Free FRM Quantitative Analysis Practice Questions & Answers
400 exam-style Quantitative Analysis questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
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Question 241
Duration of a perpetuity (consol bond paying C per period at yield y) equals:
Select an option first.
Correct answer: B — (1 + y) / y
Explanation: B
Question 242
In the US fixed income market, the benchmark interest rate has shifted from LIBOR to:
Select an option first.
Correct answer: B — SOFR (Secured Overnight Financing Rate), based on transactions in the US Treasury repurchase agreement market
Explanation: B
Question 243
A floating rate note (FRN) with a spread of 50 bps over SOFR has a duration of approximately:
Select an option first.
Correct answer: B — Very short — approximately equal to the time to the next coupon reset date (e.g., 3 months for quarterly resets)
Explanation: B
Question 244
The price of a bond at a premium will converge to:
Select an option first.
Correct answer: B — Par value (face value) by maturity — a process called 'pull to par'
Explanation: B
Question 245
A credit spread option gives the holder:
Select an option first.
Correct answer: B — The right to receive or pay a payment based on the change in credit spread of a reference bond — profiting from spread widening (long spread option) or tightening (short spread option)
Explanation: B
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The dollar duration of a bond portfolio used for hedging calculations equals:
Select an option first.
Correct answer: B — Modified duration × Portfolio value — giving the dollar change in portfolio value per unit change in yield
Explanation: B
Question 247
An increase in credit spread of a corporate bond while the risk-free rate is unchanged will:
Select an option first.
Correct answer: B — Increase the bond's yield (credit spread widens → YTM rises) and decrease its price
Explanation: B
Question 248
The yield to worst (YTW) of a callable bond is:
Select an option first.
Correct answer: B — The lowest of the yields calculated for each possible call date plus maturity — representing the worst-case return the investor would receive assuming the issuer acts adversely
Explanation: B
Question 249
Effective duration for bonds with embedded options differs from modified duration because:
Select an option first.
Correct answer: B — Effective duration accounts for the fact that option exercise changes cash flows when rates change, using price changes from shifting the entire yield curve
Explanation: B
Question 250
The Z-spread on a bond is:
Select an option first.
Correct answer: B — The constant spread added to the entire spot rate curve so that the present value of bond cash flows equals its market price
Explanation: B
Question 251
A barbell portfolio has:
Select an option first.
Correct answer: B — Concentration in very short and very long maturities, matching a target duration but with higher convexity than a bullet portfolio of the same duration
Explanation: B
Question 252
The carry of a bond position represents:
Select an option first.
Correct answer: B — The return from holding a bond position over time, consisting of yield income minus financing cost (repo rate), adjusted for any price changes from rolling down the yield curve
Explanation: B
Question 253
Convexity bias in interest rate swap pricing arises because:
Select an option first.
Correct answer: B — Futures-based forward rates differ from OTC forward rates due to daily mark-to-market (futures settlement) creating a correlation between the futures P&L and the discount rate, requiring a convexity adjustment to swap rates
Explanation: B
Question 254
The risk-neutral dynamics of interest rates in the Vasicek model follow:
Select an option first.
Correct answer: B — dr = κ(θ - r)dt + σ dW — a mean-reverting Ornstein-Uhlenbeck process where κ is the speed of mean reversion, θ is the long-run mean, and σ is the volatility of rate changes
Explanation: B
Question 255
The principal component analysis (PCA) of yield curve changes shows that the first three principal components typically represent:
Select an option first.
Correct answer: B — Level (parallel shift ~80% of variance), Slope/twist (~15%), and Curvature/butterfly (~5%) — together explaining ~99% of yield curve variance
Explanation: B
Question 256
The swap spread (swap rate minus government bond yield) is affected by:
Select an option first.
Correct answer: B — Interbank credit risk, regulatory capital treatment (leverage ratio reducing bank supply of government bonds), funding supply and demand across maturities, and flight-to-quality dynamics during stress
Explanation: B
Question 257
The Fama-Bliss model for the term structure extracts forward rates from Treasury prices and uses them to predict:
Select an option first.
Correct answer: B — Whether current forward rates predict future spot rates better than the expectations hypothesis alone — finding that forward rate 'excess returns' (risk premia) vary with the slope of the yield curve
Explanation: B
Question 258
The Libor Market Model (LMM / BGM model) is used for:
Select an option first.
Correct answer: B — Modelling the dynamics of a set of forward LIBOR/SOFR rates simultaneously, capturing the full yield curve dynamics and allowing consistent pricing of caps, floors, swaptions, and path-dependent interest rate derivatives
Explanation: B
Question 259
Duration weighting in a portfolio swap involves:
Select an option first.
Correct answer: B — Adjusting position sizes so that each bond contributes equally to total portfolio DV01, creating a risk-weighted portfolio rather than a notional-weighted one
Explanation: B
Question 260
Probability of default (PD) refers to:
Select an option first.
Correct answer: B — The likelihood that a borrower will fail to meet its contractual obligations within a specified time horizon
Explanation: B
Question 261
Loss given default (LGD) is:
Select an option first.
Correct answer: B — The percentage of exposure lost when a default occurs, equal to (1 - Recovery Rate)
Explanation: B
Question 262
Exposure at default (EAD) is:
Select an option first.
Correct answer: B — The outstanding credit exposure at the time a default occurs
Explanation: B
Question 263
A credit default swap (CDS) is:
Select an option first.
Correct answer: B — A financial instrument where the protection buyer pays periodic premiums and receives compensation if a reference entity defaults
Explanation: B
Question 264
A credit rating downgrade of a bond issuer typically causes:
Select an option first.
Correct answer: B — Bond price to fall and yield (credit spread) to rise, reflecting increased perceived default risk
Explanation: B
Question 265
Expected Loss (EL) for a credit exposure is:
Select an option first.
Correct answer: B — PD × LGD × EAD — the probability-weighted average loss
Explanation: B
Question 266
Recovery rate in credit risk modelling is:
Select an option first.
Correct answer: B — The fraction of the exposure recovered after a credit event (default), typically expressed as a percentage of the outstanding balance
Explanation: B
Question 267
A credit default swap provides the buyer with:
Select an option first.
Correct answer: B — Insurance-like protection against a credit event of the reference entity — the seller compensates the buyer if a defined credit event (default, restructuring) occurs
Explanation: B
Question 268
Loss Given Default (LGD) for a senior secured loan is typically:
Select an option first.
Correct answer: B — Lower than for senior unsecured debt because collateral reduces the loss upon default — secured creditors have priority claim on collateral assets
Explanation: B
Question 269
A bond rated BB is classified as:
Select an option first.
Correct answer: B — Speculative grade (high-yield / 'junk') — below BBB-/Baa3 is below investment grade
Explanation: B
Question 270
The Merton model for credit risk treats the firm's equity as:
Select an option first.
Correct answer: B — A call option on the firm's assets, with the debt value as the strike price
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