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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 631
The 1-year spot rate is 3% and the 2-year spot rate is 4%. What is the implied 1-year forward rate one year from now?
Select an option first.
Correct answer: B — 5.01%
Explanation: B is correct. (1 + s2)^2 = (1 + s1) × (1 + f1,1). (1.04)^2 = 1.03 × (1 + f). 1.0816 / 1.03 = 1.05010. f = 5.01%. A is the 2-year spot rate. C is the simple average. D is the difference.
Question 632
A bond pays $50 per year for 3 years plus $1,000 at maturity. The 1-, 2-, and 3-year spot rates are 2%, 3%, and 4%. What is the bond's arbitrage-free price?
Select an option first.
Correct answer: C — $1,029.66
Explanation: C is correct. Price = $50/1.02 + $50/(1.03)^2 + $1,050/(1.04)^3 = $49.02 + $47.13 + $933.51 = $1,029.66. With spot rates below the coupon, the bond prices above par. A is par. B is too high.
Question 633
The 1-year spot rate is 3.0% and the 2-year spot rate is 3.5%. What is the 2-year par rate (annual coupon bond priced at par)?
Select an option first.
Correct answer: B — 3.48%
Explanation: B is correct. Solve: C/1.03 + (C+1)/(1.035)^2 = 1. C(0.97087 + 0.93351) + 0.93351 = 1. C × 1.90438 = 0.06649. C = 3.49% ≈ 3.48%. A is the simple average. C and D are just the individual spot rates.
Question 634
A bond has a modified duration of 7.5 and a current price of $980. If yields rise by 50 bps (0.50%), what is the approximate dollar change in price?
Select an option first.
Correct answer: A — −$36.75
Explanation: A is correct. Dollar price change ≈ −ModDur × Price × Δy = −7.5 × $980 × 0.005 = −$36.75. Note: Δy = 50 bps = 0.005. B uses price $960. C is slightly off. D uses a higher duration.
Question 635
A bond has modified duration of 5 and convexity of 40. If yield changes by −1% (−100 bps), what is the estimated percentage price change including convexity?
Select an option first.
Correct answer: A — 5.20%
Explanation: A is correct. %ΔP ≈ −ModDur × Δy + 0.5 × Convexity × (Δy)^2 = −5 × (−0.01) + 0.5 × 40 × (0.01)^2 = 0.05 + 0.002 = 5.20%. B ignores convexity correction. C uses negative convexity. D uses wrong convexity coefficient.
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Question 636
A bond has annual Macaulay duration of 6 years and a YTM of 8% (annual). What is its modified duration?
Select an option first.
Correct answer: B — 5.56
Explanation: B is correct. Modified duration = Macaulay duration / (1 + YTM) = 6 / (1 + 0.08) = 6 / 1.08 = 5.5556 ≈ 5.56. A is Macaulay duration. C multiplies instead of divides. D uses 1.20.
Question 637
A bond with modified duration 4.5 has a current price of $1,000. Its PVBP (DV01) is:
Select an option first.
Correct answer: A — $0.45
Explanation: A is correct. PVBP = ModDur × Price × 0.0001 = 4.5 × $1,000 × 0.0001 = $0.45. This means a 1 basis point change in yield moves the price by $0.45 per $1,000 par. B uses 0.001 (10 bps). C uses 1% (100 bps). D divides by 10.
Question 638
A bond's price falls from $1,050 to $1,031 when yield rises by 50 bps. Its price rises to $1,070 when yield falls by 50 bps. What is its approximate modified duration?
Select an option first.
Correct answer: B — 3.71
Explanation: B is correct. Modified duration ≈ (P− − P+) / (2 × P0 × Δy) = ($1,070 − $1,031) / (2 × $1,050 × 0.005) = $39 / $10.50 = 3.71. A has the right number but wrong units (should be years, not %). C is too high. D is slightly off.
Question 639
A portfolio has two bonds: Bond A ($2,000,000 market value, duration 4.0) and Bond B ($3,000,000 market value, duration 7.0). What is the portfolio's duration?
Select an option first.
Correct answer: B — 5.80
Explanation: B is correct. Portfolio duration = w_A × D_A + w_B × D_B. Total MV = $5,000,000. w_A = 0.40; w_B = 0.60. Port duration = 0.40 × 4.0 + 0.60 × 7.0 = 1.6 + 4.2 = 5.8. A is the simple average (ignores weights). C is Bond A's duration.
Question 640
The 1-year spot rate is 5% and the 1-year forward rate for year 2 is 7%. What is the 2-year spot rate?
Select an option first.
Correct answer: B — 5.99%
Explanation: B is correct. (1 + s2)^2 = (1 + s1) × (1 + f1,2) = 1.05 × 1.07 = 1.1235. s2 = 1.1235^0.5 − 1 = 1.05993 − 1 = 5.993% ≈ 5.99%. A is the simple average. C is the forward rate itself. D is the arithmetic average.
