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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 211
An interest rate floor provides:
Select an option first.
Correct answer: A — The buyer with payment when the reference rate falls below the floor rate — typically used by floating-rate investors
Explanation: A is correct: a floor is the opposite of a cap. Each floorlet pays max(0, K − L) × notional × Δt, where K is the floor rate and L is the reference rate. Floating-rate lenders (e.g. banks with floating-rate loans) buy floors to protect against falling income when rates decline. A is correct. B is wrong — that describes a cap. C is wrong — cap pays on rate rises; floor on rate falls. D is wrong — floors are interest rate instruments.
Question 212
Put-call parity in the context of swaptions states that:
Select an option first.
Correct answer: A — A payer swaption minus a receiver swaption equals the value of a pay-fixed swap (under same terms)
Explanation: A is correct: analogous to put-call parity for options, swaption put-call parity states: value of payer swaption − value of receiver swaption = value of pay-fixed forward-starting swap (both with the same maturity and terms). A is correct. B is wrong — payer and receiver swaptions have different values. C is wrong — relative value depends on the current rate vs strike. D is wrong — swaption value also depends on volatility.
Question 213
The Hull-White interest rate model is a short-rate model where the short rate follows:
Select an option first.
Correct answer: B — A mean-reverting process: dr = (θ(t) − ar)dt + σdW, where a is the mean reversion speed, σ is volatility, and θ(t) is time-dependent drift calibrated to the current yield curve
Explanation: B is correct: the Hull-White model is an affine term structure model where the short rate mean-reverts to a time-varying mean θ(t)/a, with the speed of reversion parameter a and constant volatility σ. The time-dependent drift θ(t) is calibrated to the current market yield curve, ensuring the model exactly fits observed prices. A is wrong — GBM describes lognormal asset prices. C is wrong — no mean reversion. D is wrong — pure random walk overstates long-rate variability.
Question 214
In commodity futures markets, the relationship F = S × e^{(r+u−y)T} holds where y is the convenience yield. If the convenience yield exceeds storage costs and financing (y > r + u), then:
Select an option first.
Correct answer: B — The futures price is below the spot price (backwardation) — the convenience yield's benefit makes holding spot inventory more attractive than holding futures
Explanation: B is correct: when y > r + u, the effective carry cost is negative: e^{(r+u−y)T} < 1. So F < S, meaning the futures is at a discount to spot — this is backwardation. High convenience yield means physical holders of the commodity value it so highly that spot commands a premium. A is wrong — contango requires F > S (y < r + u). C is wrong — equality only if y = r + u. D is wrong — no-arbitrage holds; backwardation is consistent with equilibrium when convenience yield prevents cash-and-carry arbitrage.
Question 215
The Vasicek model for interest rates:
Select an option first.
Correct answer: B — Is the simplest mean-reverting model: dr = a(b − r)dt + σdW, allowing negative interest rates and producing analytically tractable bond prices
Explanation: B is correct: the Vasicek model is dr = a(b − r)dt + σdW, with mean reversion speed a, long-run mean b, and constant volatility σ. It is analytically tractable (closed-form bond prices exist) but allows negative interest rates (Gaussian model). A is wrong — Vasicek has constant volatility. C is wrong — Vasicek allows negative rates. D is wrong — it is a one-factor model.
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Question 216
The Cox-Ingersoll-Ross (CIR) model differs from Vasicek in that:
Select an option first.
Correct answer: B — CIR uses a square-root diffusion term σ√r dW, making the volatility proportional to the square root of the short rate — this prevents negative rates (if 2ab > σ²)
Explanation: B is correct: the CIR model: dr = a(b − r)dt + σ√r dW. The diffusion term σ√r ensures that as r approaches zero, volatility also approaches zero, preventing the rate from going negative (given the Feller condition 2ab > σ²). A is wrong — CIR has mean reversion. C is wrong — CIR volatility is deterministic (function of r). D is wrong — CIR is a one-factor model.
