CFA® Level I Fixed Income

The 19 learning modules

1. 01 Fixed-Income Instrument Features

   The basic features of a bond: issuer, maturity, par value, coupon rate and frequency, seniority and contingency provisions. It also covers the indenture, sources of repayment, and the difference between affirmative and negative covenants.

   5 lessons in the Academy →

2. 02 Fixed-Income Cash Flows and Types

   How the cash flows of a bond can be structured: bullet, fully and partially amortising, sinking fund, floating-rate, step-up, index-linked, zero-coupon and deferred coupon. You also meet callable, putable and convertible bonds, and the legal, regulatory and tax differences between domestic, foreign and Eurobond issues.

   7 lessons · 2 videos in the Academy →

3. 03 Fixed-Income Issuance and Trading

   The main bond market segments, who issues and who invests, and how fixed-income indexes are built. It then covers primary market issuance (public offerings, auctions, shelf registrations and private placements) and how bonds trade in dealer-driven secondary markets.

   5 lessons in the Academy →

4. 04 Fixed-Income Markets for Corporate Issuers

   Short-term funding for companies and banks, such as bank loans, commercial paper, deposits and interbank funding, with a closer look at repurchase agreements, repo rates, haircuts and their risks. It ends with how investment-grade and high-yield long-term issuance differ in covenants, maturity and features.

   6 lessons · 1 video in the Academy →

5. 05 Fixed-Income Markets for Government Issuers

   Why governments borrow, the characteristics of sovereign debt, and how it is issued at auction and traded. It also covers debt issued by agencies, regional and local governments and supranational organisations.

   5 lessons in the Academy →

6. 06 Fixed-Income Bond Valuation: Prices and Yields

   Pricing a bond as the present value of its cash flows, the link between yield-to-maturity and price, and how to split the full price into flat price and accrued interest. It covers the coupon, maturity and convexity effects on price, the pull to par over time, and matrix pricing for bonds that rarely trade.

   6 lessons · 5 videos in the Academy →

7. 07 Yield and Yield Spread Measures for Fixed-Rate Bonds

   Converting yields between compounding frequencies, the street convention and true yield, current and simple yield, and yield-to-worst for callable bonds. The second half covers spreads over a benchmark: the G-spread, I-spread and Z-spread.

   6 lessons · 3 videos in the Academy →

8. 08 Yield and Yield Spread Measures for Floating-Rate Instruments

   How the quoted margin and discount margin of a floating-rate note are defined and linked to its price. It also covers money market conventions: discount-basis versus add-on rates, 360- versus 365-day years, and conversion to a bond equivalent yield.

   5 lessons · 2 videos in the Academy →

9. 09 The Term Structure of Interest Rates: Spot, Par, and Forward Curves

   Spot rates and pricing a bond with a different rate for each cash flow, then deriving par rates and implied forward rates from the spot curve. You learn how the three curves relate to each other when the spot curve slopes up, slopes down or is flat.

   6 lessons · 4 videos in the Academy →

10. 10 Interest Rate Risk and Return

    The sources of return on a bond (coupons, reinvestment income and capital gains or losses) and how an investor's horizon decides whether price risk or reinvestment risk matters more. It introduces Macaulay duration and the duration gap.

    5 lessons · 4 videos in the Academy →

11. 11 Yield-Based Bond Duration Measures and Properties

    Modified duration and its approximation from prices at higher and lower yields, money duration and the price value of a basis point. It also covers the duration of zero-coupon, perpetual and floating-rate bonds, and how coupon, maturity and yield affect duration.

    6 lessons · 3 videos in the Academy →

12. 12 Yield-Based Bond Convexity and Portfolio Properties

    Convexity as the second-order correction to the duration estimate, and how to combine the two to estimate a price change. You also calculate portfolio duration and convexity and learn when the weighted-average approach is a fair approximation.

