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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 811
A bond has modified duration 9.0 and price $980. Yields decline by 50 bps. The duration-only estimated price change is:
Select an option first.
Correct answer: A — $44.10
Explanation: A is correct. ΔP ≈ ModDur × Price × Δy = 9.0 × $980 × 0.005 = $44.10 (price rises when yields fall). Duration-only estimate ignores convexity. B uses price $1,000. C uses 4% duration. D overstates.
Question 812
A 5-year bond has annual coupon 8%, $1,000 par, and Macaulay duration ≈ 4.27 years. An investor has a 4.27-year investment horizon. If rates immediately fall after purchase, what dominates?
Select an option first.
Correct answer: C — Both risks perfectly offset — this is immunization
Explanation: C is correct. When the investment horizon equals the Macaulay duration, the positive price gain from falling rates is offset by reduced reinvestment income—and vice versa for rate rises. This is the essence of immunization: the two risks exactly cancel at the duration-matched horizon.
Question 813
A CLO has total assets of $500M: Senior = $400M, Mezzanine = $75M, Equity = $25M. If losses = 6% ($30M), how are losses distributed?
Select an option first.
Correct answer: A — Equity absorbs $25M; mezzanine absorbs $5M; senior absorbs $0
Explanation: A is correct. Losses flow bottom-first: equity ($25M) absorbs first. Remaining losses = $30M − $25M = $5M, absorbed by mezzanine. Senior tranche is unaffected. B is wrong—losses follow seniority. C reverses the order.
Question 814
A bond manager holds $100M of bonds with duration 8.0 and wants to target duration 5.0 using T-note futures (duration 7.0, notional $100,000 per contract). How many contracts to sell?
Select an option first.
Correct answer: A — 428.57 ≈ 429 contracts
Explanation: A is correct. Contracts = (D_target − D_current) × MV / (D_futures × Futures notional) = (5.0 − 8.0) × $100,000,000 / (7.0 × $100,000) = −$300,000,000 / $700,000 = −428.57. Sell 429 contracts. B uses duration difference with round numbers incorrectly.
Question 815
Bond A: price $950, modified duration 7. Bond B: price $1,050, modified duration 4. Both holdings are $10M face. Yields rise 50 bps. Which bond loses more in dollar terms?
Select an option first.
Correct answer: A — Bond A loses $332,500; Bond B loses $210,000 — Bond A loses more
Explanation: A is correct. Bond A MV = 0.95 × $10M = $9.5M. Loss A = 7 × $9.5M × 0.005 = $332,500. Bond B MV = 1.05 × $10M = $10.5M. Loss B = 4 × $10.5M × 0.005 = $210,000. Bond A loses more. B doubles the yield change.
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Question 816
A bond has face $1,000,000. Recovery rate = 35%. What is the dollar loss given default?
Select an option first.
Correct answer: A — $650,000
Explanation: A is correct. LGD = (1 − Recovery rate) × Face = (1 − 0.35) × $1,000,000 = 0.65 × $1,000,000 = $650,000. The recovery amount is $350,000 (= 35% × $1M). B is the recovery (not LGD). C is the full face.
Question 817
Portfolio: Bond A ($5M MV, spread duration 3.0) + Bond B ($5M MV, spread duration 6.0). Credit spreads widen by 20 bps. Dollar loss:
Select an option first.
Correct answer: A — −$90,000
Explanation: A is correct. Bond A spread loss = −3.0 × $5M × 0.002 = −$30,000. Bond B spread loss = −6.0 × $5M × 0.002 = −$60,000. Total = −$90,000. B doubles the spread change. C uses 10 bps. D uses 2% change.
Question 818
A 5-year amortizing bond pays equal annual principal of $200,000 plus 6% interest on outstanding balance. Initial balance = $1,000,000. What is the total year 1 payment?
Select an option first.
Correct answer: A — $260,000
Explanation: A is correct. Year 1 payment = Principal + Interest = $200,000 + 6% × $1,000,000 = $200,000 + $60,000 = $260,000. B is only principal. C is only interest. D uses $200,000 × 0.6 + $200,000.
Question 819
A putable bond is valued at $98. The equivalent non-putable bond is worth $95. What is the implied value of the put option?
Select an option first.
Correct answer: A — $3
Explanation: A is correct. Value of putable = Value of straight + Value of put → $98 = $95 + Put → Put = $3. B subtracts both. C is the putable price. D overstates the put value.
