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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 871
A $10 million bond position has a modified duration of 5. A portfolio manager wants to reduce duration to 3 using T-bond futures with a duration of 6 and a futures price of $100,000. How many futures contracts should be sold?
Select an option first.
Correct answer: A — 33
Explanation: Duration reduction needed: (5-3) = 2 years. Dollar duration to reduce = $10M × 2 = $20M years. Futures contracts = $20M / (6 × $100,000) = $20,000,000 / $600,000 = 33.3 ≈ 33. A is correct.
Question 872
A bond with Macaulay duration of 5.3 years has a YTM of 6% (semi-annual). What is the modified duration?
Select an option first.
Correct answer: A — 5.15 years
Explanation: For semi-annual bonds: Modified Duration = Macaulay Duration / (1 + YTM/2) = 5.3 / (1 + 0.03) = 5.3 / 1.03 = 5.15 years. B is Macaulay (unadjusted). C and D are wrong.
Question 873
A portfolio has two bonds: Bond A worth $5M with DV01 of $3,500, and Bond B worth $3M with DV01 of $1,800. What is the total portfolio DV01?
Select an option first.
Correct answer: A — $5,300
Explanation: Portfolio DV01 = Sum of individual DV01s = $3,500 + $1,800 = $5,300. Simple addition since DV01 is additive across positions. B and C are individual DV01s. D is wrong.
Question 874
A corporate bond is priced at $950. If its credit spread widens by 50 bps and its spread duration is 4, what is the approximate new price?
Select an option first.
Correct answer: A — $931
Explanation: % price change = −Spread Duration × ΔSpread = −4 × 0.005 = −2.0%. New price = $950 × (1 − 0.02) = $950 × 0.98 = $931. B shows a price increase (wrong direction). C and D are wrong.
Question 875
A bond has modified duration 6, convexity 50, and price $1,000. If yields rise by 0.5%, what is the estimated price?
Select an option first.
Correct answer: A — $970.63
Explanation: % change = −Mod Dur × Δy + ½ × Convexity × (Δy)² = −6×0.005 + 0.5×50×(0.005)² = −0.030 + 0.000625 = −0.029375. New price = $1,000 × (1 − 0.029375) = $970.63. B ignores convexity. C and D are wrong.
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Question 876
The expected loss on a bond is 0.9%. If the probability of default is 3%, what is the recovery rate?
Select an option first.
Correct answer: B — 70%
Explanation: EL = PD × LGD → 0.009 = 0.03 × LGD → LGD = 0.30 = 30%. Recovery rate = 1 − LGD = 1 − 0.30 = 70%. A is LGD not recovery. C and D are wrong.
Question 877
Two bonds have the same YTM but different maturities. Bond A has a duration of 3 and Bond B has a duration of 8. If yields rise by 1%, the approximate price decline for Bond B versus Bond A is:
Select an option first.
Correct answer: A — Bond B declines 5% more
Explanation: Price change ≈ −Duration × Δy. Bond A: −3%; Bond B: −8%. Difference = 8% − 3% = 5%. Bond B declines ~5 percentage points more. B and C are wrong. D ignores duration differences.
Question 878
A bond has a modified duration of 4 and is priced at $1,000. If yields fall by 75 bps, what is the estimated new price?
Select an option first.
Correct answer: A — $1,030
Explanation: % change = −4 × (−0.0075) = +0.03 = +3%. New price = $1,000 × 1.03 = $1,030. B uses 100 bps. C shows a decrease (wrong direction). D is too high.
Question 879
A bond's price rises from $1,000 to $1,035 when yields fall 50 bps, and falls to $967 when yields rise 50 bps. What is the approximate modified duration?
Select an option first.
Correct answer: A — 6.8
Explanation: ModDur = (P+ − P−) / (2 × P0 × Δy) — wait, using symmetry: avg price change = (1035-1000 + 1000-967)/2 = (35+33)/2 = 34. But modified duration = average % change / Δy = (34/1000) / 0.005 = 0.034/0.005 = 6.8. Answer A.
Question 880
A bond has a Macaulay duration of 6 years and a YTM of 4% (annual). What is the dollar duration of a $100,000 position?
Select an option first.
