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Free Questions › CFA › Derivatives
Free CFA Derivatives Practice Questions & Answers
500 exam-style Derivatives questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 91
A volatility surface is best described as:
Select an option first.
Correct answer: C — A 3D plot of volatility vs. strike and maturity.
Explanation: Why C is right: Volatility surface = 3D representation of implied volatility across strike and maturity. Why others are wrong: A, B: Only one dimension of variation. D: Not about volatility.
Question 92
A dynamic hedging strategy for an option involves:
Select an option first.
Correct answer: B — Adjusting the hedge ratio as the underlying price and time change.
Explanation: Why B is right: Dynamic hedging means rebalancing the hedge (e.g., delta hedging) as market conditions change. Why others are wrong: A: That’s static hedging. C: Too late to hedge. D: Underlying asset is usually part of the hedge.
Question 93
In a delta‑neutral portfolio, the main remaining risk is:
Select an option first.
Correct answer: B — Gamma and vega risk.
Explanation: Why B is right: Delta‑neutral removes first‑order price sensitivity, but gamma (curvature) and vega (volatility) risks remain. Why others are wrong: A: Delta hedging already addresses first‑order price risk. C: Interest rate risk may matter but is not the main Greek left. D: There is still risk.
Question 94
The theta of a long option position is usually:
Select an option first.
Correct answer: B — Negative, because time decay reduces value.
Explanation: Why B is right: Long options usually lose value as time passes, all else equal; theta is typically negative. Why others are wrong: A: Opposite sign. C: Time clearly matters. D: Both calls and puts usually have negative theta when long.
Question 95
A deep in‑the‑money American call on a non‑dividend‑paying stock is:
Select an option first.
Correct answer: B — Never optimal to exercise early.
Explanation: Why B is right: For non‑dividend‑paying stocks, it is never optimal to exercise a call early; you lose time value and give up interest on the strike. Why others are wrong: A, C: Contradict the standard result. D: Not equivalent to a put.
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Question 96
A deep in‑the‑money American put on a non‑dividend‑paying stock:
Select an option first.
Correct answer: A — Is often optimal to exercise early.
Explanation: Why A is right: Deep ITM puts may be exercised early to receive cash sooner and invest it, especially when interest rates are positive. Why others are wrong: B: False for puts. C: Deep ITM still can have time value. D: Not equivalent.
Question 97
A European call on a futures contract can be valued using the Black model with:
Select an option first.
Correct answer: A — Futures price as underlying and risk‑free discounting of strike.
Explanation: Why A is right: Black model: underlying = futures price, payoff discounted at risk‑free rate. Why others are wrong: B, C, D: Mis‑specify underlying or discounting.
Question 98
In a two‑period binomial model, the number of terminal stock price nodes is:
Select an option first.
Correct answer: B — 3
Explanation: Why B is right: Two periods with recombining tree: up‑up, up‑down (= down‑up), down‑down → 3 distinct terminal prices. Why others are wrong: A: That’s one period. C: Non‑recombining tree. D: Not applicable.
Question 99
In a recombining binomial tree with (n) steps, the number of distinct terminal nodes is:
Select an option first.
Correct answer: B — (n+1)
Explanation: Why B is right: Recombining tree: terminal nodes = (n+1). Why others are wrong: D: That’s non‑recombining. A, C: Incorrect counts.
Question 100
All else equal, how does a higher expected dividend yield on a stock index affect its fair forward price?
Select an option first.
Correct answer: B — Decreases the forward price
Explanation: B is correct: Dividends are benefits of holding the index; they reduce the net cost of carry, lowering the fair forward price. A: Opposite of correct. C: Only true if dividend yield is zero. D: Only at maturity does forward equal spot.
Question 101
A portfolio manager wants to temporarily reduce equity exposure for 3 months without selling underlying stocks. Which instrument is most suitable?
Select an option first.
Correct answer: B — Sell equity index futures
Explanation: B is correct: Selling index futures synthetically reduces equity exposure without liquidating holdings. A: Increases exposure. C/D: Options provide asymmetric payoffs, not a clean linear hedge
Question 102
You are long a 3×9 FRA (receive fixed, pay floating). At settlement, the reference 6‑month rate is higher than the FRA fixed rate. The FRA’s value to you at settlement is:
Select an option first.
