CFA Level 2 Fixed Income: notes and free practice
CFA Level 2 Fixed Income analyzes bond values, term structures and credit risk. Select the relevant curve and cash flows, distinguish rate changes from spread changes, and check the assumptions behind the valuation model.
The key ideas, at a glance
Use the whole curve
Read the visual, then follow the worked example below. Use the stated case assumptions.
Illustrative worked case
% annual rate
- 1-year spot
- 4
- 2-year spot
- 5
- 1-year forward
- 6.01
Under annual compounding, (1 + forward) × 1.04 = 1.05². The forward is about 6.01%, not a guaranteed realized future rate.
| Concept | Rule or decision | Common mistake |
|---|---|---|
| Use the whole curve | Annual forward: 1 + f(1,2) = (1 + s2)² / (1 + s1) | A single parallel duration does not capture every twist in the yield curve. |
| Work backward through a node | Node value = discounted risk-neutral expected next cash flow | Adding the coupon after discounting incorrectly moves its payment date. |
| Identify who owns the option | Callable = straight - issuer call; putable = straight + investor put | Higher volatility can help the issuer’s call and reduce the callable bond’s value, other inputs fixed. |
| Separate probability and severity | Expected loss = PD × exposure × (1 - recovery) | Expected loss is not the maximum loss or the cash payment in every default. |
01Use the whole curve
Annual forward: 1 + f(1,2) = (1 + s2)² / (1 + s1)
Watch for: A single parallel duration does not capture every twist in the yield curve.
02Work backward through a node
Node value = discounted risk-neutral expected next cash flow
Watch for: Adding the coupon after discounting incorrectly moves its payment date.
03Identify who owns the option
Callable = straight - issuer call; putable = straight + investor put
Watch for: Higher volatility can help the issuer’s call and reduce the callable bond’s value, other inputs fixed.
04Separate probability and severity
Expected loss = PD × exposure × (1 - recovery)
Watch for: Expected loss is not the maximum loss or the cash payment in every default.
Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.
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CFA Level II: 20 practice MCQs
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Put the method to work
One worked example, from facts to answer
Given
One-year spot 4%, two-year spot 5%, annual compounding.
Method
1.05² / 1.04 - 1 = about 6.01%.
Answer and interpretation
The implied one-year rate starting in a year is about 6.01%.
Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.
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10 free Fixed Income questions
Five mini-cases, two questions each. Read the case facts, choose an answer and review the method. Short teaching cases, not complete exam item sets or a mock.
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- Question 1 of 10Level II topic sample · Case 1 of 5Fixed IncomeMultiple choice
Case facts
Iris observes annual-compounded one-year and two-year risk-free spot rates of 3% and 4%. An option-free two-year bond pays an annual coupon of 4 per 100 face value, with principal at year 2. Settlement is on a coupon date, and there are no credit or liquidity spreads.
Iris’s implied one-year forward rate starting at year 1 is closest to:
Answer and explanations
(1.04² / 1.03 - 1) × 100 = approximately 5.01% with annual compounding.
Review the method- A: 4% is the two-year spot rate, not the one-year forward.
- B - correct: (1.04² / 1.03 - 1) × 100 = approximately 5.01% with annual compounding.
- C: The difference between spot rates alone is not the forward rate.
- Question 2 of 10Level II topic sample · Case 1 of 5Fixed IncomeMultiple choice
Case facts
Iris observes annual-compounded one-year and two-year risk-free spot rates of 3% and 4%. An option-free two-year bond pays an annual coupon of 4 per 100 face value, with principal at year 2. Settlement is on a coupon date, and there are no credit or liquidity spreads.
The arbitrage-free bond price using Iris’s spot curve is closest to:
Answer and explanations
4 / 1.03 + 104 / 1.04² = approximately 100.04 per 100 face.
Review the method- A: 100.00 uses the two-year rate for both cash flows instead of the actual curve.
- B: 103.88 does not discount the principal and final coupon to year zero correctly.
- C - correct: 4 / 1.03 + 104 / 1.04² = approximately 100.04 per 100 face.
- Question 3 of 10Level II topic sample · Case 2 of 5Fixed IncomeMultiple choice
Case facts
At year 1, a bond’s ex-coupon continuation values are 96 in the up-rate node and 104 in the down-rate node. It pays a coupon of 5 at that date in either node. The one-year discount rate at time zero is 4%, and risk-neutral probabilities are 0.5 each.
The bond’s time-zero value from the given one-step tree is closest to:
Answer and explanations
[0.5 × (96 + 5) + 0.5 × (104 + 5)] / 1.04 = 100.96.
Review the method- A - correct: [0.5 × (96 + 5) + 0.5 × (104 + 5)] / 1.04 = 100.96.
- B: 96.15 discounts continuation value while omitting the coupon.
- C: 105.00 is the undiscounted expected next-period amount.
