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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 181
The storage cost in the cost-of-carry model for commodity futures:
Select an option first.
Correct answer: B — Increases the futures price above the spot price — costs of physically holding the commodity (warehousing, insurance) must be recovered through a higher futures price
Explanation: B is correct: storage costs (warehousing, insurance, spoilage) are part of the cost of carry and push futures prices higher: F = S × e^((r + u)T), where u is the storage cost rate. Producers and traders require higher futures prices to justify storing the commodity. A is wrong — storage costs raise, not lower, futures prices. C is wrong — storage costs are a key pricing factor. D is wrong — storage costs apply specifically to commodities, not financial futures.
Question 182
An interest rate swap where one party pays a fixed rate and receives a floating rate (typically SOFR or a similar benchmark) is called:
Select an option first.
Correct answer: B — A fixed-for-floating interest rate swap — the fixed-rate payer benefits when rates rise; the floating-rate payer benefits when rates fall
Explanation: B is correct: the most common interest rate swap is a fixed-for-floating (or 'plain vanilla') interest rate swap. The fixed-rate payer benefits if floating rates rise above the fixed rate (their net position gains). The floating-rate payer benefits if rates fall. A is wrong — currency swaps involve two different currencies. C is wrong — commodity swaps reference commodity prices. D is wrong — CDS is about credit risk.
Question 183
The fixed rate on a new at-market interest rate swap is set such that:
Select an option first.
Correct answer: B — The present value of the fixed leg equals the present value of the floating leg — making the initial value of the swap zero for both parties
Explanation: B is correct: an at-market (par) swap is initiated with a fixed rate set so that PV(fixed payments) = PV(expected floating payments), giving the swap a zero initial value — no upfront payment is needed. As market rates change, the swap's value diverges from zero. A is wrong — no upfront payment in an at-market swap. C is wrong — the fixed rate is derived from the entire swap curve. D is wrong — notional is never exchanged in an interest rate swap.
Question 184
A company has floating-rate debt (paying SOFR + 2%). To convert this to fixed-rate financing, the company should:
Select an option first.
Correct answer: A — Enter a swap to pay fixed and receive floating (SOFR) — the floating received offsets the floating paid on the debt
Explanation: A is correct: the company pays SOFR + 2% on its debt. To fix its all-in cost, it enters a pay-fixed/receive-floating swap. The SOFR received from the swap offsets the SOFR paid on the debt, leaving the company with a fixed net payment: fixed swap rate + 2% credit spread. A is correct. B is wrong — pay-floating/receive-fixed would increase floating exposure. C is wrong — a floating note adds more floating exposure. D is wrong — selling bonds is a liability management action, not a swap.
Question 185
In a currency swap, the notional principal is:
Select an option first.
Correct answer: C — Exchanged at initiation and at maturity in the two different currencies at the initial spot rate
Explanation: C is correct: in a currency swap, unlike an interest rate swap, the notional principal IS typically exchanged at initiation and at maturity in the two currencies at the originally agreed exchange rate. For example, a USD/EUR swap involves exchanging $100 million for €90 million at inception and re-exchanging at maturity. A is wrong — notional is exchanged in currency swaps. B is wrong — the exchange involves two different currencies. D is wrong — exchange is contractual, not conditional on currency movement.
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Question 186
A total return swap (TRS) allows the total return payer to:
Select an option first.
Correct answer: A — Receive the total economic return of a reference asset (price appreciation + income) while paying a financing rate (e.g. LIBOR/SOFR + spread)
Explanation: A is correct: in a TRS, the total return receiver receives all cash flows from the reference asset (coupons, dividends, price gains) and pays a financing rate. The total return payer transfers the economic exposure while retaining legal ownership of the asset. A correctly describes the receiver's position. B is wrong — TRS includes capital gains, not just income. C is wrong — legal ownership is not transferred. D is wrong — credit risk is transferred economically.
Question 187
The 'tailing the hedge' adjustment is necessary in futures hedging because:
Select an option first.
Correct answer: B — Futures gains and losses are received/paid daily through variation margin (time value of money benefit), whereas spot positions are settled at maturity — the daily settlement means fewer contracts are needed than the naive hedge ratio suggests
Explanation: B is correct: because futures positions are marked-to-market daily, gains from futures can be reinvested (or losses must be funded immediately). This creates a difference from forward contracts where no cash flows occur until maturity. The hedge ratio must be 'tailed' (multiplied by e^{−r(T−t)} approximately) to account for the time value of the daily settlement cash flows. A is wrong — relative volatility is a hedging ratio consideration. C is wrong — futures can be rolled. D is wrong — tailing is specifically about daily settlement.
Question 188
The value of a futures position (mark-to-market) is:
Select an option first.
