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Free FRM Financial Markets and Products Practice Questions & Answers
400 exam-style Financial Markets and Products questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 241
A 'fixed-for-floating' commodity swap where a producer receives a fixed price and pays floating:
Select an option first.
Correct answer: B — Locks in a certain revenue regardless of market prices — the producer receives fixed and pays the market price, effectively selling forward at the fixed swap price
Explanation: B is correct: the commodity producer has natural exposure to falling prices (they sell at market). By entering a fixed-for-floating swap as the fixed receiver, they lock in a known revenue regardless of where the spot price settles. If spot falls below the fixed rate, they receive a net payment from the swap that compensates. B is correct. A is wrong — this swap hedges rising price exposure is not accurate; it locks in prices. C is wrong — it reduces, not adds, leverage. D is wrong — commodity swaps are typically cash-settled.
Question 242
In equity index futures, the 'cost of carry' model gives the futures price as F = S × e^{(r−q)T} where q is the dividend yield. When dividends are higher than the risk-free rate:
Select an option first.
Correct answer: B — The futures price is below the spot price (backwardation-like) — high dividend yield makes spot more valuable than futures
Explanation: B is correct: when q > r, the cost of carry (r − q) is negative, so F = S × e^{(r−q)T} < S. The futures trades at a discount to spot because spot holders receive dividend income while futures holders do not. This is analogous to backwardation in commodity markets. A is wrong — contango requires r > q. C is wrong — prices differ when q ≠ r. D is wrong — arbitrage is still possible.
Question 243
A 'funding value adjustment' (FVA) in derivatives pricing accounts for:
Select an option first.
Correct answer: B — The cost of funding the uncollateralised portion of derivative positions — reflecting that dealers must post initial margin or fund positive MTM positions at their own funding rate (above OIS)
Explanation: B is correct: FVA was introduced post-crisis to account for the fact that banks must fund derivative positions at their own cost of funding (which may exceed OIS when uncollateralised). FVA = funding benefit (when the bank has a net receive position requiring the counterparty to fund) − funding cost (when the bank must fund net pay positions). FVA is controversial in academic finance but widely used in practice. A is wrong — that is CVA. C is wrong — FVA is about funding. D is wrong — receiving VM is a funding benefit within FVA.
Question 244
Margin requirements for derivatives consist of initial margin (IM) and variation margin (VM). Segregation of initial margin means:
Select an option first.
Correct answer: B — The initial margin is held in a segregated account at a third-party custodian, protected from the CCP's or dealer's insolvency
Explanation: B is correct: segregation means the IM is held separately from the collecting party's own assets, protected in bankruptcy. This protects the posting party if the collecting party (CCP or bilateral counterparty) defaults. Under BCBS-IOSCO non-cleared margin rules, IM must be segregated in third-party custody. A is wrong — commingling would be non-segregated. C is wrong — both cash and securities (subject to haircuts) are acceptable. D is wrong — IM is calculated by the clearing member or counterparty.
Question 245
The sensitivity of a futures portfolio to a 1 basis point change in the yield curve (DV01 or BPV) is used to:
Select an option first.
Correct answer: B — Quantify interest rate risk and construct hedges — matching the DV01 of the futures hedge to the DV01 of the position to be hedged
Explanation: B is correct: DV01 (dollar value of a basis point) measures how much a portfolio's value changes for a 1 bps parallel shift in yields. To hedge a bond position with futures: number of futures contracts = (DV01 of position) / (DV01 of futures contract). B correctly describes this hedging application. A is wrong — DV01 is for fixed income. C is wrong — option delta is a different calculation. D is wrong — initial margin is based on volatility estimates.
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Question 246
In an equity-linked note (ELN), the investor typically receives:
Select an option first.
Correct answer: B — Principal protection plus participation in the upside of an equity index — effectively a zero-coupon bond plus a long call option on the equity index
Explanation: B is correct: an ELN is a principal-protected structured product: the issuer invests a portion of the proceeds in a zero-coupon bond (to return principal at maturity) and uses the remainder to purchase a call option on an equity index (to provide upside participation). B correctly describes the structure. A is wrong — ELNs don't typically pay dividends. C is wrong — principal protection is the defining feature. D is wrong — the coupon depends on equity performance.