- Question 4 of 10Level II topic sample · Case 2 of 5Fixed IncomeMultiple choice
Case facts
At year 1, a bond’s ex-coupon continuation values are 96 in the up-rate node and 104 in the down-rate node. It pays a coupon of 5 at that date in either node. The one-year discount rate at time zero is 4%, and risk-neutral probabilities are 0.5 each.
What is the appropriate interpretation of the supplied 0.5 node probabilities?
Answer and explanations
These weights are used with the node discount rate in the arbitrage-free pricing calculation, not asserted as physical probabilities.
Review the method- A: Pricing probabilities need not equal historical or physical frequencies.
- B - correct: These weights are used with the node discount rate in the arbitrage-free pricing calculation, not asserted as physical probabilities.
- C: A pricing procedure does not remove the bond’s risk exposure.
- Question 5 of 10Level II topic sample · Case 3 of 5Fixed IncomeMultiple choice
Case facts
An option-free bond is valued at 104. An otherwise identical issuer-callable version embeds a call worth 6 to the issuer. A separate otherwise identical investor-putable version embeds a put worth 3 to the investor. Ignore additional features and changes in credit quality.
The issuer-callable bond’s value under the given decomposition is:
Answer and explanations
Callable value = option-free value 104 - issuer call value 6 = 98.
Review the method- A: 110 adds the issuer’s option benefit to the investor’s bond.
- B: 104 ignores the issuer’s valuable call right.
- C - correct: Callable value = option-free value 104 - issuer call value 6 = 98.
- Question 6 of 10Level II topic sample · Case 3 of 5Fixed IncomeMultiple choice
Case facts
An option-free bond is valued at 104. An otherwise identical issuer-callable version embeds a call worth 6 to the issuer. A separate otherwise identical investor-putable version embeds a put worth 3 to the investor. Ignore additional features and changes in credit quality.
Holding the straight bond value and other inputs fixed, greater interest-rate volatility that raises the issuer call’s value would:
Answer and explanations
The holder is short the issuer’s option, so a more valuable call reduces the callable bond’s value.
Review the method- A - correct: The holder is short the issuer’s option, so a more valuable call reduces the callable bond’s value.
- B: Greater call value benefits the issuer, not the callable bondholder.
- C: The decomposition directly subtracts the changing call value.
- Question 7 of 10Level II topic sample · Case 4 of 5Fixed IncomeMultiple choice
Case facts
A lender has a one-year exposure of $10m, a 3% default probability and 40% recovery on that exposure after default. Ignore discounting. A separate cash-settled CDS has $10m notional and settles at the same 40% recovery after a covered credit event; ignore premium accruals.
The lender’s undiscounted one-year expected credit loss is:
Answer and explanations
0.03 × $10m × (1 - 0.40) = $180,000 expected loss.
Review the method- A: 300,000 omits the supplied 40% recovery.
- B - correct: 0.03 × $10m × (1 - 0.40) = $180,000 expected loss.
- C: 6m is loss conditional on default, not probability-weighted expected loss.
- Question 8 of 10Level II topic sample · Case 4 of 5Fixed IncomeMultiple choice
Case facts
A lender has a one-year exposure of $10m, a 3% default probability and 40% recovery on that exposure after default. Ignore discounting. A separate cash-settled CDS has $10m notional and settles at the same 40% recovery after a covered credit event; ignore premium accruals.
After the covered event, the specified CDS cash settlement to the protection buyer is:
Answer and explanations
$10m notional × (1 - 40% recovery) = $6m under the specified settlement terms.
Review the method- A: 180,000 applies an ex-ante probability after the event has already occurred.
- B: 4m is the recovery amount rather than the covered loss.
- C - correct: $10m notional × (1 - 40% recovery) = $6m under the specified settlement terms.
- Question 9 of 10Level II topic sample · Case 5 of 5Fixed IncomeMultiple choice
Case facts
A bond priced at 100 is worth 103.2 after a 50-basis-point downward parallel benchmark shift and 96.8 after an upward shift of the same size. Its 2-, 5- and 10-year key rate durations are 1.2, 3.0 and 2.2. A separate nonparallel scenario shifts those yields by +10, -20 and +30 basis points.
The bond’s effective duration from the parallel repricing scenario is:
Answer and explanations
(103.2 - 96.8) / (2 × 100 × 0.005) = 6.4, using a decimal yield shift.
Review the method- A - correct: (103.2 - 96.8) / (2 × 100 × 0.005) = 6.4, using a decimal yield shift.
- B: 3.2 effectively counts the two-sided shift twice.
- C: 0.064 mis-scales the basis-point yield change.
- Question 10 of 10Level II topic sample · Case 5 of 5Fixed IncomeMultiple choice
Case facts
A bond priced at 100 is worth 103.2 after a 50-basis-point downward parallel benchmark shift and 96.8 after an upward shift of the same size. Its 2-, 5- and 10-year key rate durations are 1.2, 3.0 and 2.2. A separate nonparallel scenario shifts those yields by +10, -20 and +30 basis points.
Ignoring convexity, the separate nonparallel key-rate scenario implies a price return of:
Answer and explanations
-[1.2 × 0.001 + 3.0 × (-0.002) + 2.2 × 0.003] = -0.0018, or -0.18%.
