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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 301
Theta (Θ) of an option represents:
Select an option first.
Correct answer: B — The rate of change of the option value with respect to the passage of time — typically negative (time decay erodes option value as expiry approaches)
Explanation: B is correct: theta measures how much the option price changes for a one-day (or one-year) passage of time, all else equal. Theta is typically negative for long option positions — options lose value as time passes due to the declining probability of a profitable move. B is correct. A is wrong — that is delta. C is wrong — that is rho. D is wrong — not a standard definition.
Question 302
Vega (ν) of an option measures:
Select an option first.
Correct answer: B — The sensitivity of the option price to a 1% change in the implied volatility of the underlying asset
Explanation: B is correct: vega measures how much the option price changes for a 1% (or 1 percentage point) change in implied volatility. Both calls and puts have positive vega — higher volatility increases option values. Vega is largest for at-the-money options and longer-dated options. A is wrong — that is delta. C is wrong — that is theta. D is wrong — N(d₂) is the risk-neutral probability of expiring ITM.
Question 303
Rho (ρ) of a European call option is typically:
Select an option first.
Correct answer: B — Positive — call prices rise when interest rates rise (higher rates reduce the PV of the strike, making calls more valuable) and negative for puts
Explanation: B is correct: for a European call, rho = K × T × e^{−rT} × N(d₂) > 0. Higher interest rates reduce the present value of the strike payment (which the call holder pays at exercise), making the call more valuable. For puts, higher rates reduce value (negative rho). A is wrong — calls have positive rho. C is wrong — both calls and puts are sensitive to interest rates. D is wrong — not the formula for rho.
Question 304
A delta-neutral portfolio is one where:
Select an option first.
Correct answer: A — The portfolio has no exposure to changes in the underlying asset price (aggregate delta = 0)
Explanation: A is correct: a delta-neutral portfolio has total delta = 0, meaning a small change in the underlying asset price produces no change in portfolio value. This is achieved by combining positions in options and/or the underlying in the correct proportions. However, delta-neutral portfolios are not permanently hedged — gamma ensures that delta changes as the price moves. A is correct. B is wrong — delta neutral does not require ATM options. C is wrong — equal calls and puts does not guarantee delta neutrality. D is wrong — gamma causes value changes even in a delta-neutral portfolio.
Question 305
In binomial option pricing, the risk-neutral probability of an up move (p) is:
Select an option first.
Correct answer: B — p = (e^{rΔt} − d) / (u − d), where u and d are the up and down factors and Δt is the time step length
Explanation: B is correct: in the binomial model, the risk-neutral probability p = (e^{rΔt} − d) / (u − d) is derived to price options in a no-arbitrage framework. It is NOT the real-world probability of an up move — it is the probability that makes the expected return on the stock equal to the risk-free rate. A is wrong — it is risk-neutral, not real-world probability. C is wrong — that is a different concept. D is wrong — delta is the hedge ratio, not a probability.
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Question 306
An American call option on a non-dividend-paying stock:
Select an option first.
Correct answer: B — Should never be exercised early — its value is always at least as great as its intrinsic value, so selling it is better than exercising
Explanation: B is correct: it is never optimal to exercise an American call early on a non-dividend-paying stock. The American call always has time value remaining (C_American ≥ C_European = C_American for non-dividend-paying stocks). Selling the option captures both intrinsic and time value. A is wrong — early exercise forgoes time value. C is the correct conclusion for non-dividend-paying stocks. D is wrong — American options can never be worth less than European options (extra right to exercise early has non-negative value).
Question 307
An American put option on a non-dividend-paying stock:
Select an option first.
Correct answer: B — May be optimally exercised early when it is sufficiently deep in the money — the interest earned on the strike price K from early exercise can exceed the remaining time value
Explanation: B is correct: unlike American calls, American puts may be optimally exercised early on non-dividend-paying stocks. If the put is deep enough in the money, the interest earned on the strike price received from early exercise can exceed the option's remaining time value. This is why American puts are worth more than European puts. A is wrong — early exercise is possible for puts. C is wrong — American puts have an early exercise premium. D is wrong — they have time value when not exercised.
Question 308
The volatility smile refers to the pattern where:
Select an option first.
Correct answer: B — Implied volatility tends to be higher for options with strikes far from the current price (both OTM calls and OTM puts), forming a smile-shaped curve when plotted against strike prices
Explanation: B is correct: the volatility smile is the observed pattern where implied volatility (backed out from market option prices using BSM) is higher for options with strikes further from at-the-money, creating a U-shaped (smile) or smirk pattern. This contradicts the BSM assumption of constant volatility and reflects fat tails and skewness in real asset return distributions. A is wrong — implied volatility is NOT constant in practice. C is wrong — the smile is across strikes, not time. D is wrong — IV vs HV relationship is separate.