    6 lessons · 2 videos in the Academy →

13. 13 Curve-Based and Empirical Fixed-Income Risk Measures

    Effective duration and effective convexity, which measure sensitivity to shifts in the benchmark curve and are used for bonds with embedded options. It adds key rate durations for non-parallel shifts and empirical duration, estimated from observed price data.

    5 lessons · 2 videos in the Academy →

14. 14 Credit Risk

    Probability of default, loss given default and expected loss, the traditional Cs of credit analysis, and how credit ratings and rating changes work. It then covers the macroeconomic, market and issuer-specific drivers of credit spreads and how a spread change affects price.

    8 lessons · 2 videos in the Academy →

15. 15 Credit Analysis for Government Issuers

    The qualitative and quantitative factors behind a sovereign's creditworthiness, such as institutions, fiscal and external positions and monetary flexibility. It also looks at credit risk for agencies, development banks, supranationals and regional governments.

    6 lessons in the Academy →

16. 16 Credit Analysis for Corporate Issuers

    Assessing a company's creditworthiness from its business model, industry, strategy and governance, and from profitability, coverage and leverage ratios. It covers the ranking of claims in default, secured versus unsecured debt, recovery rates, and why issue ratings can be notched away from the issuer rating.

    6 lessons · 2 videos in the Academy →

17. 17 Fixed-Income Securitization

    Why loans are securitised and who benefits: issuers, investors and the wider financial system. It walks through the process and the parties involved, with a focus on the special purpose entity that separates the assets from the originator.

    5 lessons · 1 video in the Academy →

18. 18 Asset-Backed Security (ABS) Instrument and Market Features

    Covered bonds and how they differ from ABS, internal and external credit enhancement, and credit tranching with a payment waterfall. It also covers non-mortgage ABS (credit card receivables and solar loans) and collateralised debt obligations such as CLOs.

    7 lessons · 1 video in the Academy →

19. 19 Mortgage-Backed Security (MBS) Instrument and Market Features

    Residential mortgage features, prepayment risk (contraction and extension), and agency versus non-agency RMBS. It covers pass-throughs, time-tranched CMOs including sequential-pay and PAC structures, and the structure and risks of commercial MBS.

    5 lessons · 3 videos in the Academy →

What the questions cover

• Bond features, indentures, covenants and cash flow structures, including embedded options
• How corporate and government issuers raise debt, and how bonds are issued and traded
• Pricing from a yield or from spot rates, full and flat prices, and accrued interest
• Yield measures and spreads for fixed-rate bonds, floating-rate notes and money market instruments
• Spot, par and forward rates, and what the shape of each curve implies
• Duration, convexity, money duration and PVBP, including effective and key rate duration
• Credit risk, credit analysis for sovereign and corporate issuers, and securitised products (ABS and MBS)

Key formulas

Bond price from yield-to-maturity

$\displaystyle PV = \sum_{t=1}^{N} \frac{PMT}{(1 + r)^{t}} + \frac{FV}{(1 + r)^{N}}$r is the yield per period and N the number of periods. With spot rates, discount each cash flow at its own rate, (1 + z_t)^t, instead.

Full price, accrued interest and flat price

$\displaystyle PV^{Full} = PV \times (1 + r)^{t/T}, \quad AI = \frac{t}{T} \times PMT, \quad PV^{Flat} = PV^{Full} - AI$PV is the price on the last coupon date, t the days since that date and T the days in the coupon period, both under the bond's day count convention.

Implied forward rate from spot rates

$\displaystyle (1 + z_A)^{A} \times (1 + IFR_{A,B-A})^{B-A} = (1 + z_B)^{B}$IFR_{A,B-A} is the rate for B − A years starting in year A, so IFR_{2,1} is the 2y1y rate.

Modified duration from Macaulay duration

$\displaystyle \text{ModDur} = \frac{\text{MacDur}}{1 + r}$r is the yield per period. If MacDur is measured in periods, divide the result by the number of periods per year to annualise it.