Review the method- A: -0.64% applies a single 10-basis-point parallel move instead of the three supplied shifts.
- B - correct: -[1.2 × 0.001 + 3.0 × (-0.002) + 2.2 × 0.003] = -0.0018, or -0.18%.
- C: The positive sign reverses the net duration-weighted price effect.
Four ideas to put to work
Find the method you need
Start with: Bond cash flows, spot discounting, basis points and the distinction between price and yield.
METHOD 01
Use the whole curve
Annual forward: 1 + f(1,2) = (1 + s2)² / (1 + s1)
- Discount each fixed cash flow using the spot rate for its own maturity.
- Distinguish an implied forward rate from a guaranteed future spot rate.
- For nonparallel shifts, approximate return as minus the sum of key rate duration times each yield change.
Worked example
- Given
- One-year spot 4%, two-year spot 5%, annual compounding.
- Calculate / decide
- 1.05² / 1.04 - 1 = about 6.01%.
- Result
- The implied one-year rate starting in a year is about 6.01%.
Watch for: A single parallel duration does not capture every twist in the yield curve.
Practise this ideaMETHOD 02
Work backward through a node
Node value = discounted risk-neutral expected next cash flow
- Include next-period coupons as well as continuation values.
- Use the probabilities and short rate specified for that node.
- Work back to today; risk-neutral probabilities need not equal real-world forecasts.
Worked example
- Given
- Next ex-coupon values 98 and 102, coupon 4, equal probabilities, discount rate 5%.
- Calculate / decide
- (0.5 × 102 + 0.5 × 106) / 1.05 = 99.05.
- Result
- The current model value is about 99.05 per 100 face.
Watch for: Adding the coupon after discounting incorrectly moves its payment date.
Practise this ideaMETHOD 03
Identify who owns the option
Callable = straight - issuer call; putable = straight + investor put
- Subtract the issuer’s call benefit from the option-free bond value.
- Add the holder’s put benefit to the option-free bond value.
- Use repriced cash flows for effective duration when options may change exercise behavior.
Worked example
- Given
- Straight value 102; issuer call value 4; investor put value 2.
- Calculate / decide
- Callable value = 98; separate putable value = 104.
- Result
- The owner of the embedded option determines the sign.
Watch for: Higher volatility can help the issuer’s call and reduce the callable bond’s value, other inputs fixed.
Practise this ideaMETHOD 04
Separate probability and severity
Expected loss = PD × exposure × (1 - recovery)
- Apply recovery to the exposure amount using the stated settlement convention.
- Expected loss weights loss severity by default probability.
- After a covered CDS event, settlement uses realized loss severity, not ex-ante default probability.
Worked example
- Given
- Exposure 5m, one-year PD 2%, recovery 40%, no discounting.
- Calculate / decide
- 5m × 0.02 × 0.60 = 60,000.
- Result
- Expected loss is 60,000; conditional loss upon default is 3m.
Watch for: Expected loss is not the maximum loss or the cash payment in every default.
Practise this ideaQuestions about this topic
- Why might a bond lose value when benchmark rates do not move?
- A wider credit or liquidity spread can increase the required discount rate. Embedded-option or cash-flow assumptions can also change. Separate benchmark-rate risk from the other drivers in the case.
- Why use a term structure instead of one yield for all payments?
- Cash flows occur at different maturities. An arbitrage-free framework values them using consistent maturity-specific discounting or the supplied interest-rate model, rather than assuming one yield always captures the entire curve.
- Does collateral eliminate issuer default risk?
- No. Collateral and seniority can affect recovery, but repayment can still fail or be delayed. Evaluate default likelihood and claim-specific loss severity separately.
Apply the topic to a focused case
CFA Level 2 credit analysis within fixed-income item sets
Identify who owes the payment and which cash flows service that obligation. Operating earnings, cash generation, leverage, coverage and refinancing needs give different views of credit capacity. A company may report a profit while lacking cash for a near-term maturity. Distinguish a temporary liquidity problem from a weak long-term business and use the case’s forward assumptions rather than a ratio in isolation.
- Case facts
- A one-year exposure is 750,000. Default probability is 3% and recovery is 65%. Ignore discounting and exposure changes.
- Apply the method
- LGD = 1 - 0.65 = 0.35. Expected loss = 750,000 × 0.03 × 0.35 = 7,875.
- Interpretation
- The modeled expected loss is 7,875, or 1.05% of exposure. This is an expectation across outcomes, not a certain loss or the market credit spread.
Independent teaching cases under the stated assumptions, rather than official questions or scoring keys.
Sources and curriculum scope
Official outlines establish curriculum scope. The explanations and worked examples are independent teaching material; the sources do not verify or endorse them.
- 2026 CFA Level II outline: Fixed Income
- Official Level 2 format and curriculum
- 2026 CFA Level 2 curriculum outline
- 2026 credit analysis models
- 2027 CFA Level 2 curriculum outline
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