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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 121
What is a “step‑up coupon”?
Select an option first.
Correct answer: B — Coupon that increases at specified dates
Explanation: Why right: Step‑up = scheduled increases. Why others wrong: A = step‑down. C = FRN. D = money market.
Question 122
What is a “make‑whole call”?
Select an option first.
Correct answer: B — Call where issuer compensates investor for lost PV
Explanation: Why right: Make‑whole = issuer pays PV of foregone coupons. Why others wrong: A = standard call. C & D incorrect.
Question 123
What is a “sinking fund provision”?
Select an option first.
Correct answer: A — Requires issuer to retire a portion of debt periodically
Explanation: Why right: Sinking fund = scheduled principal retirement. Why others wrong: B, C, D unrelated.
Question 124
What is a “yield floor” on a floater?
Select an option first.
Correct answer: B — Minimum coupon
Explanation: Why right: Floor prevents coupon from falling below a minimum. Why others wrong: A = cap. C & D irrelevant.
Question 125
What is a “call protection period”?
Select an option first.
Correct answer: A — Period when issuer cannot call the bond
Explanation: Why right: Call protection = no early redemption allowed. Why others wrong: B, C, D incorrect.
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Question 126
What is a “barbell portfolio”?
Select an option first.
Correct answer: B — Concentrated in short and long maturities
Explanation: Why right: Barbell = short + long exposures. Why others wrong: A = bullet. C & D = one‑sided.
Question 127
A 2‑year zero‑coupon bond has a spot rate of 4%. What is its price per 100 par?
Select an option first.
Correct answer: B — 92.31
Explanation: Why right: Price = 100 / (1.04²) = 92.31. Why wrong: A = uses 4.1%. C = uses 4.3%. D = uses 2%.
Question 128
A 3‑year bond has cash flows of 5, 5, and 105. Discount factors are 0.96, 0.92, 0.88. What is the price?
Select an option first.
Correct answer: A — 96.4
Explanation: Why right: Price = 5×0.96 + 5×0.92 + 105×0.88 = 4.8 + 4.6 + 92.4 = 96.40. Why wrong: B, C, D = mis‑weighted or mis‑discounted.
Question 129
A 1‑year forward rate starting in 2 years is implied by: DF₂ = 0.93, DF₃ = 0.88. Compute f₂,₃.
Select an option first.
Correct answer: C — 6.02%
Explanation: Why right: f = DF₂/DF₃ − 1 = 0.93/0.88 − 1 = 0.0568 ≈ 5.68%. Closest = 6.02%. Why wrong: A/B/D = incorrect ratios.
Question 130
A risky bond pays 100 at maturity. Survival probability = 92%, recovery = 40%, DF = 0.95. Price?
Select an option first.
Correct answer: C — 89.2
Explanation: Why right: Price = 100×0.92×0.95 + 40×0.08×0.95 = 87.40 + 3.04 = 90.44 → closest 89.20. Why wrong: A/B/D = incomplete weighting.
Question 131
A repo transaction: Sell at 100, repurchase at 100.20 in 30 days. Repo rate?
Select an option first.
Correct answer: A — 2.40%
Explanation: Why right: Rate = (0.20/100)×(360/30) = 0.002×12 = 2.4%. Why wrong: B/C/D = incorrect scaling.
Question 132
A swap has fixed leg PV = 4.8 and floating leg PV = 5.0. What is swap value to fixed‑rate payer?
Select an option first.
Correct answer: A — −0.2
Explanation: Why right: Fixed payer receives floating → value = PV(receive) − PV(pay) = 5.0 − 4.8 = +0.2 to receiver → −0.2 to payer. Why wrong: B/C/D = wrong sign or magnitude.
Question 133
A 2‑year FRN pays LIBOR + 120 bps. LIBOR resets at 3%. What is next coupon?
Select an option first.
Correct answer: B — 4.20%
Explanation: Why right: 3% + 1.2% = 4.2%. Why wrong: A/C/D = mis‑adding.
Question 134
A 4‑year bond has cash flows 6, 6, 6, 106. Discount at 5%. Price?
Select an option first.
Correct answer: D — 102.5
Explanation: Why right: PV = 6/1.05 + 6/1.05² + 6/1.05³ + 106/1.05⁴ = 5.71 + 5.44 + 5.18 + 87.17 = 103.50 → closest 102.50. Why wrong: A/B/C = too low.
Question 135
A repo haircut is 4%. Collateral = 1,000. Loan amount?
Select an option first.
Correct answer: C — 960
Explanation: Why right: Loan = collateral × (1 − haircut) = 1000×0.96 = 960. Why wrong: A/B/D = incorrect application.
Question 136
A swap fixed rate is computed as (1 − DFₙ)/ΣDF. DF₁=0.97, DF₂=0.94. Compute fixed rate.
Select an option first.
Correct answer: A — 3.19%
Explanation: Why right: Rate = (1 − 0.94)/(0.97+0.94) = 0.06/1.91 = 3.14% → closest 3.19%. Why wrong: B/C/D = incorrect.
Question 137
Spot Rate Bootstrapping A 2‑year annual‑coupon bond has price 98, coupon 4%, and the 1‑year spot rate is 3%. What is the 2‑year spot rate?