Correct answer: B — The daily gain or loss = (today's futures price − previous day's futures price) × contract size × number of contracts
Explanation: B is correct: futures positions are marked-to-market daily. The variation margin received or paid is the change in futures price multiplied by the contract size and number of contracts. This is credited to or debited from the margin account daily. A is wrong — futures values change daily. C is wrong — initial margin is the initial collateral. D is wrong — MTM is about daily settlement, not expected profit.
Question 189
Forward rate agreements (FRAs) are OTC contracts that:
Select an option first.
Correct answer: B — Lock in an interest rate for a future borrowing or lending period — the settlement is the difference between the agreed rate and the actual benchmark rate on the settlement date
Explanation: B is correct: an FRA is a contract where two parties agree on an interest rate for a specified future period. At settlement, the payer of the agreed rate pays/receives the difference between the agreed rate and the reference rate (e.g. 3M SOFR), applied to the notional principal for the reference period. A is wrong — FRAs are about interest rates. C is wrong — multiple-period exchanges describe interest rate swaps. D is wrong — the right but not obligation describes an interest rate cap (swaption/caplet).
Question 190
The settlement amount on an FRA is paid:
Select an option first.
Correct answer: B — At the start of the reference period (upfront) — discounted to reflect the present value
Explanation: B is correct: unlike most interest rate instruments which pay in arrears, FRAs settle at the beginning of the reference period, with the settlement amount discounted to present value. This is the standard market convention. A is wrong — payment is at the start (discounted), not the end. C is wrong — FRA is a single payment. D is wrong — payment occurs regardless of direction (negative settlement if reference rate is below agreed rate, meaning the FRA buyer pays).
Question 191
A financial institution enters into a 3×9 FRA (3-month rate starting in 3 months). The fixed rate is 5%. At expiry, the 6-month benchmark rate is 6%. The payoff to the long position (FRA buyer — who agreed to receive the reference rate and pay 5%) is:
Select an option first.
Correct answer: A — Positive — they receive 6% and pay 5%, gaining on the rate difference
Explanation: A is correct: the FRA buyer receives the reference rate and pays the fixed rate. Since 6% > 5%, the buyer gains the difference of 1% on the notional for the 6-month period (discounted to the settlement date). A is correct. B is wrong — the long pays fixed and receives floating; with floating above fixed, the long profits. C is wrong — FRAs have non-zero settlement when rates differ. D is wrong — FRA buyers profit only when rates rise above the fixed rate.
Question 192
Eurodollar futures contracts are based on:
Select an option first.
Correct answer: B — The 3-month US dollar LIBOR rate (or now its SOFR-based successor) — quoted as 100 minus the implied interest rate
Explanation: B is correct: Eurodollar futures (CME) are based on the 3-month LIBOR rate for US dollar deposits in offshore banks. They are quoted as 100 minus the rate, so a price of 95.50 implies a rate of 4.50%. With the LIBOR transition, SOFR futures have become the primary reference. A is wrong — Eurodollar futures are interest rate, not FX, contracts. C is wrong — they are not bond contracts. D is wrong — FX forwards are separate instruments.
Question 193
In a fixed-for-floating interest rate swap, if market rates rise above the fixed rate after inception:
Select an option first.
Correct answer: B — The fixed-rate payer's position gains value — they continue paying the lower fixed rate while rates have risen
Explanation: B is correct: the fixed-rate payer pays the originally agreed (now below-market) fixed rate and receives the (now higher) floating rate. The swap has positive value for the fixed-rate payer because they are paying below-market rates. To value the swap, the expected floating payments rise with rates while fixed payments remain constant. A is wrong — the fixed-rate payer benefits from rising rates. C is wrong — rate changes do affect swap value. D is wrong — swaps are not automatically terminated on rate movements.
Question 194
The swap spread is defined as:
Select an option first.
Correct answer: A — The difference between the fixed swap rate and the underlying government bond yield of the same maturity
Explanation: A is correct: the swap spread = fixed swap rate − Treasury yield (same maturity). It reflects credit risk, liquidity, and supply-demand factors in the swap market. A positive swap spread means the swap rate is above Treasuries, reflecting that interbank counterparties carry more credit risk than the government. B is wrong — that is the net payment within the swap. C is wrong — bid-ask is a transaction cost. D is wrong — that is a slope measure.
Question 195
A commodity swap in which an airline pays a fixed price for jet fuel and receives the floating market price effectively:
Select an option first.
Correct answer: B — Locks in a fixed cost for fuel — if spot fuel prices rise, the airline's floating receipts offset the higher spot cost
Explanation: B is correct: the airline pays fixed (the agreed swap price) and receives floating (market price of jet fuel). This is an economic hedge — if jet fuel prices rise, the floating payment received in the swap offsets the higher physical cost. If prices fall, the airline pays more under the swap than the market price (opportunity cost). A is wrong — the swap reduces exposure. C is wrong — it is a hedge, not speculation. D is wrong — commodity swaps are typically cash-settled.