Question 217
In a swaption pricing context, the swap rate's lognormal distribution (Black's model) gives rise to:
Select an option first.
Correct answer: A — The Black-Scholes formula applied to swap rates for pricing receiver and payer swaptions
Explanation: A is correct: Black's model (the market's standard swaption pricing model) assumes the forward swap rate follows a lognormal process and derives a closed-form formula analogous to Black-Scholes for both payer and receiver swaptions. The key inputs are the forward swap rate, strike, time to expiry, and implied volatility of swap rates. A is correct. B is wrong — swaption pricing requires volatility and a probabilistic model. C is wrong — swaption pricing requires the volatility. D is wrong — the process is stochastic.
Question 218
Under convexity adjustment in futures vs forward rates, futures rates are:
Select an option first.
Correct answer: B — Higher than corresponding forward rates because of the daily mark-to-market mechanism — when rates fall, futures position holders receive a payment that can be reinvested at lower rates, creating a systematic disadvantage that is corrected by the convexity adjustment
Explanation: B is correct: the convexity adjustment accounts for the difference between futures rates and forward rates due to daily settlement. The daily mark-to-market of futures creates a convexity disadvantage for the long position (gain when rates fall → reinvest at lower rates; loss when rates rise → funded at higher rates). Therefore futures rates are higher than corresponding forward rates by the convexity adjustment amount (≈ ½σ²T₁T₂). A is wrong — they differ. C is wrong — futures rates are higher, not lower. D is wrong — they are mathematically related.
Question 219
An equity forward contract is priced at F = $55 with time to expiry of 6 months. The current stock price is $50 and the risk-free rate is 4% continuously compounded. The expected dividend payment is $2 in 3 months. The correct forward price is:
Select an option first.
Correct answer: A — $50 × e^(0.04×0.5) − $2 × e^(0.04×0.25) = $51.01 − $2.02 = $48.99
Explanation: A is correct: forward price = (S₀ − PV(dividends)) × e^{rT}. PV of dividend = $2 × e^{−0.04×0.25} = $2 × 0.9900 = $1.98. Forward price = ($50 − $1.98) × e^{0.04×0.5} = $48.02 × 1.0202 = $48.99 approximately. A is closest. B is wrong — ignoring the dividend overstates the forward price. C is wrong — the dividend should be discounted. D is wrong — mixing continuous and discrete compounding.
Question 220
A repo rate of 3% applies to a $100 million 30-day repo. The total repurchase price is:
Select an option first.
Correct answer: B — $100,083,562 = $100m × (1 + 0.03 × 30/360)
Explanation: B is correct: the repurchase price = initial proceeds × (1 + repo rate × days/360) = $100,000,000 × (1 + 0.03 × 30/360) = $100,000,000 × 1.0025 = $100,250,000. Wait — 0.03 × 30/360 = 0.0025, so $100,000,000 × 1.0025 = $100,250,000. A gives $100,250,000 which is correct. B gives $100,083,562 which would be for a shorter period. A is correct: $100,000,000 × (1 + 0.03 × 30/360) = $100,000,000 × 1.0025 = $100,250,000.
Question 221
The variation margin on a short futures position is:
Select an option first.
Correct answer: B — Positive when futures prices fall (shorts profit when futures decline) and negative when futures prices rise
Explanation: B is correct: a short futures position profits when futures prices decline. If the futures price falls by $1 per unit and the contract covers 1,000 units, the short receives $1,000 as variation margin. Conversely, if the price rises, the short pays variation margin. B is correct. A is wrong — short positions lose if futures rise. C is wrong — variation margin fluctuates daily. D is wrong — VM is paid/received daily.
Question 222
LIBOR was phased out primarily because:
Select an option first.
