official outline
CFA Institute 2026 Level I Topic Outlines (learning outcomes)
Questions on this page
6
Updated
Nov 3, 2026
Share of the exam
5-8%

  1. Question 1, hard

    A non-dividend-paying stock trades at $40. The 1-year risk-free rate is 6% (annually compounded), so the theoretical no-arbitrage 1-year forward price is $42.40. The forward is actually quoted in the market at $43.00. Which strategy would a trader use to capture a riskless arbitrage profit, and what is that profit closest to?

    • A.Borrow $40 to buy the stock now and simultaneously sell (go short) the forward contract. A cash-and-carry trade locking in about $0.60 of riskless profit
    • B.Short the stock now, invest the proceeds at the risk-free rate, and buy the forward contract (reverse cash-and-carry)
    • C.Do nothing, since the forward is fairly priced
    • D.Buy the forward contract and short the stock simultaneously, with no clear profit
    Show answer and explanationHide answer

    Correct answer: A. Borrow $40 to buy the stock now and simultaneously sell (go short) the forward contract. A cash-and-carry trade locking in about $0.60 of riskless profit

    Since the market forward price ($43.00) exceeds the theoretical fair value ($42.40), the forward is overpriced relative to the underlying's cost of carry. The arbitrage is a cash-and-carry: borrow $40 today, buy the stock, and sell the forward at $43. At expiration, deliver the stock into the forward for $43 and repay the loan of $40 × 1.06 = $42.40, capturing a riskless $0.60 profit. Choice B (reverse cash-and-carry) is the correct strategy only when the forward is underpriced relative to fair value, not overpriced as here. Choice C ignores the clear mispricing. Choice D describes an incomplete, ambiguous strategy with no defined profit.

    • A. Correct. Since the forward is overpriced relative to fair value, the cash-and-carry trade (borrow to buy the stock, short the forward) locks in the $0.60 gap ($43.00 − $42.40) as riskless profit.
    • B. Incorrect. The reverse cash-and-carry (short stock, buy forward) is the correct strategy when the forward is underpriced, not overpriced as it is here.
    • C. Incorrect. The $0.60 gap between the market forward price and the no-arbitrage price means the forward is mispriced, so an arbitrage opportunity does exist.
    • D. Incorrect. Buying the forward while shorting the stock is the wrong-direction trade here; the correct arbitrage sells the overpriced forward while buying the stock for a clear, locked-in profit.

  2. Question 2, easy

    An investor holds a long call option with a strike price of $60. At expiration, the underlying stock is trading at $45. What is the payoff to the option holder at expiration, before considering the premium originally paid?

    • A.$0
    • B.$15
    • C.-$15
    • D.$60
    Show answer and explanationHide answer

    Correct answer: A. $0

    A call option's payoff at expiration is max(0, S − K), where S is the stock price and K is the strike price. Here, S = $45 and K = $60, so S − K = −$15, and the payoff floor of zero applies: the holder simply lets the option expire worthless rather than exercising it to buy at $60 what's available in the market for $45. The payoff is $0, not a negative number, because the option holder is never obligated to exercise. B computes K − S, which is actually the put option payoff formula, not the call's. D incorrectly equates payoff with the strike price itself.

    • A. Correct. A call is only exercised if the stock price exceeds the strike; with the stock at $45 against a $60 strike, the call expires worthless, so the payoff is $0.
    • B. Incorrect. $15 would be the payoff only if the stock were trading $15 above the strike, not $15 below it.
    • C. Incorrect. Option payoffs before the premium can't be negative; the holder simply lets the option expire unexercised rather than exercising at a loss.
    • D. Incorrect. $60 is the strike price itself, not a payoff; the payoff is max(0, stock price − strike), which here equals $0.

  3. Question 3, medium

    A call option has a strike price of $40. The underlying stock currently trades at $45, and the call's market premium is $7. What is the time value (also called extrinsic value) of this option?

    • A.$2.00
    • B.$5.00
    • C.$7.00
    • D.$12.00
    Show answer and explanationHide answer

    Correct answer: A. $2.00

    An option's premium is the sum of intrinsic value and time value. Intrinsic value for a call is max(0, S − K) = max(0, $45 − $40) = $5. Time value = Premium − Intrinsic value = $7 − $5 = $2.00. Choice B reports intrinsic value alone, mistaking it for time value. Choice C reports the full premium without separating out the intrinsic component. Choice D incorrectly adds the two components instead of subtracting.

