Fixed Income

Fixed Income in short lessons: bond prices and yields, the term structure, duration and convexity, credit risk and securitised debt, each with worked examples, calculator keys and exam traps.

How this topic is tested, its exam weight and study tips: Fixed Income exam guide.

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Fixed Income formula sheet

All 184 formulas of the topic, each explained. Every module page ends with its own formulas; the key formulas are here. Downloads come with a subscription or a pass; the free trial does not include them.

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  1. 01

    Fixed-Income Instrument Features

    5 lessons · ~65 min 38 cards

    The building blocks of every bond and loan: who issues it, when it matures, how much principal is repaid, how interest is paid (fixed, floating or zero), where it ranks and what options it carries; how those features turn into cash flows and simple yield measures; and what the indenture says about sources of repayment, collateral and the affirmative and negative covenants that protect lenders.

  2. 02

    Fixed-Income Cash Flows and Types

    7 lessons · ~89 min2 videos 45 cards

    How a bond's principal can be repaid (bullet, fully or partially amortizing, sinking fund, waterfall), how its coupon can be set (fixed, floating, step-up, credit-linked, PIK, index-linked, zero and deferred), which embedded options help the issuer or the investor (call, put, conversion, CoCo), and how the place of issue and tax rules change a bond's legal and after-tax profile.

  3. 03

    Fixed-Income Issuance and Trading

    5 lessons · ~64 min 40 cards

    How bond markets are carved up by issuer type, credit quality and maturity, which issuers borrow and which investors lend in each segment, how fixed-income indexes differ from equity indexes, and how new bonds are sold in the primary market and traded afterwards in a mostly over-the-counter secondary market, compared at each step with equities.

  4. 04

    Fixed-Income Markets for Corporate Issuers

    6 lessons · ~79 min1 video 40 cards

    How companies and banks raise short-term money (credit lines, secured loans, commercial paper, deposits, interbank loans and repos), how a repurchase agreement works and what can go wrong with it, and why long-term borrowing looks so different for investment-grade and high-yield issuers.

  5. 05

    Fixed-Income Markets for Government Issuers

    5 lessons · ~65 min 40 cards

    How public-sector borrowers raise and trade debt: what sets a sovereign apart, how developed and emerging market governments fund themselves, the bills, notes and bonds they issue and why they spread them across maturities, how sovereign auctions work and differ from corporate underwriting, why on-the-run government bonds serve as benchmarks, and how agencies, regional governments and supranationals choose their funding.

  6. 06

    Fixed-Income Bond Valuation: Prices and Yields

    6 lessons · ~80 min5 videos 41 cards

    How to price a fixed-rate bond from its market discount rate on and between coupon dates, how to read the yield-to-maturity back out of a price, how coupon, maturity and yield shape price behaviour, and how matrix pricing estimates prices for bonds that rarely trade.

  7. 07

    Yield and Yield Spread Measures for Fixed-Rate Bonds

    6 lessons · ~84 min3 videos 44 cards

    How to state a bond's yield on a comparable basis (periodicity, effective annual rates and market conventions), how to measure the yield of a callable bond (yield-to-call, yield-to-worst, option-adjusted yield), and how to split a yield into a benchmark rate and a spread: benchmark spread, G-spread, I-spread, Z-spread and OAS.

  8. 08

    Yield and Yield Spread Measures for Floating-Rate Instruments

    5 lessons · ~63 min2 videos 37 cards

    How floating-rate notes are priced against a market reference rate, what the gap between the quoted margin and the discount margin says about price and credit risk, and how money market discount rates and add-on rates are converted to a bond equivalent yield so short-term instruments can be compared fairly.

  9. 09

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

    6 lessons · ~77 min4 videos 42 cards

    How default-risk-free spot rates describe the term structure of interest rates, how to price bonds with them, how par rates and implied forward rates are derived from them (and spot rates back from forwards), and how the shapes of the spot, par and forward curves are linked.