Correct answer: A — $576,923
Explanation: Modified duration = 6/1.04 = 5.769. Dollar duration = ModDur × Position value = 5.769 × $100,000 = $576,923. B uses Macaulay, not modified. C is a rounding. D is wrong.
Question 881
A bond with convexity of 60 and modified duration of 7 has a price of $1,000. Yields fall 2%. What is the estimated price change?
Select an option first.
Correct answer: B — +15.2%
Explanation: % change = −7×(−0.02) + 0.5×60×(0.02)² = 0.14 + 0.5×60×0.0004 = 0.14 + 0.012 = 0.152 = +15.2%. A ignores convexity. C and D are wrong.
Question 882
A bond has a credit spread of 150 bps and a spread duration of 5. If the spread widens to 200 bps, what is the estimated percentage price change?
Select an option first.
Correct answer: A — -2.5%
Explanation: Spread change = 200 − 150 = 50 bps = 0.005. % Price change = −Spread Duration × ΔSpread = −5 × 0.005 = −2.5%. B has wrong sign. C uses wrong spread change. D is wrong.
Question 883
An MBS pool has $100M outstanding. In a given month, the scheduled principal is $500,000 and the prepayment is $1,200,000. What percentage of the pool was prepaid?
Select an option first.
Correct answer: B — 1.2%
Explanation: Prepayment as % of pool = $1,200,000 / $100,000,000 = 1.2%. A uses scheduled principal. C is total principal/pool. D misplaces decimal.
Question 884
A bond has modified duration 5.5 and convexity 35. Yields rise 1.5%. What is the estimated % price change?
Select an option first.
Correct answer: A — -7.86%
Explanation: % change = −5.5×0.015 + 0.5×35×(0.015)² = −0.0825 + 0.5×35×0.000225 = −0.0825 + 0.003938 = −0.07856 ≈ −7.86%. B ignores convexity. C and D are wrong.
Question 885
A portfolio has bonds with modified durations and values as follows: Bond A: $2M, duration 3; Bond B: $3M, duration 7. What is the portfolio's weighted average duration?
Select an option first.
Correct answer: B — 5.4
Explanation: Portfolio duration = (2×3 + 3×7)/(2+3) = (6+21)/5 = 27/5 = 5.4. A uses simple average (wrong). C and D are wrong.
Question 886
A bond has a 1% probability of default per year, an LGD of 50%, and a yield of 6%. What credit spread is implied by the expected loss?
Select an option first.
Correct answer: A — 0.5%
Explanation: Expected loss = PD × LGD = 1% × 50% = 0.5%. The bond's spread should approximately equal expected loss = 0.5% (in a risk-neutral world). B is just PD. C would double count. D is too low.
Question 887
An investor holds a $5M bond position with modified duration 6 and wants to reduce it to 4. Each $1M notional interest rate swap (receive fixed) has a modified duration of 5. What notional of swaps is needed?
Select an option first.
Correct answer: B — $2M
Explanation: Duration reduction needed = 6 − 4 = 2 years. Dollar duration to shed = 2 × $5M = $10M. Swap notional = Dollar duration / swap duration = $10M / 5 = $2M. A, C, D are wrong.
Question 888
A bond with a face value of $1,000 and modified duration 8 is priced at $900. A 20 bps yield increase reduces its price to approximately what?
Select an option first.
Correct answer: A — $885.60
Explanation: % price change = −8 × 0.002 = −1.6%. New price = $900 × (1 − 0.016) = $900 × 0.984 = $885.60. B, C, D are wrong.
Question 889
A CDO's senior tranche is rated AAA while the underlying pool of bonds is rated BB on average. This enhancement in credit quality is primarily due to:
Select an option first.
Correct answer: B — Subordination and the waterfall structure
Explanation: Subordination means junior tranches absorb losses before the senior tranche. Combined with the waterfall (senior paid first), the AAA tranche is protected from typical levels of defaults in the pool. A is wrong. C may help slightly. D manages rate risk, not credit risk.
Question 890
An investor expects interest rates to fall sharply. Which bond characteristic would maximize their potential gain?
Select an option first.