Question 247
When a futures trader 'closes out' a long position, they:
Select an option first.
Correct answer: B — Enter an equal and opposite (short) futures position in the same contract, resulting in a net zero position
Explanation: B is correct: closing out a futures position involves taking the opposite position — if long, you sell the same number of contracts in the same contract month. The exchange then nets out the offsetting positions, leaving zero net exposure. Only about 2-3% of futures contracts result in physical delivery. A is wrong — delivery is one alternative, not closing out. C is wrong — futures positions are not bilaterally transferred. D is wrong — expiring without action may result in automatic delivery.
Question 248
The 'gamma of gamma' (speed) measures:
Select an option first.
Correct answer: B — The rate of change of gamma with respect to the underlying asset price — relevant for dynamic hedging as it indicates how quickly the delta hedge needs to be rebalanced when price moves
Explanation: B is correct: speed (sometimes called the 'third derivative' or 'DgammaDspot') = ∂Γ/∂S. It indicates how much gamma changes when the underlying moves, which tells a delta-hedger how quickly their gamma changes and how often they must rebalance. B is correct. A is wrong — that is gamma itself. C is wrong — that is theta. D is wrong — third derivative of value with respect to time is a different concept (charm involves time and delta).
Question 249
Delivery options embedded in futures contracts (quality option, timing option, wild card option) provide value to:
Select an option first.
Correct answer: B — The short futures position — optionality in what, when, and how to deliver creates additional value embedded in the futures short
Explanation: B is correct: the short futures position holds various delivery options: (1) quality option — which eligible bond to deliver; (2) timing option — which day within the delivery month to deliver; (3) wild card option — the delivery notification after 2pm when prices are fixed but cash markets can still trade. These options give the short an advantage, which is why futures prices are generally below the full carry price. A is wrong — longs are disadvantaged by these options. C is wrong — CCP benefits from clearing fees, not delivery options. D is wrong — the options exclusively benefit the short.
Question 250
The 'vanna' of an option measures:
Select an option first.
Correct answer: B — The rate of change of delta with respect to volatility (or equivalently, the rate of change of vega with respect to the underlying price) — relevant for volatility trading strategies
Explanation: B is correct: vanna = ∂Δ/∂σ = ∂ν/∂S. It measures how delta changes as volatility changes (or how vega changes with the underlying price). Vanna is important for managing options books where both delta and vega are being hedged simultaneously, particularly when constructing volatility surface exposures. A is wrong — that is gamma. C is wrong — that involves charm. D is wrong — convexity applies to bonds.
Question 251
A 'basis swap' is a floating-for-floating swap where:
Select an option first.
Correct answer: B — Both parties exchange floating rate payments but referenced to different benchmarks (e.g. 3-month SOFR vs 6-month SOFR, or SOFR vs Fed funds rate) — used to hedge or arbitrage basis differentials
Explanation: B is correct: a basis swap exchanges one floating rate for another (both variable). Common examples include: 3-month SOFR vs 6-month SOFR; SOFR vs prime rate; EUR vs USD SOFR in a cross-currency basis swap. These are used to hedge basis risk when assets and liabilities are linked to different floating rates. A is wrong — both sides are floating. C is wrong — amortising swap has changing notional. D is wrong — that is a cross-currency swap feature.
Question 252
In the pricing of futures on non-dividend-paying stock indices, the futures price exceeds the spot price because:
Select an option first.
Correct answer: B — Futures buyers forgo the dividends that spot holders receive — but without dividends (q=0), the futures price = S×e^{rT} > S since r>0
Explanation: B is correct: for non-dividend-paying stocks or indices, F = S × e^{rT}. Since r > 0 and T > 0, F > S. The spot price is lower because the holder of spot must finance the holding cost (r) — the futures price incorporates this financing cost. Alternatively, the futures buyer avoids paying for the asset today and earns interest on the cash instead — the futures price is adjusted upward to compensate. A is wrong — cost of carry, not expected return, explains the futures premium. C and D are wrong.
