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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 451
Portfolio insurance using options involves:
Select an option first.
Correct answer: B — Buying put options on the portfolio (or index) to limit the downside
Explanation: ✔ Why correct: Portfolio insurance uses long puts (or equivalent dynamic strategies) to guarantee a minimum portfolio value. The put provides a floor on losses while maintaining upside participation. ✘ Why others are wrong: A earns income but adds downside risk. C is speculative. D is a rebalancing strategy, not portfolio insurance.
Question 452
The net premium for a collar strategy (long stock + long put + short call) is typically:
Select an option first.
Correct answer: B — Low or near zero because the short call premium offsets the put cost
Explanation: ✔ Why correct: A zero-cost collar is structured so the call premium received approximately equals the put premium paid, making the hedge nearly free. The tradeoff is capped upside. ✘ Why others are wrong: A is possible but is avoided by adjusting strikes. C can occur with specific strikes but is not typical. D is the spread, not the premium.
Question 453
The strategy of selling volatility typically involves:
Select an option first.
Correct answer: B — Selling straddles, strangles, or other short-gamma strategies
Explanation: ✔ Why correct: Selling volatility means collecting option premium (short gamma, short vega). Strategies like short straddles/strangles earn income when actual volatility is lower than implied volatility. ✘ Why others are wrong: A is buying volatility. C is irrational. D is buying volatility via variance swaps. Derivative Applications
Question 454
A commodity producer (wheat farmer) who wants to lock in a selling price for the upcoming harvest would:
Select an option first.
Correct answer: B — Sell wheat futures
Explanation: ✔ Why correct: The farmer has natural long exposure (will produce wheat). Selling futures locks in the price, eliminating downside risk but also capping upside. ✘ Why others are wrong: A increases exposure. C gives the right to buy (useless for a seller). D creates additional obligation.
Question 455
A market maker in options manages risk primarily by:
Select an option first.
Correct answer: B — Delta hedging the position to reduce directional risk and managing vega and theta exposures
Explanation: ✔ Why correct: Market makers aim for delta-neutral books, collecting the bid-ask spread. They also manage gamma (rebalancing costs), vega (volatility risk), and theta (daily time decay income). ✘ Why others are wrong: A would eliminate the market-making business. C is too restrictive. D is part of the business but not the risk management approach.
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Question 456
The 'vega risk' of an options portfolio refers to:
Select an option first.
Correct answer: B — The risk that implied volatility changes, affecting option values
Explanation: ✔ Why correct: Vega risk is the exposure to changes in implied volatility. Long option positions lose value if IV falls; short positions gain. Managing vega requires offsetting long and short vega positions. ✘ Why others are wrong: A is gamma risk. C is theta risk. D is rho risk.
Question 457
A barrier option is an option that:
Select an option first.
Correct answer: B — Comes into existence or ceases to exist when the underlying hits a specified barrier price
Explanation: ✔ Why correct: Barrier options are path-dependent. A knock-in activates when the barrier is hit; a knock-out deactivates. They are cheaper than standard options because the buyer takes on barrier risk. ✘ Why others are wrong: A is an option on a static asset. C is an automatic exercise feature. D describes an Asian option.
Question 458
A digital (binary) option pays:
Select an option first.
Correct answer: B — A fixed dollar amount if the option expires in the money, and zero otherwise
Explanation: ✔ Why correct: A digital (cash-or-nothing) option pays a predetermined fixed amount if the underlying exceeds (call) or falls below (put) the strike at expiration. ✘ Why others are wrong: A is a vanilla option. C is a form of Asian option payoff. D is an asset-or-nothing option.
Question 459
A chooser option gives the holder the right to:
Select an option first.
Correct answer: B — Choose at a specified date whether the option will be a call or a put
Explanation: ✔ Why correct: A chooser option allows the holder to decide, on a predetermined date, whether the option becomes a call or a put. It is valuable when direction is uncertain. ✘ Why others are wrong: A describes a flexible strike option. C is automatic selection, not a chooser. D is an extension option.