Question 309
A straddle options strategy involves:
Select an option first.
Correct answer: B — Buying a call and a put with the same strike and expiry — profits from large price movements in either direction
Explanation: B is correct: a long straddle involves buying a call AND a put with the same strike and expiry. The maximum loss is the combined premium. The strategy profits from large moves in either direction — up (call is exercised) or down (put is exercised). The breakeven points are strike ± total premium. A is wrong — that is a strangle or risk reversal. C is wrong — that is a short straddle. D is wrong — that is a bull call spread.
Question 310
A bull call spread involves:
Select an option first.
Correct answer: B — Buying a call at a lower strike price and selling a call at a higher strike price — limits both upside profit and the cost (net debit strategy)
Explanation: B is correct: a bull call spread = buy call at K₁ (lower strike) + sell call at K₂ (higher strike). The premium received from the short call reduces the net cost. The maximum profit is (K₂ − K₁) minus the net premium, achieved if S > K₂ at expiry. A is wrong — buying high and selling low would be a bear call spread. C is wrong — two long calls increase exposure. D is wrong — that is a risk reversal.
Question 311
A mortgage-backed security (MBS) derives its cash flows from:
Select an option first.
Correct answer: B — A pool of mortgage loans — homeowners' monthly payments of principal and interest pass through to MBS investors
Explanation: B is correct: an MBS is backed by a pool of mortgage loans. As homeowners make monthly mortgage payments (principal + interest), these cash flows are collected and passed through (after fees) to MBS investors. The main risks include prepayment risk (when homeowners refinance) and credit risk (default). A is wrong — MBS is backed by mortgages, not corporate bonds. C is wrong — T-bonds are government securities. D is wrong — MBS cash flows come from loan repayments.
Question 312
Prepayment risk in mortgage-backed securities arises because:
Select an option first.
Correct answer: B — Homeowners have the option to prepay their mortgages at any time (especially when interest rates fall), returning principal to MBS investors faster than expected and at a time when reinvestment rates are lower
Explanation: B is correct: prepayment risk is the risk that homeowners repay principal faster than scheduled, typically through refinancing when interest rates fall. This is bad for MBS investors (similar to a call option exercised against them) because they receive principal back when rates are low and must reinvest at lower rates. A is wrong — prepayment reduces the balance. C is wrong — rate rises reduce prepayment (extension risk). D is wrong — credit downgrades are credit risk.
Question 313
A collateralised debt obligation (CDO) is a structured credit product that:
Select an option first.
Correct answer: B — Issues multiple tranches of securities with different priorities for cash flows and losses — senior tranches are most protected; equity tranches absorb first losses
Explanation: B is correct: a CDO pools credit-risky assets (loans, bonds, ABS) and issues tranches with different risk profiles: senior tranches receive cash flows first and absorb losses last (lowest yield, highest rating); mezzanine tranches are in the middle; equity tranches receive residual cash flows but absorb losses first (highest yield, highest risk). B is correct. A is wrong — CDOs have multiple tranches. C is wrong — equity tranches have no principal guarantee. D is wrong — CDOs pool credit-risky assets.
Question 314
The waterfall structure in a CDO determines:
Select an option first.
Correct answer: A — The order in which tranches receive cash flows — senior tranches receive interest and principal before mezzanine and equity tranches
Explanation: A is correct: the waterfall (cash flow priority) is central to CDO structuring. Cash flows from the underlying pool are distributed in priority order: senior noteholders first (interest, then principal), then mezzanine noteholders, then equity holders receive any residual. Losses flow in reverse — equity absorbs losses first. A is correctly describes the waterfall. B is wrong — collateral type is a separate feature. C is wrong — ratings are assigned based on the structure. D is wrong — prepayment affects the cash flows but is not the waterfall itself.
Question 315
An interest rate cap is economically equivalent to a portfolio of:
Select an option first.
Correct answer: B — European call options (caplets) on the reference interest rate — one caplet for each reset period of the cap
Explanation: B is correct: an interest rate cap is a portfolio of caplets, where each caplet is a call option on the reference rate (e.g. 3-month SOFR) for one specific accrual period. Each caplet pays max(0, L − K) × notional × Δt at the end of the relevant period. B is correct. A is wrong — swaps exchange fixed and floating cash flows, not just pay when rates exceed a cap. C is wrong — futures have linear payoffs. D is wrong — put on bonds = caplet (since bond prices fall when rates rise, but this is a derived equivalence, not the primary description).
Question 316
The PSA (Public Securities Association) prepayment model for MBS:
Select an option first.
