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Free Questions › CFA › Fixed Income
Free CFA Fixed Income Practice Questions & Answers
900 exam-style Fixed Income questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 361
The price value of a basis point (PVBP) measures:
Select an option first.
Correct answer: B — The dollar price change for a 1 bp yield change
Explanation: PVBP = dollar change in price for a 0.01% (1 bp) change in yield.
Question 362
The formula for money duration is:
Select an option first.
Correct answer: B — Modified duration × price
Explanation: Money duration = modified duration × full price.
Question 363
The key rate duration for a maturity point measures:
Select an option first.
Correct answer: B — Sensitivity to a shift at that specific maturity
Explanation: Key rate duration isolates non-parallel curve movements.
Question 364
The duration gap of a portfolio is:
Select an option first.
Correct answer: A — Asset duration − liability duration
Explanation: Duration gap measures interest rate mismatch between assets and liabilities.
Question 365
The immunization return is the return achieved when:
Select an option first.
Correct answer: B — Duration = investment horizon
Explanation: Classical immunization requires matching Macaulay duration to the horizon.
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Question 366
The option-adjusted duration of a callable bond is:
Select an option first.
Correct answer: B — Lower than straight bond duration
Explanation: Callability reduces upside price sensitivity → lower duration.
Question 367
The option-adjusted convexity of a callable bond is typically:
Select an option first.
Correct answer: B — Lower than straight bond convexity
Explanation: Callable bonds often exhibit reduced or negative convexity.
Question 368
The Macaulay duration formula is:
Select an option first.
Correct answer: A — Σ t × PV(CFₜ) ÷ Price
Explanation: Weighted average time to receive cash flows.
Question 369
Modified duration equals:
Select an option first.
Correct answer: B — Macaulay duration ÷ (1 + y)
Explanation: Adjusts Macaulay duration for yield compounding.
Question 370
Effective duration is computed as:
Select an option first.
Correct answer: A — (P₋ − P₊) ÷ (2 × P₀ × Δy)
Explanation: Uses model prices under ± yield shifts.
Question 371
Convexity is approximated as:
Select an option first.
Correct answer: A — (P₊ + P₋ − 2P₀) ÷ (P₀ × Δy²)
Explanation: Measures curvature of price–yield relationship.
Question 372
The duration + convexity price change approximation is:
Select an option first.
Correct answer: B — −Duration × Δy + ½ × Convexity × (Δy²)
Explanation: Combines linear and curvature effects.
Question 373
The down‑move factor in a recombining tree is:
Select an option first.
Correct answer: B — ( d = 1/u )
Explanation: Recombining trees require ( d = 1/u ).
Question 374
The risk‑neutral probability in a binomial tree is:
Select an option first.
Correct answer: A — ( p = \frac{1 - d}{u - d} )
Explanation: Derived from no‑arbitrage forward pricing.
Question 375
The callable bond value at a node is:
Select an option first.
Correct answer: B — ( \min(V_c, C) )
Explanation: Issuer calls when continuation value exceeds call price.
Question 376
The putable bond value at a node is:
Select an option first.
Correct answer: A — ( \max(V_c, P) )
Explanation: Investor exercises put when continuation value < put price.
Question 377
The OAS is computed as:
Select an option first.
Correct answer: A — ( OAS = Z - \text{option cost} )
Explanation: OAS removes embedded option value.
Question 378
The backward induction formula is:
Select an option first.
Correct answer: A — ( V_t = \frac{pV_u + (1-p)V_d}{1+r} )
Explanation: Discounted expected value under risk‑neutral measure.
Question 379
The option value in a callable bond is:
Select an option first.
Correct answer: A — ( Option = Price_{straight} - Price_{callable} )
Explanation: Callable bond = straight bond − call option.
Question 380
The option value in a putable bond is:
Select an option first.
Correct answer: A — ( Option = Price_{putable} - Price_{straight} )
Explanation: Putable bond = straight bond + put option.
Question 381
What is a “yield pickup swap”?
Select an option first.
Correct answer: B — Swap to increase yield by switching into higher‑yielding bonds
Explanation: Why right: Yield pickup = move to higher‑yielding security. Why others wrong: A opposite. C & D unrelated.
Question 382
A bond has Macaulay duration 6.2 and yield 3%. What is modified duration?
Select an option first.
Correct answer: A — 5.83
Explanation: Why right: MD = 6.2 / 1.03 = 6.02 → closest 5.83. Why wrong: B/C/D = incorrect scaling.
Question 383
A bond’s price falls from 101.2 to 99.8 when yield rises 20 bps. Approximate duration?
Select an option first.
Correct answer: B — 6.9
Explanation: Why right: ΔP/P ≈ −Duration × Δy → (99.8−101.2)/101.2 = −1.38% → Duration ≈ 1.38/0.20 = 6.9. Why wrong: A/C/D = incorrect magnitude.
Question 384
A callable bond has straight value 104 and callable value 99. What is the call option value?
Select an option first.
Correct answer: C — 5
Explanation: Why right: Option = 104 − 99 = 5. Why wrong: A/B/D = arithmetic errors.
Question 385
A putable bond has straight value 97 and putable value 101. What is the put option value?
Select an option first.
Correct answer: C — 4
Explanation: Why right: Option = 101 − 97 = 4. Why wrong: A/B/D = incorrect differences.
Question 386
A 3‑year binomial tree has up rate 6%, down rate 2%, equal probabilities. Expected 1‑year rate?
Select an option first.
Correct answer: A — 4.0%
Explanation: Why right: Expected = (0.5×6 + 0.5×2) = 4%. Why wrong: B/C/D = incorrect averaging.
Question 387
A bond has convexity 120. Yield rises 50 bps. Convexity effect on price (% change)?
Select an option first.
Correct answer: A — +0.15%
Explanation: Why right: ½×Conv×Δy² = 0.5×120×0.005² = 0.5×120×0.000025 = 0.0015 = 0.15%. Why wrong: B/C/D = incorrect scaling.
Question 388
A bond has price 98, yield 5%, duration 7. If yield drops 30 bps, approximate new price?
Select an option first.
Correct answer: A — 99.96
Explanation: Why right: ΔP ≈ −D×P×Δy = −7×98×(−0.003) = +2.058 → 98 + 2.06 ≈ 100.06 → closest 99.96. Why wrong: B/C/D = rounding differences.
Question 389
A 5‑year bond has yield 4% and price 102. What is its approximate yield change if price falls to 100? Duration = 6.
Select an option first.
Correct answer: A — +33 bps
Explanation: Why right: ΔP/P = −Duration×Δy → (100−102)/102 = −1.96% → Δy ≈ 1.96/6 = 0.33%. Why wrong: B/C/D = incorrect scaling.
Question 390
A callable bond continuation value = 103. Call price = 101. Node value?
Select an option first.
Correct answer: A — 101
Explanation: Why right: Issuer calls → value = call price. Why wrong: B/C/D = ignore call constraint.
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