Question 460
A 'knock-out' call option (down-and-out) expires worthless if:
Select an option first.
Correct answer: B — The underlying price falls below the barrier level during the option's life
Explanation: ✔ Why correct: A down-and-out knock-out call terminates if the underlying touches or crosses below a pre-set barrier. The holder loses protection precisely when the underlying falls. ✘ Why others are wrong: A is the opposite — that would make a standard call valuable. C is not the trigger. D is European exercise mechanics. Market Structure
Question 461
A 'margin period of risk' (MPOR) in derivatives risk management refers to:
Select an option first.
Correct answer: B — The time assumed for closing out a defaulted counterparty's position, during which additional losses can accumulate
Explanation: ✔ Why correct: MPOR is the assumed time to close out a defaulted portfolio. A longer MPOR = larger initial margin requirement, as the clearinghouse or counterparty is exposed to more market movement during close-out. ✘ Why others are wrong: A is the settlement lag. C is not a standard term. D is ATM window.
Question 462
Compression in derivatives trading refers to:
Select an option first.
Correct answer: B — Eliminating offsetting derivative contracts to reduce the total notional outstanding and simplify portfolios
Explanation: ✔ Why correct: Trade compression cancels offsetting positions, reducing gross notional and operational complexity without changing net market risk. It is widely used in interest rate swap portfolios. ✘ Why others are wrong: A is a volatility phenomenon. C is market making. D is settlement conversion.
Question 463
In a local volatility model (Dupire), volatility is a function of:
Select an option first.
Correct answer: B — Both the current stock price and time
Explanation: ✔ Why correct: The Dupire local volatility model fits the entire volatility surface by making σ a deterministic function of S and t: σ(S, t). This ensures the model matches all observed market option prices. ✘ Why others are wrong: A would be a time-varying but not stock-dependent model. C is historical volatility, not a model specification. D is only one point on the surface.
Question 464
The volatility term structure refers to:
Select an option first.
Correct answer: B — The relationship between implied volatility and option expiration
Explanation: ✔ Why correct: The volatility term structure shows how implied volatility varies across different maturities (short-term vs. long-term options). It is upward or downward sloping depending on market conditions. ✘ Why others are wrong: A is the volatility smile/skew. C is a time-series concept. D is a spread concept.
Question 465
Vanna is a second-order Greek that measures:
Select an option first.
Correct answer: A — The change in delta relative to a change in implied volatility
Explanation: ✔ Why correct: Vanna = ∂²V/(∂S∂σ) = rate of change of delta with respect to volatility (or equivalently, the change in vega with respect to the underlying price). It matters for risk management of portfolios with both directional and volatility exposure. ✘ Why others are wrong: B is vomma/volga. C is not a standard Greek name. D is rho.
Question 466
The 'vol of vol' or volatility of volatility measures:
Select an option first.
Correct answer: B — The uncertainty or variability of implied volatility itself
Explanation: ✔ Why correct: Vol of vol is the volatility of the implied volatility process. High vol-of-vol makes options on volatility (e.g., VIX options) more valuable and complicates vega hedging. ✘ Why others are wrong: A is the realized volatility. C is vol-rate correlation. D is gamma.
Question 467
In derivatives markets, 'smile interpolation' is used to:
Select an option first.
Correct answer: A — Smooth and fill in implied volatility values for strikes and maturities where options are not actively traded
Explanation: ✔ Why correct: Traders and risk managers need implied volatility estimates for every possible strike and maturity. Smile interpolation (e.g., SABR, SVI) constructs a smooth surface from observed market quotes. ✘ Why others are wrong: B is a numerical methods problem. C is a model conversion. D is calibrating r.
Question 468
The primary reason the Black-Scholes-Merton model remains widely used in practice despite its limitations is:
Select an option first.