  10. 10

    Interest Rate Risk and Return

    5 lessons · ~64 min4 videos 37 cards

    Where a fixed-rate bond investor's return really comes from, how to measure the realized (horizon) yield when rates move, why reinvestment risk and price risk pull in opposite directions, and how Macaulay duration marks the holding period at which the two cancel.

  11. 11

    Yield-Based Bond Duration Measures and Properties

    6 lessons · ~78 min3 videos 40 cards

    How to turn a bond's cash flows into one number for its interest rate risk: Macaulay and modified duration, the approximate (price-based) modified duration, money duration and the PVBP, the special cases of zero-coupon, perpetual and floating-rate bonds, and how maturity, coupon and yield push duration up or down.

  12. 12

    Yield-Based Bond Convexity and Portfolio Properties

    6 lessons · ~78 min2 videos 34 cards

    Why duration alone misjudges large yield moves, how convexity measures the curvature of the price-yield relationship, how to combine duration and convexity into a sharper price-change estimate (in percent and in currency), and how to measure and interpret the duration and convexity of a bond portfolio.

  13. 13

    Curve-Based and Empirical Fixed-Income Risk Measures

    5 lessons · ~63 min2 videos 37 cards

    Interest rate risk measured against a benchmark yield curve instead of a bond's own yield: effective duration and effective convexity for bonds with embedded options, the negative convexity of callable bonds, price estimates for a curve shift, key rate durations for non-parallel moves, and why empirical duration can beat analytical duration for bonds with credit risk.

  14. 14

    Credit Risk

    8 lessons · ~108 min2 videos 45 cards

    What credit risk is and where it comes from, how expected loss splits into probability of default and loss given default, what credit ratings can and cannot tell you, which macroeconomic, market and issuer-specific forces move yield spreads, and how a spread change feeds through to a bond's price via duration and convexity.

  15. 15

    Credit Analysis for Government Issuers

    6 lessons · ~77 min 39 cards

    How credit analysis changes when the borrower is a government: why sovereigns repay from taxes and must be judged on willingness as well as ability to pay, the qualitative and quantitative factors behind a sovereign rating (institutions, fiscal, monetary, economic and external), and how agencies, public banks, supranationals and regional governments, including general obligation and revenue bonds, are assessed.

  16. 16

    Credit Analysis for Corporate Issuers

    6 lessons · ~79 min2 videos 45 cards

    How a credit analyst judges a non-financial company's ability to repay: the qualitative picture (business model, industry, business risk, governance and covenants), the quantitative factors and the profitability, coverage and leverage ratios that measure them, and how seniority, collateral and the priority of claims drive recovery, issue ratings and notching.

  17. 17

    Fixed-Income Securitization

    5 lessons · ~64 min1 video 38 cards

    How loans and receivables are pooled, sold to a special purpose entity and turned into asset-backed securities; who benefits (issuers, investors, economies and markets) and what risks remain; the parties and legal documents involved; why the bankruptcy-remote SPE is the heart of the deal; and how tranching decides who is paid first and who absorbs losses first.

  18. 18

    Asset-Backed Security (ABS) Instrument and Market Features

    7 lessons · ~97 min1 video 40 cards

    How covered bonds keep loans on the bank's balance sheet yet give investors two layers of protection, how securitizations use overcollateralization, excess spread and subordination to absorb losses, how credit card and solar ABS pay investors over their life, and how CDOs and CLOs use an active collateral manager to run a leveraged pool of loans.

  19. 19

    Mortgage-Backed Security (MBS) Instrument and Market Features

    5 lessons · ~68 min3 videos 45 cards

    How mortgage loans work and why the borrower's right to prepay makes their cash flows uncertain, how residential pass-throughs and CMOs package and reshuffle that prepayment risk, and why commercial MBS behave differently: call protection, balloon risk, concentration risk and the DSC and LTV ratios.