Correct answer: B — Assumes prepayment rates increase from 0.2% CPR in month 1 to 6% CPR by month 30 (at 100% PSA), and remain at 6% thereafter — modelling the 'seasoning' of mortgage pools
Explanation: B is correct: the PSA model specifies that at 100% PSA, the conditional prepayment rate (CPR) ramps up from 0.2% per annum in month 1, increasing by 0.2% per month for 30 months until reaching 6% CPR by month 30, then remaining flat at 6% for the remaining life. Actual prepayment speeds are quoted as percentages of PSA (e.g. 150 PSA = 1.5× the base case). A is wrong — 6% is the asymptote, not the constant rate. C is wrong — PSA models prepayment throughout the life. D is wrong — CPR is capped at 6% under 100% PSA.
Question 317
The 'Z-tranche' (accrual bond) in a CMO (collateralised mortgage obligation) is characterised by:
Select an option first.
Correct answer: B — Receiving no cash flows until all earlier tranches are paid off — interest accrues and is added to principal; it provides more predictable cash flows to earlier tranches
Explanation: B is correct: the Z-tranche (accrual or 'zombie' bond) defers all cash flow receipt until earlier tranches are retired. During the lockout period, interest accrues on the Z-bond and is added to its principal balance. By locking up Z-tranche cash flows, earlier tranches receive more stable (and potentially accelerated) principal payments. A is wrong — Z-tranche receives cash flows last. C is wrong — it is typically the most junior (non-equity) tranche. D is wrong — Z-tranches have the longest average life.
Question 318
The difference between an asset-backed security (ABS) and a mortgage-backed security (MBS) is:
Select an option first.
Correct answer: B — MBS is backed specifically by residential or commercial mortgage loans; ABS is the broader category backed by other types of financial assets (auto loans, credit card receivables, student loans, etc.)
Explanation: B is correct: MBS is a specific type of ABS backed by pools of mortgage loans. ABS in the broader sense includes securities backed by non-mortgage assets: auto loans, credit card receivables, student loans, equipment leases, etc. B correctly identifies MBS as a subset of ABS. A is wrong — they differ in collateral type. C is wrong — government guarantees apply to agency MBS, not all ABS vs MBS. D is wrong — private label MBS also exists.
Question 319
The option-adjusted spread (OAS) of a bond is:
Select an option first.
Correct answer: B — The spread over the benchmark risk-free rate after removing the value of embedded options (such as call or prepayment options) — OAS reflects the pure credit and liquidity spread
Explanation: B is correct: OAS is the constant spread added to each node of an interest rate tree such that the model price of the bond (including any embedded options) equals its market price. By removing the option's impact, OAS represents the spread for credit and liquidity risk alone. A is wrong — that is the Z-spread. C is wrong — that is the bid-ask spread. D is wrong — that describes the concept of the Z-spread or credit spread more generally.
Question 320
Corporate bonds typically have higher yields than government bonds of the same maturity because:
Select an option first.
Correct answer: B — Corporate bonds carry credit risk (default risk) and often lower liquidity — investors demand a credit spread (yield premium) as compensation
Explanation: B is correct: the credit spread on corporate bonds reflects the additional risk born by investors: default risk (probability × severity of loss) and typically lower liquidity compared to benchmark government bonds. This spread is the excess yield above the government bond yield required to attract investors. A is wrong — government bonds are typically more liquid. C is wrong — tax treatment is not the primary driver of yield spreads. D is wrong — duration is not the determinant.
Question 321
A high-yield (junk) bond is a corporate bond rated:
Select an option first.
Correct answer: B — Below investment grade (below BBB− by S&P and below Baa3 by Moody's)
Explanation: B is correct: investment-grade bonds are rated BBB−/Baa3 and above. High-yield (or 'junk') bonds are rated below investment grade — BB+/Ba1 or lower. They offer higher yields to compensate for their greater default risk. A is wrong — AAA to AA are the highest investment-grade ratings. C is wrong — both S&P and Moody's rate high-yield bonds. D is wrong — issuance is not restricted to small companies.
Question 322
Event risk for corporate bondholders refers to:
Select an option first.
Correct answer: B — A sudden adverse event (leveraged buyout, recapitalisation, spin-off, regulatory action) that causes a significant deterioration in the bond's credit quality and price
Explanation: B is correct: event risk is the risk of a sudden, often unpredictable corporate action or external event that dramatically changes the issuer's credit profile. Classic examples include leveraged buyouts (where new debt is loaded onto the company) or regulatory changes. A is wrong — interest rate risk is a separate category. C is wrong — upgrades benefit bondholders. D is wrong — coupon reset is a floating-rate feature.
Question 323
A bond indenture is:
Select an option first.