Correct answer: A — Positive
Explanation: Long FRA = receive fixed, pay floating. If floating > fixed, you receive a positive cash settlement (you locked in a lower rate than market). B: Opposite. C: Only if rates equal. D: We have enough information about direction.
Question 103
In a Treasury bond futures contract with a delivery basket, the short typically delivers:
Select an option first.
Correct answer: D — The bond with the lowest delivery cost
Explanation: D is correct: The short chooses the bond that minimizes the effective cost of delivery (cheapest-to-deliver). A/B/C: These characteristics may influence cost but are not the objective by themselves.
Question 104
If a bond is relatively cheap to deliver into a futures contract, its implied repo rate is most likely:
Select an option first.
Correct answer: A — Very high
Explanation: A high implied repo rate means buying the bond and delivering into the future is attractive—hence it tends to be cheapest-to-deliver. B: Low implied repo suggests unattractive carry. C: Only in special cases. D: Incorrect; implied repo is central to CTD analysis.
Question 105
A plain-vanilla fixed-for-floating interest rate swap (receive fixed, pay floating) is economically equivalent to:
Select an option first.
Correct answer: A — Long fixed-rate bond, short floating-rate bond
Explanation: A is correct: Receiving fixed and paying floating mirrors holding a fixed-rate bond and issuing a floating-rate bond. B: Reverse of the described swap. C/D: Do not match the cash flow pattern.
Question 106
In a fixed-for-fixed currency swap, which is typically true at initiation?
Select an option first.
Correct answer: B — Notional amounts are set using the spot exchange rate
Explanation: B is correct: Notional principals are set so that their values are equal at the spot rate at inception. A/C: Ignore the need for economic equivalence. D: In many currency swaps, principals are exchanged at start and end.
Question 107
A fund wants equity exposure to an index without buying the underlying shares, while paying a floating money market rate. Which swap structure fits?
Select an option first.
Correct answer: B — Receive equity return, pay floating
Explanation: B is correct: Receiving equity total return and paying floating rate replicates synthetic equity exposure funded by borrowing. Others do not match the desired economic exposure.
Question 108
If two portfolios generate exactly the same cash flows in all future states of the world, which statement is most consistent with no-arbitrage pricing?
Select an option first.
Correct answer: A — They must have the same current value.
Explanation: A. Correct: If two portfolios have identical future cash flows in all states, they must trade at the same price today; otherwise, arbitrage exists. B. Incorrect: Risk is irrelevant here because the cash flows are identical in all states—risk is the same. C. Incorrect: Notional size is already reflected in the cash flows; equal cash flows imply equal notionals in effect. D. Incorrect: No-arbitrage requires equality today, not just at maturity.
Question 109
Which feature most clearly distinguishes a futures contract from a forward contract?
Select an option first.
Correct answer: B — Futures are traded on exchanges with daily settlement; forwards are private agreements.
Explanation: B. Correct: Futures are exchange-traded, standardized, and marked to market daily; forwards are OTC and privately negotiated. A. Incorrect: It is the opposite—futures are standardized, forwards are customized. C. Incorrect: Both can be either physical or cash settled depending on contract terms. D. Incorrect: Forwards typically have more counterparty credit risk; futures reduce it via clearinghouse and margin.
Question 110
The basis in a futures market is defined as:
Select an option first.
Correct answer: B — Spot price minus futures price.
Explanation: B. Correct: Basis = spot price − futures price. A. Incorrect: Futures vs forward is not the standard definition of basis. C. Incorrect: That’s just a difference but not the standard basis definition. D. Incorrect: Futures minus strike is not a standard concept.
Question 111
If an asset has no income and no storage costs, and the forward price is below the no-arbitrage level, an arbitrageur can:
Select an option first.
Correct answer: A — Short the asset and go long the forward.
Explanation: A. Correct: If forward is too cheap, short the asset (receive cash), invest proceeds, and go long the forward to cover later. Profit from mispricing. B. Incorrect: That trade benefits when forward is too high, not too low. C. Incorrect: Shorting both does not lock in a risk-free gain. D. Incorrect: Buying both is not an arbitrage structure here.
Question 112
A single-period forward rate agreement (FRA) is most similar to:
Select an option first.