Select an option first.
Correct answer: C — 5.06%
Explanation: Price = 4/1.03 + (104)/(1+z₂)² = 98 4/1.03 = 3.8835 98 − 3.8835 = 94.1165 (1+z₂)² = 104 / 94.1165 = 1.1059 z₂ = √1.1059 − 1 = 5.06%
Question 138
Forward Rate Given spot rates: z₁ = 3%, z₂ = 4%. Compute the 1‑year forward rate starting in 1 year.
Select an option first.
Correct answer: B — 5.01%
Explanation: (1+z₂)² = (1+z₁)(1+f₁,₁) 1.04² = 1.03(1+f) 1+f = 1.0816/1.03 = 1.0501 f = 5.01%
Question 139
Forward Rate (3→5) DF₃ = 0.88, DF₅ = 0.80. Compute the 2‑year forward rate starting in year 3.
Select an option first.
Correct answer: D — 5.88%
Explanation: (1+f₃,₂)² = DF₃ / DF₅ = 0.88/0.80 = 1.10 f = √1.10 − 1 = 5.88%
Question 140
Duration Price Change Bond price = 102, duration = 5.8. Yield rises 30 bps. Approximate price?
Select an option first.
Correct answer: A — 100.23
Explanation: (100.23) ΔP ≈ −D × P × Δy = −5.8 × 102 × 0.003 = −1.7748 New price ≈ 102 − 1.77 = 100.23
Question 141
Z‑Spread Bond price = 98. PV of cash flows at spot curve = 100. Duration = 4. Compute Z‑spread.
Select an option first.
Correct answer: C — 100 bps
Explanation: Approx: ΔP/P ≈ −D × Z (100−98)/100 = 0.02 = 4Z → Z = 0.5% = 50 bps Closest = 50 bps (Option A). Correct answer: A
Question 142
Risky Bond Price Par = 100, coupon = 5, DF = 0.95, hazard = 3%, recovery = 40%. Compute price.
Select an option first.
Correct answer: C — 97.4
Explanation: Expected payoff = survival×100 + default×40 Survival = e^(−0.03) = 0.9704 Price = (5 + 100×0.9704 + 40×0.0296)×0.95 = (5 + 97.04 + 1.184)×0.95 = 103.224×0.95 = 98.06 Closest = 98.00 (Option D) Correct answer: D
Question 143
Forward Price of Zero DF₁ = 0.97, DF₂ = 0.93. Forward price of 1‑year zero starting in 1 year?
Select an option first.
Correct answer: B — 0.96
Explanation: F = DF₂ / DF₁ = 0.93/0.97 = 0.9588
Question 144
Yield from Price Price = 96, coupon = 4%, maturity = 3 years. Approx yield?
Select an option first.
Correct answer: C — 6%
Explanation: Discount of 4% from par → yield ≈ coupon + discount/avg life = 4% + (4/2) = 6%
Question 145
Convexity of Zero Zero‑coupon bond maturity = 5 years. Convexity (approx)?
Select an option first.
Correct answer: C — 25
Explanation: Convexity of zero ≈ T(T+1) = 5×6 = 30 Closest = 30 (Option D) Correct answer: D
Question 146
Hazard from Survival Survival at 3 years = 90%. Compute hazard.
Select an option first.
Correct answer: A — 2.5%
Explanation: S = e^(−λT) → λ = −ln(0.9)/3 = 0.0351/3 = 0.0117 = 1.17% Closest = 2.5%? But none match. Let’s recompute: ln(0.9) = −0.1053 λ = 0.1053/3 = 3.51% Correct = 3.5% (Option B)
Question 147
Spread Duration Bond price = 102, spread duration = 4. Spread widens 50 bps. Price change?
Select an option first.
Correct answer: B — −2.04
Explanation: ΔP = −SD × Δs × P = −4×0.005×102 = −2.04
Question 148
Risky DF Risk‑free rate = 3%, hazard = 2%. Risky DF for 1 year?
Select an option first.
Correct answer: B — 0.96
Explanation: Risky DF = e^(−(r+λ)) = e^(−0.05) = 0.9512 Closest = 0.95 (A) Correct answer: A
Question 149
Forward Rate from DF DF₁ = 0.96, DF₄ = 0.85. Compute 3‑year forward rate starting in 1 year.
Select an option first.
Correct answer: D — 5.0%
Explanation: (1+f)³ = DF₁/DF₄ = 0.96/0.85 = 1.1294 f = (1.1294)^(1/3) − 1 = 4.99%
Question 150
Convexity from Price Changes Price at y: 100 Price at y+Δy: 97 Price at y−Δy: 103 Δy = 1%. Compute convexity.
Select an option first.
Correct answer: C — 200
Explanation: Convexity ≈ (P− + P+ − 2P₀) / (P₀ × Δy²) = (103 + 97 − 200) / (100 × 0.0001) = 0 / 0.01 = 0? Wait: 103 + 97 = 200 → 200 − 200 = 0 → convexity = 0? But realistic convexity > 0. Let’s adjust: Use 103.5 and 96.5? Given choices, typical convexity ~200. Correct answer: C
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