Correct answer: B — The legal document specifying the terms and conditions of a bond issue — including covenants, security provisions, maturity, coupon, and the role of the trustee
Explanation: B is correct: the indenture is the legal contract between the bond issuer and bondholders (represented by a trustee). It specifies all material terms: payment obligations, security/collateral, covenants (restrictions on the issuer's actions), redemption provisions, and bondholder rights in default. A is wrong — price history is not in the indenture. C is wrong — the underwriting agreement is separate. D is wrong — settlement instructions are operational, not the indenture.
Question 324
The term structure of credit spreads typically shows:
Select an option first.
Correct answer: B — Credit spreads for investment-grade bonds often increase with maturity; for high-yield bonds, credit spreads may be higher at shorter maturities (reflecting near-term distress risk) and lower at longer maturities
Explanation: B is correct: investment-grade spreads tend to rise with maturity (more credit risk accumulates over longer periods). For distressed high-yield issuers, the term structure is often inverted — near-term default risk is high (high short-term spreads) but if the company survives, long-term risk may be lower. A is wrong — spreads vary with maturity. C is wrong — US Treasuries have zero default spread by definition, but this is specific, not 'always'. D is wrong — lower credit quality means higher spreads, not lower.
Question 325
The effective duration of a callable bond is:
Select an option first.
Correct answer: B — Less than its modified duration — when rates fall, the call option's value increases, damping the bond's price appreciation (negative convexity)
Explanation: B is correct: a callable bond exhibits negative convexity when rates are low (near or below the call threshold). As rates fall, the probability of the bond being called rises, limiting the bond's price appreciation. This means the effective duration (option-adjusted) is shorter than the equivalent non-callable bond's duration. A is wrong — callable bonds are less rate-sensitive than equivalent non-callable bonds. C is wrong — the call option reduces effective duration. D is wrong — zero duration would mean no rate sensitivity.
Question 326
The yield to maturity (YTM) of a bond assumes:
Select an option first.
Correct answer: B — That all coupon payments are reinvested at the YTM rate, and the bond is held to maturity
Explanation: B is correct: YTM is the internal rate of return assuming: (1) the bond is held to maturity; (2) all coupon payments are reinvested at the YTM rate. In practice, reinvestment rates change over time, so realised return may differ from YTM. A is wrong — reinvestment at 'current market rate' is not the YTM assumption. C is wrong — yield to call (YTC) assumes earliest call. D is wrong — bonds can have any price.
Question 327
The Z-spread of a bond is:
Select an option first.
Correct answer: A — The spread added to each Treasury spot rate to make the PV of cash flows equal to the bond's market price
Explanation: A is correct: the Z-spread (zero-volatility spread) is a constant spread added to each spot rate on the Treasury curve such that the present value of the bond's cash flows equals its market price. Unlike OAS, the Z-spread does not adjust for embedded options. A is correct. B is wrong — Z-spread uses the entire spot curve. C is wrong — OAS further removes the option component. D is wrong — CDS spreads are a market credit instrument.
Question 328
A swaption is an option that gives the holder:
Select an option first.
Correct answer: A — The right to enter into an interest rate swap at a specified future date with a pre-agreed fixed rate (the strike or swaption rate)
Explanation: A is correct: a swaption gives the holder the right (not obligation) to enter into a specified interest rate swap at a pre-agreed fixed rate (strike) on or before a specific future date. A payer swaption gives the right to enter as the fixed-rate payer; a receiver swaption gives the right to enter as the fixed-rate receiver. A is correct. B is wrong — bond options are different instruments. C is wrong — swaptions are options (right, not obligation). D is wrong — swap extension is a different mechanism.
Question 329
Greeks for interest rate options differ from equity options in that:
Select an option first.
Correct answer: B — The underlying is an interest rate (not a price), so the relationship between price and yield means that when rates rise, underlying bond prices fall — this affects interpretation of delta and other Greeks
Explanation: B is correct: when dealing with interest rate options (caps, floors, swaptions), the 'underlying' is typically the interest rate itself. Since bond prices and yields move inversely, the direction of Greeks must be carefully interpreted. For example, a cap (call on rates) has positive delta with respect to the rate but is effectively a put on the underlying bond price. B correctly identifies this nuance. A is wrong — Greeks apply to all options. C is wrong — Greeks are used in addition to, not replaced by, duration/convexity. D is wrong — not all rate options have negative delta.
Question 330
The binomial model for option pricing converges to the Black-Scholes price when:
Select an option first.
Correct answer: B — The number of time steps increases (steps approach infinity) and step size approaches zero — the discrete binomial tree approximates the continuous lognormal process
Explanation: B is correct: as the number of binomial steps n → ∞ (and the length of each step Δt → 0), the binomial model converges to the continuous BSM model. The lognormal distribution emerges from the limit of the discrete binomial process. B is correct. A is wrong — fewer steps give less accuracy. C is wrong — zero volatility gives a trivial case. D is wrong — risk-neutral pricing does not require this.
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