Correct answer: B — It provides a simple, consistent framework and common language (implied volatility) for option markets
Explanation: ✔ Why correct: BSM's greatest contribution is the concept of implied volatility as a common language. Even when traders know BSM assumptions are violated, they quote prices in IV terms, and BSM provides a tractable starting point for more complex models. ✘ Why others are wrong: A is wrong; BSM has known limitations. C is wrong; other models are acceptable. D is the opposite — BSM assumes constant volatility.
Question 469
A 5‑year CDS has an annual premium of 180 bps on a notional of 40M. What is the annual premium payment?
Select an option first.
Correct answer: C — 680,000
Explanation: Premium = 0.018 × 40M = 720,000. C is correct; others use wrong bps or notional.
Question 470
A CDS protection buyer pays 500,000 per year. PV of premium leg = 1.8M, PV of protection leg = 2.1M. What is the CDS value to the buyer?
Select an option first.
Correct answer: C — +0.3M
Explanation: Value = 2.1 − 1.8 = +0.3M. A is wrong sign; others ignore difference.
Question 471
A bond has LGD = 60% and PD (5‑year cumulative) = 8%. Expected loss as % of notional?
Select an option first.
Correct answer: B — 3.60%
Explanation: EL = PD × LGD = 0.08 × 0.60 = 4.8%. C is correct; others mis‑multiply.
Question 472
A 3‑name basket default swap pays out on first default. Each name has PD = 4% (5‑year), independent. Approximate probability of at least one default?
Select an option first.
Correct answer: C — 11.50%
Explanation: P(no default) ≈ (1−0.04)^3 ≈ 0.885; so P(≥1) ≈ 11.5%. Others use simple sums.
Question 473
A CDO equity tranche covers 0–5% of a 200M pool. If portfolio loss is 7%, what is the dollar loss to the equity tranche?
Select an option first.
Correct answer: A — 5M
Explanation: Equity absorbs first 5%: 0.05×200M=10M. Correct is 10M; A is wrong if using 5M; others misapply attachment.
Question 474
A mezzanine tranche covers 5–10% of a 300M pool. Portfolio loss = 8%. Dollar loss to mezz tranche?
Select an option first.
Correct answer: A — 6M
Explanation: Loss hitting tranche = (8%−5%)×300M=9M. D is correct; others mis‑compute.
Question 475
A senior tranche covers 10–15% of a 400M pool. Portfolio loss = 12%. Dollar loss to senior tranche?
Select an option first.
Correct answer: A — 4M
Explanation: Loss in tranche = (12%−10%)×400M=8M. C is correct; others mis‑apply attachment.
Question 476
A 5‑year CDS has an upfront of 2% and running spread of 100 bps on 50M notional. What is the upfront payment?
Select an option first.
Correct answer: B — 1.0M
Explanation: Upfront = 0.02×50M=1.0M. Others use wrong percentage.
Question 477
A credit‑linked note (CLN) pays 6% coupon vs 3% risk‑free. Notional = 20M. Annual credit spread embedded?
Select an option first.
Correct answer: C — 3%
Explanation: Spread = 6% − 3% = 3%; in dollars = 0.03×20M=0.6M.
Question 478
A synthetic CDO tranche has PV of premium leg = 5.5M and PV of protection leg = 5.0M. Value to protection seller?
Select an option first.
Correct answer: A — −0.5M
Explanation: Seller receives premium, pays protection. Value to seller = 5.5 − 5.0 = +0.5M; to buyer = −0.5M. A is buyer’s value; others mix perspectives.
Question 479
A stock index is at 2,500, dividend yield = 2%, r = 5% (cont.), T = 1. Fair futures price?
Select an option first.
Correct answer: C — 2,600
Explanation: F = 2500·e^{(0.05−0.02)} ≈ 2500·1.0305 ≈ 2576 → 2,600.
Question 480
Spot FX = 1.20 USD/GBP, r_USD = 3%, r_GBP = 1% (annual). 2‑year forward?
Select an option first.
Correct answer: C — 1.272
Explanation: F = 1.20·(1.03²/1.01²) ≈ 1.272. Others mis‑apply parity.
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