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33 multiple-choice questions and 53 flashcards on Derivatives, about 8% of the CFA Level II bank. Every one carries a written rationale.
Derivatives is one of 10 chapters in CoStudy's CFA Level II bank, and it holds 33 of the bank's 401 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Using a one-period binomial model with u = 1.20, d = 0.85, risk-free rate r = 3% (per period), the risk-neutral probability of an up move is closest to:
Answer: A — 0.51 per calc approx
A) Correct — the computed value is 0.51. B) 0.56 per calc approx — off-by-percent numeric trap. C) 0.46 per calc approx — off-by-percent numeric trap. D) 0.61 per calc approx — off-by-percent numeric trap.
Under put-call parity for European options on a non-dividend stock: C + PV(K) = P + S. If C = $7, K = $50, r = 4%, T = 1 year, S = $48, then P =
Answer: D — C + PV(K) − S = 7 + 48.04 − 48 =
A) Black-Scholes closed-form price — wrong option pricing method. B) FRA fixed-rate future rate lock — related concept, not the definition. C) Currency forward IRP-consistent — related concept, not the definition. D) Correct — this identifies C + PV(K) − S = 7 + 48.04 − 48 = $7.04.
A stock index trades at 4,000. The continuously compounded risk-free rate is 6%, the continuously compounded dividend yield is 2%, and a one-year forward contract is being priced. The no-arbitrage forward price is closest to:
Answer: A — $4,163.24, using F0 = S0 × e^((r−δ)T) with continuous compounding over the full one-year horizon
A) Correct — F0 = 4,000 × e^((0.06 − 0.02) × 1) = 4,000 × e^0.04 ≈ 4,000 × 1.0408 ≈ $4,163.24. B) Ignores the dividend yield, which lowers the forward price by reducing the net cost of carry; this overstates the forward price. C) Reverses the sign of the net carry term (uses δ − r instead of r − δ), producing a forward price below spot when the risk-free rate exceeds the dividend yield — the wrong direction. D) Uses linear rather than continuous compounding for the carry adjustment, a close but technically incorrect approximation given the stated continuously compounded rates.
A trader delta-hedges a long call option position by shorting shares equal to the position's delta. As the underlying price rises, the call's positive gamma causes delta to increase further. To remain delta-neutral, the trader must NEXT:
Answer: D — Short additional shares, since a higher delta requires a larger offsetting short position
A) Positive gamma on a long call means delta rises as the stock rises, not falls — this would move the hedge in the wrong direction. B) Gamma describes the rate of change of delta itself, so it directly affects how the delta hedge must be adjusted. C) Trading more options changes the position's gamma and vega profile and is not the simplest way to restore delta-neutrality from an existing equity hedge. D) Correct — as delta rises with the stock price, the trader must short additional shares to keep the combined position delta-neutral.
A commodity futures market is in CONTANGO. An investor rolling long futures positions monthly will experience:
Answer: A — Negative roll yield in this context
A) Correct — this identifies Negative roll yield in this context. B) Direct capitalization NOI over rate — related concept, not the definition. C) Direct lending floating-rate credit — related concept, not the definition. D) Brownfield concession-based revenue — related concept, not the definition.
An equity-index futures contract on a non-dividend-paying portfolio has theoretical price:
Answer: D — S × e^(rT) in this context
A) Gamma sensitivity of delta — related concept, not the definition. B) Vega volatility sensitivity — related concept, not the definition. C) Futures cost-of-carry model — related concept, not the definition. D) Correct — this identifies S × e^(rT) in this context.
In a one-period binomial option model: S = 100, u = 1.2, d = 0.85, r = 3%. The risk-neutral probability of an up move is:
Answer: A — (1.03 − 0.85) / (1.20 − 0.85) =
A) Correct — this identifies (1.03 − 0.85) / (1.20 − 0.85) = 0.514. B) Black-Scholes closed-form price — wrong option pricing method. C) FRA fixed-rate future rate lock — related concept, not the definition. D) Currency forward IRP-consistent — related concept, not the definition.
A binomial option pricing model uses which assumption?
Answer: B — Underlying can move to one of two
A) Black-Scholes closed-form price — wrong option pricing method. B) Correct — this identifies Underlying can move to one of two prices each period. C) FRA fixed-rate future rate lock — related concept, not the definition. D) Currency forward IRP-consistent — related concept, not the definition.
A portfolio manager holds a receive-fixed, pay-floating interest rate swap. The manager now expects short-term interest rates to rise substantially before the swap matures. To reduce the swap's negative sensitivity to rising rates, the MOST direct action is to:
Answer: B — Enter an offsetting swap to pay fixed and receive floating, neutralizing the rate exposure
A) Doubling the same receive-fixed position increases, rather than reduces, exposure to rising rates. B) Correct — a receive-fixed swap loses value as rates rise (economically equivalent to being long a fixed-rate bond and short a floater); entering an offsetting pay-fixed swap neutralizes that exposure. C) A receiver swaption pays off when rates fall, so it hedges the opposite risk and does not protect against a rate increase. D) Swap value is highly sensitive to the level of interest rates — this ignores the basic driver of swap valuation.
A trader observes that an option's implied volatility is significantly higher than realized volatility over recent periods. The MOST appropriate trade for a vol-neutral expectation of mean reversion is to:
Answer: C — Sell volatility in this context
A) Black-Scholes closed-form price — wrong option pricing method. B) FRA fixed-rate future rate lock — related concept, not the definition. C) Correct — this identifies Sell volatility in this context. D) Currency forward IRP-consistent — related concept, not the definition.
4 cards from the 53 in this chapter.
What is the difference between modified and effective duration?
Modified: assumes cash flows don't change with rates. Effective: accounts for option-adjusted cash flow changes (callable, putable, MBS). Use effective for bonds with options.
What is binomial option pricing?
Build a tree of possible asset prices over discrete steps; calculate option value backwards using risk-neutral probabilities. Converges to Black-Scholes.
What is the futures contract pricing formula (no-arbitrage)?
F = S × (1+r)^T − dividend/coupon income (FV at T). For currencies: F = S × (1+r_d)/(1+r_f) (covered interest parity).
What is a putable bond's value formula?
V(putable) = V(option-free) + V(put). Investor benefits → higher price than equivalent non-putable.
These are a sample. The full Derivatives chapter runs 86 items with per-chapter progress tracking, on the web and in the iOS app.
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