Correct answer: B — One payment period of an interest rate swap.
Explanation: B. Correct: An FRA is essentially one future fixed-vs-floating interest payment, like one period of a plain-vanilla interest rate swap. A. Incorrect: Currency swaps involve two currencies, not just rates in one currency. C. Incorrect: Fixed-for-fixed swaps exchange fixed rates in two currencies. D. Incorrect: A credit default swap is about credit risk, not interest rate levels.
Question 113
A plain-vanilla fixed-for-floating interest rate swap can be viewed as:
Select an option first.
Correct answer: A — Long a fixed-rate bond and short a floating-rate bond.
Explanation: A. Correct: Receive-fixed, pay-floating swap = long fixed bond, short floating bond. B. Incorrect: That would correspond to pay-fixed, receive-floating. C, D. Incorrect: Do not reflect the fixed-vs-floating nature of the swap.
Question 114
For a receive-fixed, pay-floating interest rate swap, the swap’s value to the fixed-rate receiver becomes positive when:
Select an option first.
Correct answer: B — Market fixed rates fall below the original fixed rate.
Explanation: B. Correct: If market fixed rates fall, the original fixed rate received is now high relative to market, so the swap is valuable. A. Incorrect: If fixed rates rise, the receiver is stuck with a low fixed rate. C, D. Floating leg resets; the key driver of value is the fixed leg vs current fixed rates.
Question 115
In a fixed-for-fixed currency swap:
Select an option first.
Correct answer: B — Notional amounts are exchanged at initiation and re-exchanged at maturity.
Explanation: B. Correct: Typical fixed-for-fixed currency swap: notionals exchanged at start and reversed at maturity. A. Incorrect: Only at maturity is not standard; usually both start and end. C. Incorrect: That’s more like many interest rate swaps in one currency. D. Incorrect: Coupons are exchanged periodically, not notionals.
Question 116
In a total return equity swap where Party A receives the total return on an equity index and pays a fixed rate, Party A’s position is economically similar to:
Select an option first.
Correct answer: B — Being long the index and short a bond.
Explanation: B. Correct: Receive index total return (like long index), pay fixed (like short fixed-rate bond). A. Incorrect: That would be receive fixed, pay equity. C, D. Ignore one side of the swap.
Question 117
A payer swaption gives its holder the right to:
Select an option first.
Correct answer: B — Pay fixed and receive floating in a swap.
Explanation: B. Correct: A payer swaption is an option to enter a swap as the fixed-rate payer (and floating receiver). A. That’s a receiver swaption. C. That’s more like a currency option, not a standard swaption. D. That’s a swap cancellation option, a different product. Questions 31–60
Question 118
A stock index has a level of 2,000. The risk-free rate is ( 5% ) (continuous compounding), and the dividend yield on the index is ( 2% ) (continuous). The fair 6‑month futures price is closest to:
Select an option first.
Correct answer: A — 2,030
Explanation: Fair futures price with continuous compounding and yield: [ F_0 = S_0 e^{(r - q)T} = 2000 e^{(0.05 - 0.02)\times 0.5} = 2000 e^{0.015} \approx 2000 \times 1.0151 \approx 2030 ] A is correct: Matches the calculation. B, C: Overstate the effect of carry; imply higher net rate. D: Ignores both interest and dividends.
Question 119
Which statement best describes the value of a forward contract after initiation?
Select an option first.
Correct answer: B — It changes as the underlying price and interest rates change.
Explanation: Forward value depends on current spot, time to maturity, and interest rates. After initiation, its value can become positive or negative. B is correct: Both underlying and rates matter. A: True only at initiation under fair pricing. C: Ignores underlying price changes. D: Ignores interest rate changes.
Question 120
Which statement best describes a plain-vanilla interest rate swap where one party pays fixed and receives floating?
Select an option first.
Correct answer: B — It is equivalent to being short a fixed-rate bond and long a floating-rate bond.
Explanation: Pay-fixed, receive-floating: you are effectively short fixed (you pay fixed coupons) and long floating (you receive floating coupons). B is correct: Matches the cash-flow pattern. A: Describes receive-fixed, pay-floating. C: Not the standard representation (though forwards can be decomposed into options). D: Swaps are highly sensitive to interest rates.
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