Correct answer: B — Long maturity, low coupon, positive convexity
Explanation: Long maturity and low coupon → high duration → maximum price gain when rates fall. Positive convexity makes gains even larger than duration alone predicts. A has low duration. C resets coupons so price stays near par. D (callable) limits price appreciation due to negative convexity.
Question 891
In the context of structured finance, overcollateralization means:
Select an option first.
Correct answer: B — The total principal of issued bonds is less than the principal of the collateral pool
Explanation: Overcollateralization means more collateral than bonds issued. If $110M of assets back $100M of bonds, the first $10M of losses are absorbed before bondholders are affected. A is excess spread. C is quality of assets. D is a cash reserve account, a different enhancement.
Question 892
Which of the following most accurately distinguishes effective duration from modified duration?
Select an option first.
Correct answer: B — Effective duration accounts for changes in cash flows (e.g., from embedded options) as yields change; modified duration assumes fixed cash flows
Explanation: Modified duration assumes cash flows are fixed regardless of yield changes. Effective duration is more general and models how embedded options (calls, puts, prepayment) cause cash flows to change with rates. A reverses the definitions. C is wrong. D is wrong.
Question 893
A senior secured tranche and a subordinated tranche from the same CDO have different yields primarily because:
Select an option first.
Correct answer: B — The senior tranche benefits from credit enhancement and thus requires less yield
Explanation: Senior tranches have lower credit risk due to subordination protection, so investors require less yield. Junior tranches compensate with higher yields for bearing first-loss risk. A, C, D are unrelated to the yield difference.
Question 894
A bond portfolio manager expects a steepening yield curve (long rates rise more than short rates). To benefit, she should:
Select an option first.
Correct answer: B — Sell long-duration bonds and buy short-duration bonds
Explanation: In a steepening, long bonds lose the most value. Selling long-duration bonds and buying short-duration bonds ('flattening the portfolio') protects against the steepening. A would increase losses. C avoids rate risk but doesn't benefit. D is unrelated.
Question 895
The term 'interest rate risk' for a bond most specifically refers to:
Select an option first.
Correct answer: B — The risk that the bond's value changes when market interest rates change
Explanation: Interest rate risk is the sensitivity of a bond's price to changes in interest rates. It is quantified by duration. A is credit risk. C is a form of reinvestment risk. D is inflation risk.
Question 896
Which of the following correctly describes the relationship between a bond's price change and yield change for a bond with positive convexity?
Select an option first.
Correct answer: B — Price increases are larger than price decreases for equal yield movements
Explanation: Positive convexity means the price-yield curve is curved favorably. For a given change in yield, the price gain (when yields fall) is larger than the price loss (when yields rise). A and D are wrong. C describes negative convexity.
Question 897
An ABS is backed by a pool of credit card receivables. Which of the following risks is most unique to this structure compared to a corporate bond?
Select an option first.
Correct answer: B — The risk that cardholders pay down balances faster than expected, causing early amortization
Explanation: ABS backed by revolving credit (credit cards) has early amortization risk — if cardholder repayments exceed expectations, the security's life shortens unexpectedly. This is analogous to prepayment risk in mortgages. A affects both. C and D affect all bonds.
Question 898
Duration matching (immunization) strategy aims to protect a bond portfolio from interest rate risk by:
Select an option first.
Correct answer: B — Setting the portfolio duration equal to the investment horizon
Explanation: Immunization sets the portfolio's Macaulay duration equal to the investment horizon. This ensures that reinvestment rate changes and price changes approximately offset each other, protecting the target return. A is too narrow. C is separate. D eliminates all rate sensitivity but may not match the horizon.
Question 899
Which of the following is true about the duration of a zero-coupon bond?
Select an option first.
Correct answer: B — It equals the bond's maturity in years (Macaulay duration)
Explanation: A zero-coupon bond has a single cash flow at maturity, so its Macaulay duration equals its maturity. There are no intermediate cash flows to reduce the weighted average. A is wrong. C is the opposite. D is wrong.
Question 900
An investor buys a bond with a modified duration of 10 and yields immediately rise 2%. The bond's price declines approximately:
Select an option first.
Correct answer: B — 20%
Explanation: % price change ≈ −Modified Duration × Δy = −10 × 0.02 = −0.20 = −20%. A uses 0.5% change. C would be −10×0.01. D would be −10×0.015.
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