Question 253
A 'digital' (binary) option on an asset pays:
Select an option first.
Correct answer: B — A fixed, predetermined amount if the underlying exceeds the strike at expiry (for a cash-or-nothing digital call) or nothing otherwise
Explanation: B is correct: a cash-or-nothing digital call pays $1 (or a fixed amount) if S > K at expiry, and $0 otherwise. An asset-or-nothing call pays the asset price S if S > K, or nothing. Digital options have a discontinuous payoff profile (unlike vanilla options) and are used in structured products and exotic hedging. A is wrong — vanilla options have proportional payoffs. C is wrong — that is a vanilla call payoff. D is wrong — premiums are always lost.
Question 254
The 'greeks' in options are called greeks because:
Select an option first.
Correct answer: B — They are denoted by Greek letters (delta, gamma, theta, vega, rho) — though vega is not an actual Greek letter but is named in the same style
Explanation: B is correct: the sensitivities of option prices are conventionally named using Greek letters: Δ (delta), Γ (gamma), θ (theta), ρ (rho). Vega (ν-like) is not actually a Greek letter but is named in the style. Volga, vanna, and charm are additional 'Greek-style' sensitivity measures. A is wrong — Black, Scholes, and Merton (American/Canadian) developed the model. C is wrong — unrelated to the Greek debt crisis. D is wrong — not a linguistic convention.
Question 255
Dynamic delta hedging of an option position requires:
Select an option first.
Correct answer: B — Continuously (or frequently) rebalancing the delta hedge as the underlying price, time, and other factors change — because delta itself changes (non-zero gamma)
Explanation: B is correct: because gamma (the rate of change of delta) is non-zero, the delta of an option changes continuously with the underlying price. A delta-neutral portfolio today becomes non-neutral as the price moves. Continuous (or frequent) rebalancing is theoretically required, but in practice hedges are rebalanced at discrete intervals (daily or more frequently). A is wrong — static hedges are insufficient. C is wrong — delta changes continuously, not just at moneyness boundaries. D is wrong — the underlying is bought/sold in both directions to maintain neutrality.
Question 256
An interest rate swap's 'reset date' is the date on which:
Select an option first.
Correct answer: B — The floating reference rate (e.g. 3-month SOFR) is observed/fixed for the upcoming payment period
Explanation: B is correct: on each reset date, the floating reference rate is observed (fixed) and determines the floating payment for the next accrual period. Typically, the rate is set at the beginning of each period and the payment is made at the end (in arrears). For SOFR-linked instruments, the rate may be compounded or averaged over the period. A is wrong — early termination is a different event. C is wrong — notional is not exchanged in IR swaps. D is wrong — the fixed rate is set at inception.
Question 257
A 'payer' swaption gives the holder the right to enter a swap as:
Select an option first.
Correct answer: B — The fixed-rate payer — if rates rise above the swaption strike, exercising the payer swaption allows the holder to pay below-market fixed rates
Explanation: B is correct: a payer swaption = option to enter a pay-fixed/receive-floating swap. It is valuable when market swap rates rise above the strike rate, allowing the holder to pay the (now below-market) strike rate. A is wrong — a receiver swaption gives the right to receive fixed. C is wrong — swaptions are either payer or receiver, not both. D is wrong — paying floating is the natural floating leg; the payer swaption gives the right to pay fixed.
Question 258
Eurodollar futures contracts are used to hedge or speculate on:
Select an option first.
Correct answer: B — Short-term US dollar interest rates (specifically 3-month LIBOR, now transitioning to SOFR) — widely used for interest rate risk management over multiple quarters
Explanation: B is correct: Eurodollar futures (CME) are based on 3-month USD LIBOR and are used to hedge or take positions on short-term US interest rates. They are one of the most actively traded futures contracts globally and a key tool for interest rate risk management over a 1-10 year horizon (through stacks of contracts). A is wrong — Eurodollar is an interest rate product. C is wrong — T-bond futures cover long rates. D is wrong — Eurodollar is fixed income.