Correct answer: B — The rate was based on submissions from a small panel of banks rather than actual transactions, making it vulnerable to manipulation — the scandals of 2012 led regulators to require transition to transaction-based risk-free rates
Explanation: B is correct: LIBOR was a polled rate — panel banks submitted estimates of their unsecured borrowing costs. The 2012 LIBOR rigging scandal (where banks manipulated their submissions for profit) exposed the benchmark's weakness. Regulators globally required transition to transaction-based rates: SOFR (USD), SONIA (GBP), €STR (EUR), TONAR (JPY), SARON (CHF). A is wrong — regulators mandated the transition. C is wrong — stability was not the issue. D is wrong — SONIA is the UK rate; SOFR is for USD.
Question 223
A variance swap is a derivative where the payoff at maturity is based on:
Select an option first.
Correct answer: B — The difference between the realised variance over the swap period and the fixed variance strike agreed at inception — the long receives the excess of realised over implied variance
Explanation: B is correct: a variance swap pays: Notional × (σ²_realised − K²_var), where σ²_realised is the actual (realised) variance over the period and K²_var is the pre-agreed variance strike. The long profits if actual volatility is higher than implied. A is wrong — it is variance (σ²), not volatility (σ). C is wrong — square root gives volatility, not variance. D is wrong — that would be a covariance swap.
Question 224
The 'convergence' of futures prices to spot prices at expiry is guaranteed by:
Select an option first.
Correct answer: B — No-arbitrage: if F ≠ S at expiry, riskless profits could be made by buying the cheaper and selling the more expensive — arbitrage forces convergence
Explanation: B is correct: at expiry, the futures price must equal the spot price. If F > S at delivery, shorts deliver the cheaper spot and receive the higher futures price — arbitrage profit. If F < S, longs take delivery and sell spot at a profit. These arbitrage forces ensure convergence. A is wrong — convergence is driven by arbitrage, not regulation. C is wrong — the exchange settles at the observed spot (final settlement price). D is wrong — it is arbitrage, not voluntary behaviour.
Question 225
Position limits in futures markets serve to:
Select an option first.
Correct answer: B — Prevent any single participant from accumulating a position so large it could distort prices or corner the market
Explanation: B is correct: position limits cap the maximum number of contracts any single participant can hold to prevent market manipulation, price distortion, or 'cornering' (where one entity controls enough of the underlying to squeeze short sellers). Regulators and exchanges set position limits for commodities and financial futures. A is wrong — position limits constrain, not maximise, profits. C is wrong — physical delivery is separate. D is wrong — minimums are not set by position limits.
Question 226
The 'T+2' settlement convention in equity markets means:
Select an option first.
Correct answer: B — Trades settle 2 business days after the transaction date — the buyer delivers cash and the seller delivers securities
Explanation: B is correct: under T+2 (standard in most equity markets including US and EU), the settlement of a trade — transfer of securities to the buyer and cash to the seller — occurs 2 business days after the trade date. Some markets are moving to T+1. A is wrong — T+0 is real-time settlement. C is wrong — T+2 means exactly 2 days. D is wrong — 2 months is not T+2.
Question 227
The 'notional principal' in a swap contract:
Select an option first.
Correct answer: B — Is typically not exchanged in interest rate swaps (used only to calculate payment amounts) but IS exchanged in currency swaps
Explanation: B is correct: in interest rate swaps, the notional principal is never exchanged — it is only used to calculate the fixed and floating interest payments. In currency swaps, the notional IS exchanged at inception and maturity in the two different currencies. B correctly distinguishes the two. A is wrong — IR swaps don't exchange notional. C is wrong — swap market value changes over time. D is wrong — there is no equity component.
Question 228
A 'quanto' derivative is one where:
Select an option first.
Correct answer: B — The payoff is based on a foreign asset but denominated in the domestic currency — the exchange rate risk is embedded in the contract
Explanation: B is correct: a quanto derivative pays off in a currency different from the currency of the underlying. For example, a quanto option on the Nikkei 225 might pay USD based on the Nikkei level rather than JPY. The FX risk is 'baked in' through the quanto adjustment. B is correct. A is wrong — that describes a basket or spread option. C and D are wrong.