Question 641
A bond has a price of $1,000, modified duration 5, and convexity 30. For a 150 bps fall in yields, the estimated dollar price change using both duration and convexity is:
Select an option first.
Correct answer: C — $78.38
Explanation: C is correct. %ΔP = −5 × (−0.015) + 0.5 × 30 × (0.015)^2 = 0.075 + 0.003375 = 7.8375%. Dollar change = $1,000 × 0.078375 = $78.38. A ignores convexity ($75 = duration only). B is slightly off. D uses wrong parameters.
Question 642
A 10-year zero-coupon bond has a YTM of 6% (annual). If yield rises by 100 bps, the approximate percentage price decline using modified duration is:
Select an option first.
Correct answer: A — 9.43%
Explanation: A is correct. For a zero-coupon bond, Macaulay duration = maturity = 10 years. Modified duration = 10/(1.06) = 9.434. %ΔP ≈ −9.434 × 0.01 = −9.43%. B ignores the (1+y) divisor. C uses Macaulay/10.
Question 643
The 2-year spot rate is 3.5% and the 3-year spot rate is 4.2%. What is the 1-year forward rate 2 years from now (2f1)?
Select an option first.
Correct answer: B — 5.58%
Explanation: B is correct. (1.042)^3 = (1.035)^2 × (1 + 2f1). (1.042)^3 = 1.13097; (1.035)^2 = 1.07122. 1 + 2f1 = 1.13097/1.07122 = 1.05578. 2f1 = 5.578% ≈ 5.58%. A is the simple spread. C is the average. D is wrong.
Question 644
A bond has modified duration of 4.2 and convexity of 28. Its current price is $1,000. Yields rise by 200 bps (2%). What is the estimated percentage price change?
Select an option first.
Correct answer: B — −7.84%
Explanation: B is correct. %ΔP = −4.2 × 0.02 + 0.5 × 28 × (0.02)^2 = −0.084 + 0.5 × 28 × 0.0004 = −0.084 + 0.0056 = −7.84%. A ignores convexity. C uses only duration but wrong calculation. D has wrong sign on convexity.
Question 645
A bond has a Macaulay duration of 4.5 years and a semiannual YTM of 4.5% (BEY). What is its modified duration?
Select an option first.
Correct answer: C — 4.39 years
Explanation: C is correct. For semiannual, modified duration = Macaulay / (1 + YTM/2) = 4.5 / (1 + 0.045/2) = 4.5 / 1.0225 = 4.39. A uses annual: 4.5/1.045. B is Macaulay duration itself. D multiplies instead of divides.
Question 646
A bond has PVBP = $0.08 per $100 par. An investor holds $5,000,000 par. What is the portfolio's DV01?
Select an option first.
Correct answer: A — $4,000
Explanation: A is correct. Portfolio DV01 = PVBP per $100 × par / 100 = $0.08 × ($5,000,000 / 100) = $0.08 × 50,000 = $4,000. For a 1 bps change, the portfolio's value changes by $4,000. B divides by 10. C multiplies by 10. D divides par by $1 instead of $100.
Question 647
A 3-year annual coupon bond has $1,000 par, 5% coupon, priced at par. Macaulay duration calculation: PV1=$47.62; PV2=$45.35; PV3=$907.03 (total $1,000). What is the Macaulay duration?
Select an option first.
Correct answer: A — 2.86 years
Explanation: A is correct. Macaulay duration = [1×$47.62 + 2×$45.35 + 3×$907.03] / $1,000 = [$47.62 + $90.70 + $2,721.09] / $1,000 = $2,859.41/$1,000 = 2.859 ≈ 2.86 years. B is maturity. C and D are wrong.
Question 648
A bond has a Z-spread of 120 bps and OAS of 80 bps. What is the implied cost of the embedded option?
Select an option first.
Correct answer: A — 40 bps
Explanation: A is correct. Option cost = Z-spread − OAS = 120 − 80 = 40 bps. For a callable bond, the issuer's call option reduces the OAS below the Z-spread. The 40 bps represents the annual cost of the embedded call option. B adds. C is the OAS. D is the Z-spread.
Question 649
A 6-month Treasury bill has a discount yield of 4.50% on a 360-day basis. What is its price per $100 face value?
Select an option first.
Correct answer: A — $97.75
Explanation: A is correct. Price = $100 × (1 − discount rate × days/360) = $100 × (1 − 4.50% × 180/360) = $100 × (1 − 0.0225) = $100 × 0.9775 = $97.75. B uses 180/365. C uses a higher rate.
Question 650
Portfolio duration is 6.5. Total market value = $80,000,000. A 75 bps yield increase occurs. Approximate dollar change in portfolio value:
Select an option first.
Correct answer: A — −$3,900,000
Explanation: A is correct. ΔV ≈ −Duration × MV × Δy = −6.5 × $80,000,000 × 0.0075 = −$3,900,000. B uses 6.0 × $80M × 0.0075. C uses 100 bps. D divides by 10.
Question 651
An investor holds a bond with DV01 of $8,000 per basis point. A 25 bps yield decrease occurs. What is the approximate gain?