Question 259
The 'cheapest to deliver' (CTD) bond in a bond futures contract will change when:
Select an option first.
Correct answer: B — Interest rates change significantly — as rates change, the relative attractiveness of different deliverable bonds changes, switching the CTD
Explanation: B is correct: the CTD is determined by the market prices of deliverable bonds relative to their conversion factors. As yields change, different bonds' durations and coupons make them more or less attractive for delivery. In a low-rate environment, high-coupon bonds tend to be CTD; in high-rate environments, low-coupon bonds tend to be CTD. B correctly identifies the driver. A is wrong — the CTD can change throughout the life of the contract. C is wrong — clearing house rules rarely change. D is wrong — prepayment is not a CTD determinant.
Question 260
The 'immunisation' condition for a bond portfolio against parallel yield curve shifts using duration is:
Select an option first.
Correct answer: B — Asset duration equals liability duration AND the asset value equals the liability value (or the dollar durations match) — ensuring both price and reinvestment effects offset
Explanation: B is correct: immunisation requires: (1) PV(assets) = PV(liabilities); (2) duration of assets = duration of liabilities; and (3) convexity of assets ≥ convexity of liabilities (for protection against non-parallel shifts). B captures the key conditions. A is wrong — duration matching alone requires the PV condition too. C is wrong — maturity and duration differ for coupon-bearing bonds. D is wrong — zero-coupon bonds are one way to immunise but not the only way.
Question 261
The minimum variance hedge ratio minimises the variance of the hedged portfolio. If the hedge ratio is 0.8, it means:
Select an option first.
Correct answer: B — For every unit of spot exposure, 0.8 units of futures contracts should be shorted — this ratio is optimal when the spot and futures returns are not perfectly correlated
Explanation: B is correct: the minimum variance hedge ratio h* = 0.8 means that 0.8 futures contracts are sold per unit of spot exposure. This accounts for the imperfect correlation between spot and futures returns. If correlation = 1 and volatilities are equal, h* = 1 (perfect hedge). A is wrong — 80% of position is not the correct interpretation. C is wrong — the hedge reduces variance by ρ² of the total, not necessarily 80%. D is wrong — 0.8 is the contract ratio, not a value ratio.
Question 262
The 'futures basis' for a short hedger (who owns the asset and shorts futures) at the time of closing the hedge is defined as:
Select an option first.
Correct answer: B — Closing spot price minus closing futures price — a strengthening basis (basis increases) benefits the short hedger
Explanation: B is correct: basis at close = spot price − futures price. For the short hedger (who is long spot, short futures): profit from hedge = initial futures price − final futures price + final spot price − initial spot price = (initial futures − initial spot) − (final futures − final spot) = −b₀ + b_T. A strengthening basis (basis increases, becomes less negative or more positive) benefits the short hedger. B correctly defines the basis at close. A is wrong — that is the spot price change. C is wrong — futures price change is basis for the futures P&L. D is wrong — same as C.
Question 263
An FRA (3×6) means:
Select an option first.
Correct answer: B — The FRA covers a 3-month borrowing period starting 3 months from now and ending 6 months from now
Explanation: B is correct: FRA notation 'n×m' means: settlement/start date is n months from now, and the end date is m months from now. So 3×6 FRA covers a 3-month loan period that starts in 3 months. The reference rate is set at month 3 and settlement occurs at the start of the reference period. A is wrong — the first number is time to settlement, not duration. C is wrong — FRA settlement is typically spot+2. D is wrong — that would be a current loan.
Question 264
In a currency forward market, 'points' refer to:
Select an option first.
Correct answer: B — The forward premium or discount expressed in pips (basis points of the exchange rate) — forward points = Forward rate − Spot rate, reflecting the interest rate differential
Explanation: B is correct: forward points = F − S (in units of the exchange rate). For example, if EUR/USD spot is 1.1000 and 1-year forward is 1.0900, the forward points are −100 (−0.0100), quoted as −100 points. Forward points directly reflect the interest rate differential between the two currencies (covered interest parity). A is wrong — percentage changes are different. C is wrong — that is the tick size. D is wrong — that is a transaction cost.