Question 820
A 10-year zero-coupon bond has modified duration 9.434 (= 10/1.06 at 6% YTM). Its market value is $558,395. The PVBP of this position is:
Select an option first.
Correct answer: A — $526.84
Explanation: A is correct. PVBP = ModDur × MV × 0.0001 = 9.434 × $558,395 × 0.0001 = $526.84. B divides by 10. C uses $1,000,000 face as price. D divides by 10 again.
Question 821
A 30-year bond has Macaulay duration 18 years and YTM 6% (annual). Modified duration = 18/1.06 = 16.98. If yields rise 100 bps, approximate percentage price change:
Select an option first.
Correct answer: A — −16.98%
Explanation: A is correct. %ΔP ≈ −ModDur × Δy = −16.98 × 0.01 = −16.98%. B has wrong sign. C uses Macaulay duration. D subtracts an arbitrary amount.
Question 822
A bond portfolio has total duration of 5.2 and total market value of $50,000,000. A 100 bps parallel rise in yields would cause an approximate dollar loss of:
Select an option first.
Correct answer: A — −$2,600,000
Explanation: A is correct. Dollar change ≈ −Duration × MV × Δy = −5.2 × $50,000,000 × 0.01 = −$2,600,000. B divides by 10. C multiplies by 10. D divides by 5.
Question 823
A CDS buyer pays a premium of 80 bps per year on notional of $50,000,000. What is the annual premium payment?
Select an option first.
Correct answer: A — $400,000
Explanation: A is correct. Annual CDS premium = Notional × spread = $50,000,000 × 0.0080 = $400,000. B divides by 10. C doubles the spread. D multiplies by 10.
Question 824
An ABS tranche has outstanding balance $50,000,000 and monthly principal payments of $1,200,000. Approximate annualized CPR (using CPR ≈ SMM × 12):
Select an option first.
Correct answer: B — 28.8%
Explanation: B is correct. SMM = $1,200,000/$50,000,000 = 2.4% per month. Approximate CPR ≈ SMM × 12 = 2.4% × 12 = 28.8%. The exact CPR using compounding is ~25.2%, but the exam-level approximation (SMM × 12) gives 28.8%. A is just the SMM.
Question 825
An immunized bond portfolio has Macaulay duration 6.5 years and a liability horizon of 5.0 years. The duration gap is +1.5 years. If rates rise 50 bps, what is the approximate impact?
Select an option first.
Correct answer: A — Price declines more than reinvestment gains — net loss for the portfolio
Explanation: A is correct. A positive duration gap (duration > horizon) means price risk dominates. When rates rise, the portfolio's price falls by more than reinvestment income increases. This creates a net loss relative to the target. B has the wrong direction. C requires a zero gap. D is wrong.
Question 826
Modified duration is best described as the approximate percentage change in a bond's price for:
Select an option first.
Correct answer: C — A 100 basis point (1%) change in the bond's yield
Explanation: Modified duration measures the approximate % price change for a 100 bps (1%) change in yield. It is the most common measure of interest rate sensitivity. A describes DV01/dollar duration per bp. B is not wrong but less precise. D is credit risk, not duration.
Question 827
Macaulay duration is best interpreted as:
Select an option first.
Correct answer: B — The present-value-weighted average time to receive the bond's cash flows
Explanation: Macaulay duration is the time-weighted present value of cash flows — essentially the average time an investor waits to receive the bond's cash flows. It is measured in years. A describes modified duration. C is not a standard concept. D is incorrect.
Question 828
Convexity is a measure of:
Select an option first.
Correct answer: B — How the bond's duration changes as yields change
Explanation: Convexity captures the curvature of the price-yield relationship. Duration gives the linear approximation; convexity corrects for the fact that the actual relationship is curved (prices rise more than duration predicts when yields fall, and fall less when yields rise). A, C, D are unrelated to convexity.
Question 829
A bond with high positive convexity is beneficial to an investor because:
Select an option first.
Correct answer: B — The bond's price increases more than predicted by duration when rates fall, and decreases less when rates rise
Explanation: Positive convexity means the price-yield curve bows toward the investor. When yields fall, price gains are larger than duration predicts; when yields rise, price losses are smaller. This asymmetry is favorable. A, C, and D are incorrect.