Question 229
In weather derivatives, the underlying variable is typically:
Select an option first.
Correct answer: B — Temperature-based indices such as Heating Degree Days (HDD) or Cooling Degree Days (CDD) — used to hedge exposure to energy demand or agricultural risk related to weather
Explanation: B is correct: the most common weather derivatives are based on HDD (sum of max(0, 65°F − daily average temperature)) and CDD (sum of max(0, daily average − 65°F)) indices. Energy companies use these to hedge revenue risk — warm winters reduce heating demand; cool summers reduce cooling demand. A is wrong — rainfall derivatives exist but are less common. C is wrong — wind is less standardised. D is wrong — HDD/CDD are single-variable.
Question 230
A freight rate forward agreement (FFA) is used by shipping companies to:
Select an option first.
Correct answer: B — Hedge or gain exposure to future freight rates — locking in rates for the future transport of cargo
Explanation: B is correct: freight rate derivatives (FFAs) allow shipping companies (both vessel owners and cargo owners) to hedge against volatility in freight rates. The underlying is typically a standardised freight index (e.g. Baltic Dry Index). Ship owners can lock in future revenue; cargo owners can lock in future transport costs. A is wrong — vessel purchase is asset acquisition. C is wrong — FFAs are financial derivatives. D is wrong — fuel hedging uses oil derivatives.
Question 231
If the current EUR/USD spot rate is 1.10, the 1-year US rate is 5%, and the 1-year EUR rate is 3%, the 1-year EUR/USD forward rate (using continuous compounding) is approximately:
Select an option first.
Correct answer: B — 1.122 (dollar at forward premium; more dollars per euro in the forward market)
Explanation: B is correct: F = S × e^{(r_USD − r_EUR) × T} = 1.10 × e^{(0.05 − 0.03) × 1} = 1.10 × e^{0.02} = 1.10 × 1.0202 = 1.1222 ≈ 1.122. Since USD has a higher interest rate, the USD is at a forward discount (each euro buys more dollars forward). More dollars per euro = higher EUR/USD rate. B is correct. A is wrong — the USD forward discount means more dollars per euro (higher EUR/USD). C is wrong — rates differ. D is wrong — not supported.
Question 232
A total return receiver in a total return swap (TRS) benefits when:
Select an option first.
Correct answer: B — The total return of the reference asset (price change + income) exceeds the financing rate they pay — they gain the excess return
Explanation: B is correct: the total return receiver pays a financing rate (e.g. SOFR + spread) and receives the total return of the reference asset. If total return > financing rate, the receiver profits. If total return < financing rate, the receiver makes a net payment. B correctly describes when the receiver benefits. A is wrong — negative total return hurts the receiver. C is wrong — receiver pays the financing rate. D is wrong — general rate movements affect the reference asset's total return but B is the specific condition.
Question 233
In the fixed income futures market, the 'invoice price' received by the short position upon delivery is:
Select an option first.
Correct answer: B — The futures settlement price multiplied by the conversion factor of the delivered bond, plus accrued interest
Explanation: B is correct: invoice price = (futures settlement price × conversion factor of delivered bond) + accrued interest. The conversion factor standardises delivery by adjusting for differences in coupon and maturity of the delivered bond relative to the notional bond underlying the futures contract. A is wrong — market price is not used directly. C is wrong — par value is separate. D is wrong — duration is not in the invoice price formula.
Question 234
The convenience yield in the futures pricing formula represents:
Select an option first.
Correct answer: B — The value of holding the physical commodity — the flow benefit from having inventory available for use or sale
Explanation: B is correct: the convenience yield captures the non-monetary benefit of physically holding a commodity — the ability to use it in production without delays, benefit from spot shortages, or avoid the cost of finding the commodity urgently. F = S × e^{(r + u − y)T}, where y is the convenience yield. B is correct. A is wrong — dividends apply to equities. C is wrong — margin interest is a separate concept. D is wrong — rollover cost is a different consideration.