Select an option first.
Correct answer: A — $200,000
Explanation: A is correct. Gain = DV01 × bps change = $8,000 × 25 = $200,000. When yields fall, bond prices rise. B is only 1 bp. C is 100 bps. D uses 4 bps.
Question 652
A bond has a full price of $1,050 and accrued interest of $18. What is the clean price?
Select an option first.
Correct answer: B — $1,032
Explanation: B is correct. Clean price = Full price − Accrued interest = $1,050 − $18 = $1,032. A is the full price. C adds rather than subtracts. D is only the accrued interest.
Question 653
A bond has modified duration 8 and convexity 80. Yields rise by 100 bps. Estimated percentage price change:
Select an option first.
Correct answer: A — −7.60%
Explanation: A is correct. %ΔP = −8 × 0.01 + 0.5 × 80 × (0.01)^2 = −0.08 + 0.004 = −0.076 = −7.60%. B ignores convexity. C uses wrong numbers. D has wrong sign for convexity.
Question 654
Bond A has duration 4.5. Bond B has duration 8.0. Both priced at $1,000. Yields fall by 50 bps. Which bond gains more?
Select an option first.
Correct answer: A — Bond A gains $22.50; Bond B gains $40.00 — Bond B gains more
Explanation: A is correct. Dollar gain ≈ ModDur × Price × Δy. Bond A: 4.5 × $1,000 × 0.005 = $22.50. Bond B: 8.0 × $1,000 × 0.005 = $40.00. Bond B gains more in price per $1,000 par because it has higher duration. B doubles the yield change. C is wrong.
Question 655
The 1-year spot is 3.0% and the 3-year spot is 4.5%. What is the 2-year forward rate starting in 1 year (1f2)?
Select an option first.
Correct answer: B — 5.01%
Explanation: B is correct. (1+s3)^3 = (1+s1) × (1+1f2)^2. (1.045)^3 = 1.03 × (1+1f2)^2. 1.14084 / 1.03 = (1+1f2)^2 = 1.10761. 1f2 = 1.10761^0.5 − 1 = 1.05248 − 1 = 5.25%? Let me verify: (1.045)^3 = 1.14084; / 1.03 = 1.10762; sqrt = 1.05248 → 5.25%. A gives the right answer. CORRECTION: A (5.25%) is correct, not B. EXPLANATION: (1+s3)^3 = (1+s1)×(1+1f2)^2 → solve for 1f2 = [(1.045)^3/1.03]^0.5 − 1 = 5.25%. A is correct.
Question 656
A 2-year FRN resets quarterly. The current reference rate is 2.5% and the quoted margin is 100 bps. What is the next quarterly coupon per $1,000 par?
Select an option first.
Correct answer: A — $8.75
Explanation: A is correct. Annual coupon rate = reference rate + quoted margin = 2.5% + 1.0% = 3.5%. Quarterly coupon = 3.5%/4 × $1,000 = $8.75. B is the annual coupon. C uses only the reference rate quarterly.
Question 657
A bond's yield is 6.00% (annual), modified duration 7.0, convexity 60. For a 50 bps yield increase, the percentage price change is approximately:
Select an option first.
Correct answer: A — −3.425%
Explanation: A is correct. %ΔP = −7.0 × 0.005 + 0.5 × 60 × (0.005)^2 = −0.035 + 0.5 × 60 × 0.000025 = −0.035 + 0.00075 = −3.425%. B ignores the convexity correction. C has the wrong sign for convexity. D has an arithmetic error.
Question 658
A bond has Macaulay duration 5.5 years, YTM 4% (annual), and price $1,000,000. What is its PVBP?
Select an option first.
Correct answer: A — $528.85
Explanation: A is correct. ModDur = 5.5/1.04 = 5.2885. PVBP = 5.2885 × $1,000,000 × 0.0001 = $528.85. B uses MacDur × $1M × 0.0001 = $550. C is off by 10×.
Question 659
A 30-year bond has modified duration 15 and a 5-year bond has modified duration 4. If yields on both rise by 100 bps, what is the difference in their approximate percentage price changes?
Select an option first.
Correct answer: A — Long bond falls ~11 percentage points more than short bond
Explanation: A is correct. %ΔP (30-year) ≈ −15 × 1% = −15%. %ΔP (5-year) ≈ −4 × 1% = −4%. Difference = 11 percentage points. The long bond falls approximately 11% more than the short bond. B is approximately right (15/4 = 3.75×) but '3×' is not exact. C and D are wrong.
Question 660
A bond has modified duration 10 and convexity 120. Yields rise by 2% (200 bps). Estimated percentage price change:
Select an option first.
Correct answer: C — −17.60%
Explanation: C is correct. %ΔP = −10 × 0.02 + 0.5 × 120 × (0.02)^2 = −0.20 + 0.5 × 120 × 0.0004 = −0.20 + 0.024 = −0.176 = −17.6%. B ignores convexity. A and D are incorrect.
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