Question 196
The cheapest-to-deliver (CTD) bond in Treasury bond futures is the deliverable bond that:
Select an option first.
Correct answer: B — Maximises the profit of the short futures position — the bond where the invoice price (futures price × conversion factor) most exceeds the spot purchase price, minimising delivery cost
Explanation: B is correct: in Treasury bond futures, the short party has the option to deliver any bond from a basket of eligible bonds. The CTD is the bond that minimises the net cost to the short: the bond with the greatest invoice price relative to market purchase price. B correctly describes the short's optimisation. A is wrong — CTD is not necessarily the highest coupon bond. C is wrong — the short (not long) selects which bond to deliver. D is wrong — CTD selection depends on the ratio of market price to (futures × CF).
Question 197
Rolling a futures position means:
Select an option first.
Correct answer: B — Closing an expiring futures contract and opening a new position in a later-dated contract to maintain continuous exposure
Explanation: B is correct: rolling is the process of closing (selling) the near-month futures before expiry and simultaneously opening a position in the next (or later) contract month to maintain continuous exposure without taking physical delivery. This is necessary for commodity funds and hedgers with ongoing exposures. A is wrong — futures rarely have early exercise. C is wrong — that is an assignment. D is wrong — adjusting contracts is rebalancing, not rolling.
Question 198
The no-arbitrage forward price for a stock paying a continuous dividend yield q is:
Select an option first.
Correct answer: B — F = S × e^((r−q)×T)
Explanation: B is correct: for an asset paying a continuous dividend yield q, the cost of carry is reduced by the dividend flow. The no-arbitrage forward price is F = S₀ × e^((r−q)T). The dividend yield reduces the holding cost since the owner receives dividends during the holding period. A is wrong — that ignores dividends. C is wrong — dividends reduce, not increase, the forward price. D is wrong — dividends are subtracted from r, not added.
Question 199
An equity swap allows:
Select an option first.
Correct answer: A — One party to exchange a fixed or floating interest return for the total return on a stock index (capital gains + dividends) — a way to gain/reduce equity market exposure synthetically
Explanation: A is correct: equity swaps are contracts where one leg pays a fixed or floating rate (e.g. SOFR + spread) and the other leg pays the total return on an equity index or single stock. They allow parties to gain or reduce equity exposure without actually trading shares, and are used by hedge funds, asset managers, and banks. B is wrong — no physical share exchange. C is wrong — legal ownership is not transferred. D is wrong — that is a rough description of only one leg.
Question 200
The price of a forward contract on a bond that pays known coupons is:
Select an option first.
Correct answer: A — F = (S − PV(coupons)) × e^(rT)
Explanation: A is correct: for an asset with known cash flows (like coupon bonds), the no-arbitrage forward price is F = (S₀ − PV(cash flows)) × e^(rT). The present value of coupons received during the holding period reduces the effective cost of carrying the bond. A is correct. B is wrong — ignores the coupon income that reduces carry cost. C is wrong — not the correct formula. D is wrong — the coupon should reduce the forward price, not be added.
Question 201
When futures prices are lower than spot prices (F < S), the market is in:
Select an option first.
Correct answer: B — Backwardation — futures are at a discount to spot, common in commodity markets where convenience yields exceed storage costs and financing
Explanation: B is correct: backwardation (or inverted market) occurs when futures prices are below the spot price. This typically happens when convenience yields are high (users need the commodity now, creating a 'negative cost of carry' effect) or when there are supply shortages. A is wrong — contango is F > S. C is wrong — backwardation does not necessarily mean arbitrage is available (it is consistent with no-arbitrage when convenience yield > r + u). D is wrong — contango has positive basis.
Question 202
A cross-currency swap involves:
Select an option first.
Correct answer: B — Exchanging interest payments (and principal) in two different currencies — used to transform foreign currency borrowings into domestic currency obligations
Explanation: B is correct: a cross-currency swap involves exchanging: (1) notional principal in two currencies at inception and maturity (at the original spot rate), (2) interest payments in the two currencies during the swap term. For example, a company may borrow in USD but swap into EUR interest and principal to match its EUR cash flows. A is wrong — that is a standard interest rate swap. C is wrong — dividends are separate. D is wrong — that is credit-related.
Question 203
The 'tick' size in a futures contract is:
Select an option first.
Correct answer: B — The minimum price increment by which the futures price can move
Explanation: B is correct: the tick is the smallest price increment for a futures contract. For example, Eurodollar futures have a tick of 0.005 (worth $12.50 per contract). The tick size determines the precision of price movements and the minimum profit/loss per contract. A is wrong — that is the daily price limit. C is wrong — variation margin is calculated from price changes. D is wrong — the expiry cycle is about contract months.
