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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 391
The 'recovery rate' in credit risk modelling represents:
Select an option first.
Correct answer: B — The fraction of the face value of a defaulted debt that creditors expect to recover after the default resolution process
Explanation: B is correct: recovery rate (RR) = amount recovered / face value of debt. Loss given default (LGD) = 1 − RR. Recovery rates vary by seniority: secured senior debt recovers more than subordinated unsecured debt. Average empirical recovery rates for senior unsecured bonds are approximately 40-50%. B is correct. A is wrong — that is probability of repayment (1 − PD). C is wrong — trading price post-default is related but distinct. D is wrong — bankruptcy duration is separate.
Question 392
In the pricing of mortgage-backed securities, the 'static cash flow yield' assumes:
Select an option first.
Correct answer: B — A fixed prepayment speed (PSA or CPR assumption) that remains constant throughout — the single yield that discounts all projected cash flows to equal the market price, ignoring the option nature of prepayment
Explanation: B is correct: the static cash flow yield (or cash flow yield) is computed by assuming a fixed prepayment speed (e.g. 150 PSA) and finding the IRR of the resulting projected cash flows given the market price. It is 'static' because the prepayment assumption doesn't change with rate scenarios — it does not capture the option value of the prepayment right. A is wrong — static yield uses a prepayment assumption (not zero). C is wrong — prepayment occurs throughout the life. D is wrong — seasonal variation is part of some models.
Question 393
A 'floor' in a floating-rate loan effectively gives the lender:
Select an option first.
Correct answer: B — A minimum interest rate on the loan — if SOFR falls below the floor, the borrower still pays the floor rate, protecting the lender's income
Explanation: B is correct: a rate floor on a floating-rate loan ensures the lender receives at least the floor rate even if the reference rate (e.g. SOFR) falls below it. This is beneficial for lenders (reduces income risk from low rates). The floor is an embedded option — equivalent to a series of floorlets (put options on the reference rate). A is wrong — that is a demand deposit or callable loan. C is wrong — financial loan, not commodity. D is wrong — that is an extension option.
Question 394
The 'mortgage duration' of a passthrough MBS is typically much shorter than the stated loan maturity because:
Select an option first.
Correct answer: B — Prepayments (refinancing, home sales) return principal ahead of schedule — effectively shortening the average life and duration of the MBS
Explanation: B is correct: 30-year mortgages rarely run to their full term. Homeowners refinance when rates fall, or sell their homes. The weighted average life (WAL) of a 30-year passthrough MBS at a typical prepayment speed might be 8-10 years, and its duration correspondingly shorter. This prepayment reduces duration but creates reinvestment risk for investors. A is wrong — mortgages are often held to maturity by servicers but prepay economically. C is wrong — no legal duration limit. D is wrong — MBS interest is not front-loaded per se.
Question 395
The 'Heston model' for option pricing is a stochastic volatility model where:
Select an option first.
Correct answer: B — Both the asset price and its variance follow correlated stochastic processes — allowing the model to capture the volatility smile and term structure observed in markets
Explanation: B is correct: the Heston (1993) model specifies: dS = μS dt + √v S dW₁ and dv = κ(θ − v)dt + ξ√v dW₂, where v is the variance (not volatility), κ is mean reversion speed, θ is long-run variance, ξ is vol of vol, and ρ is the correlation between the two Brownian motions. The correlation ρ produces the volatility skew. A is wrong — Heston has stochastic volatility. C is wrong — Heston prices differ from BSM due to the smile. D is wrong — the risk-free rate is typically constant in Heston.
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Question 396
The 'key rate duration' (KRD) analysis of a bond portfolio measures:
Select an option first.
Correct answer: B — The sensitivity of portfolio value to changes in yields at specific maturity points on the yield curve — allowing identification of exposure to curve reshaping (non-parallel shifts)
Explanation: B is correct: KRD measures how the portfolio value changes when the yield at a specific maturity (e.g. 2Y, 5Y, 10Y, 30Y) changes by 1 bps while all other maturities remain unchanged. The sum of all KRDs equals the portfolio's total duration. KRDs are used to identify and hedge exposure to curve twists and butterflies, not just parallel shifts. A is wrong — parallel shift gives total DV01/duration. C is wrong — KRD is interest rate, not credit. D is wrong — KRD is a portfolio-level measure by maturity bucket.
Question 397
An 'asset swap' converts the cash flows of a fixed-rate bond into floating-rate cash flows. The 'asset swap spread' represents:
Select an option first.
Correct answer: B — The fixed-rate coupon paid in the swap minus the par swap rate — effectively the additional spread above the floating benchmark that reflects the bond's credit and liquidity risk
Explanation: B is correct: in an asset swap, the investor buys a bond at par (or market price) and enters a swap: pays the bond's fixed coupon and receives SOFR + spread. The asset swap spread = the SOFR + spread received. It represents the credit and liquidity premium of the bond expressed as a spread over the floating benchmark. Bonds with higher credit risk have wider asset swap spreads. A is wrong — not literally the credit spread (depends on bond structure and pricing). C is wrong — YTM is the gross bond yield. D is wrong — bid-offer is a transaction cost.
Question 398
A 'puttable bond' is beneficial to the investor because:
Select an option first.
Correct answer: B — The investor has the right to sell the bond back to the issuer at a specified price (typically par) before maturity — providing downside protection if rates rise and bond prices fall
Explanation: B is correct: a put option embedded in a bond gives the holder the right to 'put' (sell back) the bond to the issuer at par on specified dates. If interest rates rise (bond prices fall), the investor can exercise the put and reinvest at higher rates. The put provides a price floor for the bond. Investors pay for this protection via a lower yield than an equivalent non-puttable bond. A is wrong — that describes a callable bond (issuer's option). C is wrong — that is a convertible. D is wrong — that is a step-up coupon feature.
Question 399
The 'cheapness' of an option strategy expressed in implied volatility terms means:
Select an option first.
Correct answer: B — The option's implied volatility is below its realised (historical) volatility — meaning the option appears underpriced relative to actual price movements, suggesting it may be worth buying
Explanation: B is correct: in volatility trading, an option is 'cheap' when its implied volatility (IV) is below the subsequently realised volatility of the underlying. If you buy an option when IV < realised vol, you pay less than what the actual movements justify — a positive P&L. Options traders compare IV to historical/realised vol to identify cheap/expensive options. A is wrong — dollar premium is irrelevant for relative valuation. C is wrong — short time to expiry increases time decay. D is wrong — moneyness is separate from cheapness.
Question 400
The 'modified duration' of a bond portfolio is additive in the sense that:
Select an option first.
Correct answer: B — The portfolio modified duration = Σ (market value weight_i × modified duration_i) — a weighted average of individual bond durations
Explanation: B is correct: portfolio modified duration = Σ w_i × D_i, where w_i = market value of bond i / total portfolio market value, and D_i = modified duration of bond i. This weighted average is the portfolio's aggregate interest rate sensitivity. A is wrong — adding bonds changes portfolio duration based on their individual durations. C is wrong — bonds with different durations can be in the same portfolio. D is wrong — portfolio duration is well-defined.
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