CFA Level I Derivatives Practice Questions
Question 1
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 explanation
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.
Question 2
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 explanation
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.
Question 3
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 explanation
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.
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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 explanation
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.