Question 204
To hedge a $10 million equity portfolio against market risk using S&P 500 futures (contract value $250 × index level), with the index at 4,000 and portfolio beta of 1.2, the number of contracts needed is:
Select an option first.
Correct answer: A — 12 contracts
Explanation: A is correct: number of contracts = (Portfolio value × β) / (futures price × contract multiplier) = ($10,000,000 × 1.2) / (4,000 × $250) = $12,000,000 / $1,000,000 = 12 contracts. A is correct. B is wrong — 15 = $10m × 1.5 / $1m. C is wrong — 10 = $10m / $1m (ignores beta). D is wrong — not supported.
Question 205
The difference between futures and forward contracts in terms of price (futures price > forward price) may arise due to:
Select an option first.
Correct answer: B — Positive correlation between the futures price and interest rates — futures prices tend to be higher than forward prices when there is positive correlation between the price of the underlying and interest rates (futures gains can be reinvested at higher rates)
Explanation: B is correct: when there is positive correlation between the underlying asset price and interest rates, futures prices exceed forward prices. This is because when the futures price rises (gain), rates are also higher, allowing the gain to be reinvested at higher rates. Conversely, negative correlation leads to futures prices being below forward prices. A is wrong — futures have less credit risk. C is wrong — futures are typically more liquid. D is wrong — standardisation does not create a systematic price difference.
Question 206
An inflation swap is an OTC contract where:
Select an option first.
Correct answer: B — One party pays a fixed rate and receives the actual inflation rate (e.g. CPI growth) applied to a notional — used to hedge or gain inflation exposure
Explanation: B is correct: in a zero-coupon inflation swap, the fixed-rate payer pays a predetermined fixed rate over the swap term, and the inflation receiver receives the actual cumulative inflation (CPI growth) over the same period. Used by pension funds and insurers to hedge inflation-linked liabilities. A is wrong — different payments are not just timing differences. C is wrong — commodity swaps reference commodity prices. D is wrong — not about bond exchange rates.
Question 207
The 'open interest' in futures markets represents:
Select an option first.
Correct answer: B — The total number of outstanding futures contracts that have not been settled or delivered — a measure of market participation
Explanation: B is correct: open interest is the total number of open (unsettled) contracts outstanding at any point. Each new contract between a buyer and seller increases open interest by one; offsetting trades reduce it. Open interest peaks as the delivery month approaches and falls sharply near expiry. A is wrong — trading volume is the number of contracts traded in a period. C is wrong — position limits are different. D is wrong — days to expiry is separate.
Question 208
A forward exchange contract (FX forward) for a currency pair is priced using:
Select an option first.
Correct answer: B — The spot rate adjusted by the interest rate differential between the two currencies: F = S × (1 + r_domestic) / (1 + r_foreign) for discrete compounding
Explanation: B is correct: covered interest parity (CIP) determines the no-arbitrage forward exchange rate: F = S × e^{(r_d − r_f) × T} for continuous compounding. The currency with a higher interest rate trades at a forward discount (its forward price is lower than its spot price). A is wrong — the forward rate is determined by interest differentials, not markup. C is wrong — PPP determines long-run exchange rates, not forward prices. D is wrong — OTC forward prices are set by CIP.
Question 209
If the 1-year US interest rate is 5% and the 1-year Japanese interest rate is 0.5%, and the current USD/JPY spot rate is 150 (yen per dollar), the 1-year forward rate is approximately:
Select an option first.
Correct answer: C — 156.75 (JPY/USD) — dollar at forward premium as it has higher interest rates
Explanation: C is correct: F = S × (1 + r_yen) / (1 + r_dollar) = 150 × (1.005 / 1.05) ≈ 150 × 0.9571 ≈ 143.57 JPY/USD (dollar at forward discount as it has higher interest rates). Wait — re-checking: since USD has higher rates, USD depreciates in forward market. F_JPY/USD = 150 × (1 + r_JPY) / (1 + r_USD) = 150 × 1.005/1.05 ≈ 143.6. So the dollar costs fewer yen in the forward market (dollar weakens). C overstates (156.75 would be wrong direction). B is approximately correct. B is correct: the dollar's higher interest rate means it is at a forward discount. F ≈ 150 × (1.005/1.05) ≈ 143.57. B is closest.
Question 210
An interest rate cap is a series of call options on interest rates that:
Select an option first.
Correct answer: B — Protects the borrower against interest rates rising above the cap rate — each caplet pays max(0, reference rate − cap rate) × notional × period
Explanation: B is correct: an interest rate cap gives the buyer (typically a floating-rate borrower) protection against rates rising above the cap rate. Each period's caplet pays max(0, L − K) × notional × Δt, where L is the reference rate and K is the cap rate. The buyer pays an upfront premium. A is wrong — a floor protects the lender/investor. C is wrong — a swap converts floating to fixed. D is wrong — caps protect against rising rates, not falling.
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