Approximate modified duration

$\displaystyle \text{ApproxModDur} = \frac{PV_{-} - PV_{+}}{2 \times \Delta\text{Yield} \times PV_{0}}$PV_− and PV_+ are the prices after the yield falls and rises by ΔYield. Enter ΔYield as a decimal.Learn it: Approximate modified duration →

Price change with duration and convexity

$\displaystyle \%\Delta PV^{Full} \approx -\text{AnnModDur} \times \Delta\text{Yield} + \tfrac{1}{2} \times \text{AnnConvexity} \times (\Delta\text{Yield})^{2}$The convexity term is positive for an option-free bond, so it adds to gains and reduces losses.

Money duration and PVBP

$\displaystyle \text{MoneyDur} = \text{AnnModDur} \times PV^{Full}, \quad PVBP = \frac{PV_{-} - PV_{+}}{2}$PV_− and PV_+ here use a 1 bp change in yield. PVBP is roughly money duration × 0.0001.Learn it: Integrated cases: duration of a bond bought mid-period →

Effective duration

$\displaystyle \text{EffDur} = \frac{PV_{-} - PV_{+}}{2 \times \Delta\text{Curve} \times PV_{0}}$The prices come from a model after the benchmark curve shifts down and up by ΔCurve. Use it for bonds with embedded options.Learn it: Effective duration: why curve duration replaces yield duration →

Expected loss

$\displaystyle \text{Expected loss} = \text{POD} \times \text{LGD}, \quad \text{LGD} = \text{Exposure} \times (1 - RR)$RR is the recovery rate. As a rough rule, the credit spread is about POD × LGD when LGD is stated as a percentage.Learn it: Expected loss: POD × LGD →

The Fixed Income formula sheet: the key formulas explained

Common mistakes

• Using the flat price where the full price is needed. Money duration, PVBP and the settlement amount a buyer pays are all based on the full price, including accrued interest.
• Mixing frequencies. For a semiannual bond, halve the coupon and the yield and double the number of periods. When annualising, divide periodic duration by the periodicity but periodic convexity by the periodicity squared.
• Multiplying by the recovery rate instead of the loss severity. Loss given default uses 1 − RR, so a 40% recovery means a 60% loss.
• Using modified duration for a callable bond or an MBS. Their cash flows change when rates change, so effective duration is the right measure, and effective convexity can be negative.
• Reading a forward rate as a spot rate. The 2y1y rate starts in two years and lasts one year; to price a bond with forward rates, multiply the successive one-period discount factors rather than discounting each cash flow at a single forward rate.
• Getting the duration gap backwards. When Macaulay duration is longer than the investment horizon, price risk dominates and the investor loses if rates rise; when it is shorter, reinvestment risk dominates and falling rates hurt.
• Treating a money market discount rate as an add-on rate, or using a 365-day year when the rate is quoted on a 360-day basis. Check both before calculating a price or interest amount.

How to study it

• Anchor everything on the price–yield relationship: prices fall when yields rise, and convexity makes the fall smaller than the rise for the same yield change.
• Before using a duration number, check which one the question gives you: Macaulay, modified, effective, key rate or money duration. The wrong one is often among the options.
• Draw the cash flows of any unfamiliar bond on a timeline before pricing it, and convert the coupon, yield and number of periods to the same frequency.
• Learn the calculator worksheets for bond pricing and yield (N, I/Y, PV, PMT, FV). Most of the numerical questions come down to entering five inputs correctly.
• Do not leave securitisation to the end. ABS and MBS questions are mostly descriptive and give steady marks to candidates who know how tranching and prepayment work.

Try 3 Fixed Income questions

Practise and prove Fixed Income

The question bank and the mock exams are the practice half of CheapMocks Academy. Try the free sample questions, see the topic weights for the whole exam and the latest Level I pass rates.

Fixed Income FAQ