Question 830
Dollar duration (DV01) measures:
Select an option first.
Correct answer: B — The approximate dollar change in a bond's price for a 1 basis point change in yield
Explanation: DV01 (dollar value of a basis point) tells you the dollar gain/loss for a 1 bps move in yield. It equals modified duration × price × 0.0001. This is essential for hedging calculations. A, C, D are not DV01.
Question 831
Which of the following bonds has the lowest duration?
Select an option first.
Correct answer: C — A 5-year floating-rate bond with quarterly resets
Explanation: Floating-rate bonds reset their coupons frequently, so their price stays close to par regardless of rate moves. Their effective duration is very short (approximately time to next reset). A has maximum duration (zero coupon). B and D are longer.
Question 832
Which of the following characteristics is associated with a callable bond compared to an otherwise identical non-callable bond?
Select an option first.
Correct answer: C — Negative convexity at low yield levels
Explanation: When yields fall far enough, the issuer is likely to call the bond, capping price appreciation. This creates negative convexity — the price-yield curve bends unfavorably. Callable bonds also have lower prices (D: higher yields) than non-callable equivalents, not higher (B). A is wrong — callable bonds have shorter effective duration due to the call.
Question 833
The probability of default and the loss given default are combined to calculate:
Select an option first.
Correct answer: C — Expected credit loss
Explanation: Expected loss = Probability of Default × Loss Given Default (= 1 − Recovery Rate). This is the core framework for pricing credit risk. A is interest rate sensitivity. B is a yield measure. D is a spread measure.
Question 834
Credit migration risk refers to:
Select an option first.
Correct answer: B — The risk that the bond's credit rating is downgraded
Explanation: Credit migration risk is the risk that an issuer's credit quality deteriorates, causing a rating downgrade and therefore a wider spread and lower bond price. A is currency risk. C is a form of default risk. D is interest rate risk.
Question 835
A mortgage-backed security (MBS) is most exposed to which unique risk not found in standard corporate bonds?
Select an option first.
Correct answer: C — Prepayment risk
Explanation: MBS holders face prepayment risk — when rates fall, homeowners refinance, returning principal early. This forces investors to reinvest at lower rates. Standard bonds don't have this risk because the issuer cannot prepay without a call provision. A affects both. B affects all bonds. D affects both.
Question 836
In the context of securitization, a 'waterfall' structure refers to:
Select an option first.
Correct answer: B — The sequential priority in which cash flows are distributed to different tranches
Explanation: The waterfall defines the payment priority: senior tranches receive cash flows first; junior (subordinate) tranches receive what remains. Losses are absorbed from the bottom up. A, C, and D describe other aspects of securitization, not the waterfall.
Question 837
Which of the following best describes credit enhancement in a securitized structure?
Select an option first.
Correct answer: B — Mechanisms that protect senior bondholders from credit losses on the underlying pool
Explanation: Credit enhancement techniques (overcollateralization, subordination, reserve accounts, third-party guarantees) absorb losses before they reach senior tranches. This makes senior tranches safer and earns higher ratings. A is not credit enhancement. C is one possible form but not the only one. D is hedging, not credit enhancement.
Question 838
Overcollateralization as a credit enhancement means:
Select an option first.
Correct answer: B — The face value of assets in the pool exceeds the face value of bonds issued against them
Explanation: In overcollateralization, the collateral pool is larger than the securities issued. For example, $110M of loans might back $100M of bonds, so the first $10M of losses are absorbed before any bondholder is harmed. A, C, and D describe other structures.
Question 839
A collateralized debt obligation (CDO) is best described as:
Select an option first.
Correct answer: B — A structured security that pools various debt instruments and issues tranches with different risk-return profiles
Explanation: CDOs pool debt instruments (bonds, loans, ABS) and issue tranches with varying seniority. Senior tranches are safer; equity tranches bear first loss but earn higher returns. A describes a basic MBS. C is an agency security. D is a putable bond.
Question 840
The effective duration of a bond with embedded options is best measured using:
Select an option first.
Correct answer: C — An option-adjusted model that simulates yield scenarios to estimate price sensitivity
Explanation: Effective (option-adjusted) duration requires modeling the option's impact across interest rate scenarios. Because embedded options change expected cash flows as rates move, simple modified duration (which assumes fixed cash flows) is not appropriate. A and B ignore option effects. D is not a standard approach.
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