    • A. Intrinsic value = max(0, $45-$40) = $5; time value = premium - intrinsic value = $7 - $5 = $2.00.
    • B. $5.00 is the option's intrinsic value, not its time value. The two must be subtracted from the premium to isolate the extrinsic component.
    • C. $7.00 is the full market premium, which combines both intrinsic and time value rather than isolating the extrinsic portion.
    • D. $12.00 incorrectly adds the premium and intrinsic value together instead of subtracting one from the other.

  4. Question 4, easy

    An investor owns a concentrated stock position with a six-month planned sale date. She wants to set a minimum net sale value while keeping upside, and accepts an option premium. Which strategy best fits?

    • A.Buy a put option on the stock with an appropriate strike and maturity.
    • B.Write an uncovered call option on a different stock, collecting premium that offsets part of any decline in the position.
    • C.Sell a put option on the stock, collecting premium that cushions a price decline while keeping the upside.
    • D.Short an equity index with imperfect correlation to the stock, without assessing the basis risk of the hedge.
    Show answer and explanationHide answer

    Correct answer: A. Buy a put option on the stock with an appropriate strike and maturity.

    A protective put sets a floor near the strike, less premium and costs, while retaining upside. Selling a put adds downside exposure and an index short introduces basis risk.

    • A. The long put creates a minimum sale value and keeps the upside, at the cost of the premium.
    • B. An uncovered call on a different stock adds unlimited risk and does not protect the concentrated position.
    • C. A short put adds downside exposure and premium only partly cushions a decline; it sets no floor.
    • D. An imperfectly correlated index short leaves basis risk and does not set a minimum sale value while keeping upside.

  5. Question 5, medium

    An investor buys a stock at $40 and writes a call option on it with a $45 strike, receiving a $2 premium. What are the position's maximum profit per share at expiration and its breakeven stock price?

    • A.$5 and $42
    • B.$7 and $38
    • C.$7 and $42
    • D.Unlimited and $38
    Show answer and explanationHide answer

    Correct answer: B. $7 and $38

    A covered call combines long stock and a short call. The maximum profit occurs at or above the strike: (45 - 40) + 2 premium = $7. The premium offsets losses, so the breakeven is the purchase price less the premium: 40 - 2 = $38.

    • A. This leaves the premium out of the maximum profit and adds it to the breakeven.
    • B. Correct: maximum profit $7, breakeven $38.
    • C. The maximum profit is right, but the premium lowers the breakeven rather than raising it.
    • D. Writing the call caps the upside at the strike, so profit is limited.

  6. Question 6, hard

    A non-dividend-paying stock currently trades at $100. European call and put options on the stock, both with a strike price of $100 and one year to expiration, are available. The annual risk-free rate is 5% (discretely compounded), and the call option currently trades for $8.00. Using put-call parity, what should the put option be worth?

    • A.$3.24
    • B.$8.00
    • C.$12.76
    • D.$4.76
    Show answer and explanationHide answer

    Correct answer: A. $3.24

    Put-call parity for European options on a non-dividend-paying stock states: C + PV(K) = P + S, where PV(K) is the strike discounted at the risk-free rate. Here, PV(K) = $100 / 1.05 = $95.24. Solving for P: P = C + PV(K) − S = $8.00 + $95.24 − $100 = $3.24. Choice B incorrectly assumes call and put premiums must be equal, which is only coincidentally true when S = PV(K) (not the case here since the risk-free rate is positive). Choice D, $4.76, is the discount amount (S − PV(K)) itself, arrived at by dropping the call premium term from the equation. Choice C reflects a sign error in rearranging the parity equation.

    • A. Correctly applying put-call parity (P = C + PV(X) − S0 = 8 + 100/1.05 − 100) gives a put value of about $3.24, reflecting that the put must be cheaper than the call once the time value of money on the strike is properly discounted.
    • B. Setting the put equal to the call price ignores put-call parity entirely; the two would only be equal if the discounted strike exactly equaled the stock price, which isn't the case here since the risk-free rate is positive.
    • C. This value comes from adding the discounted-strike adjustment to the call price instead of subtracting it. A sign error in rearranging the parity equation that overstates the put's value.
    • D. This figure isolates the interest/carry adjustment term in the parity formula but stops short of combining it correctly with the call premium, so it understates the true put value rather than representing it.

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