Question 265
'Delivery versus payment' (DVP) in securities settlement reduces:
Select an option first.
Correct answer: A — Credit risk between buyers and sellers by ensuring the exchange of cash and securities is simultaneous — eliminating principal risk
Explanation: A is correct: DVP (also called RTGS-DVP) ensures that the transfer of securities and the transfer of cash occur simultaneously and irrevocably. This eliminates principal risk — the risk that one party delivers securities without receiving payment, or vice versa. Pre-DVP settlement exposed parties to large principal losses. A is correct. B is wrong — DVP eliminates settlement risk, not market risk. C is wrong — operational errors are separate. D is wrong — custodian fees are unrelated.
Question 266
A commodity producer (e.g. oil company) uses futures to hedge its production. The appropriate hedging strategy is:
Select an option first.
Correct answer: B — Sell (short) futures contracts to lock in a sale price for their future production
Explanation: B is correct: an oil producer has a long position in the underlying commodity (future production). To hedge, they sell (short) oil futures contracts, locking in the sales price for their future output. If oil prices fall, they lose on physical sales but gain on the short futures position, offsetting the loss. A is wrong — buying futures increases exposure. C is wrong — put options are a valid alternative but more expensive; B is the direct hedge. D is wrong — hedging is prudent risk management.
Question 267
The 'gamma hedging' strategy for options involves:
Select an option first.
Correct answer: B — Managing the rate of change of delta by taking positions in options (not just the underlying) to stabilise the portfolio's delta against large underlying price moves
Explanation: B is correct: while delta hedging neutralises first-order price sensitivity, non-zero gamma means the delta changes as the underlying moves. Gamma hedging involves adding options positions (not just the underlying) to neutralise gamma, making the portfolio less sensitive to large price moves. A portfolio that is both delta and gamma neutral does not require as frequent rebalancing. A is wrong — gamma hedging is not directional. C is wrong — eliminating all gamma is impractical. D is wrong — that describes theta hedging.
Question 268
For commodity futures, the 'convenience yield' is highest when:
Select an option first.
Correct answer: B — Physical inventory is low and there is high demand — scarcity creates a high value for holding the physical commodity
Explanation: B is correct: convenience yield is highest when inventories are scarce. When supply is tight, holding physical inventory is extremely valuable (to avoid production shutdowns, meet unexpected demand, etc.). The convenience yield can push the futures curve into deep backwardation (F < S). A is wrong — high storage costs reduce the net convenience yield. C is wrong — contango typically indicates low convenience yield. D is wrong — high rates increase the cost of carry, which is separate.
Question 269
The 'Greeks' of a swap position include:
Select an option first.
Correct answer: B — DV01 (or PV01) as the key interest rate sensitivity measure, analogous to delta for a bond — measuring the dollar change in swap value for a 1 bps change in rates
Explanation: B is correct: for an interest rate swap, the primary risk measure is DV01 (dollar value of a basis point) = change in swap value for 1 bps parallel shift in the yield curve. This is analogous to bond duration/DV01 and serves as the 'delta' equivalent for fixed income. A is wrong — vega and theta are options Greeks; swaps have DV01 as their primary sensitivity. C is wrong — notional alone doesn't measure sensitivity. D is wrong — gamma is second-order and rho is an options Greek.
Question 270
In interest rate modelling, a 'parallel shift' of the yield curve means:
Select an option first.
Correct answer: B — All yields along the curve change by the same amount — used in duration/DV01 hedging as the primary risk scenario
Explanation: B is correct: a parallel shift is the most common scenario used in duration-based interest rate risk analysis — all maturities shift by the same number of basis points (e.g. +100 bps). Duration and DV01 measures are calibrated to parallel shifts. In practice, non-parallel shifts (twists, butterflies) also occur and require more sophisticated risk metrics. A is wrong — that is a twist. C is wrong — that is a pure twist/slope change. D is wrong — that is a non-parallel shift.
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