Question 235
Backwardation in a commodity market allows a 'cash and carry' arbitrage when:
Select an option first.
Correct answer: B — Futures prices exceed the no-arbitrage level (above spot + cost of carry) — buy spot, short futures, earn riskless profit
Explanation: B is correct: cash-and-carry arbitrage occurs when F > S × e^{(r+u)T}: buy the spot, finance the purchase, store the commodity, deliver into the futures at expiry. The profit is the excess of the futures price over the full carry price. Backwardation (F < S) prevents cash-and-carry arbitrage but allows reverse cash-and-carry if the commodity can be shorted. A is wrong — this would be reverse cash-and-carry territory. C and D are wrong.
Question 236
A 'swaption collar' is typically constructed by:
Select an option first.
Correct answer: B — Buying a payer swaption (right to pay fixed) and selling a receiver swaption (right to receive fixed) — creating a range within which the effective rate is bounded
Explanation: B is correct: a swaption collar combines a long payer swaption (protection if rates rise above the payer strike) with a short receiver swaption (giving up upside if rates fall below the receiver strike). The premium from the short receiver swaption partially offsets the cost of the payer swaption. This creates a band within which the effective borrowing rate varies. A is wrong — buying both creates a straddle on swap rates. C is wrong — selling both creates a short straddle. D is wrong — that is a swap with cap and floor.
Question 237
In futures markets, the 'carry return' to a long position in commodity futures equals:
Select an option first.
Correct answer: B — The total return = spot return + roll yield + collateral yield, where roll yield is positive in backwardation and negative in contango
Explanation: B is correct: the total return to a long futures position has three components: (1) spot return (change in spot price); (2) roll yield (gain from rolling into the next contract — positive in backwardation where near-term futures are above far-dated, negative in contango); (3) collateral yield (interest earned on margin posted). B correctly identifies all three. A is wrong — too narrow. C is wrong — that is basis return. D is wrong — doesn't capture all components.
Question 238
Forward guidance by a central bank affects futures and forward markets because:
Select an option first.
Correct answer: B — It shapes market expectations of future rates, which are priced into futures, forwards, and OIS rates — influencing the entire term structure of rates
Explanation: B is correct: forward guidance (communication about future policy intentions) is a powerful monetary tool. When the Fed signals rates will stay low for longer, market participants revise their expectations, which is immediately priced into short-term futures (fed funds futures, Eurodollar/SOFR futures), OIS rates, and the entire yield curve. B is correct. A is wrong — guidance does not legally fix rates. C is wrong — rate expectations affect all fixed income instruments. D is wrong — expectations about future rates drive forward pricing.
Question 239
A 'range forward' (or cylinder option) is a strategy that:
Select an option first.
Correct answer: B — Buys a put at one strike (floor) and sells a call at another (ceiling) — defining a range within which the forward rate can vary, with no premium if structured at market
Explanation: B is correct: a range forward (cylinder) sets an upper bound (sell call at upper strike) and a lower bound (buy put at lower strike) for an FX or interest rate exposure. The premium from the sold call offsets the cost of the bought put. The hedger benefits if rates move in the favourable direction within the range. B is correct. A is wrong — upside is capped by the sold call. C is wrong — the range forward defines a range, not a single rate. D is wrong — basis risk is separate.
Question 240
In the futures market, the concept of 'open outcry' refers to:
Select an option first.
Correct answer: A — A trading method where orders are shouted and hand-signalled in a physical pit — now largely replaced by electronic trading
Explanation: A is correct: open outcry was the traditional method of trading in futures exchanges (like the CBOT and CME) where traders physically gathered in trading pits and used verbal bids/offers and hand signals to execute trades. Most exchanges have transitioned to electronic trading platforms (e.g. CME Globex). A is correct. B is wrong — that describes electronic trading. C is wrong — that is interdealer brokerage. D is wrong — OTC is not futures trading.
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