Study guide · Session 2

Fixed Income

11-14% of the exam · session 2 · 19 learning modules

Fixed Income covers what bonds are, how and where they are issued and traded, how they are priced from yields and spot rates, how their prices respond to rates (duration and convexity), credit risk and securitization. Level I questions mix definitions with short calculations: prices, yields, forward rates and duration or convexity estimates.

A study feature written by ExamDragon, not part of the real exam. Each heading is one of this topic's 19 learning modules in the 2027 curriculum, named in our own words.

At a glance

Session 2

11-14%

of the exam, as CFA Institute weights it for 2027

Weight: 11-14%
Modules: 19
Key terms: 14

What this guide covers, module by module

FI.1Bond features and indenture covenants
FI.2Cash flow structures and embedded provisions
FI.3Bond market segments, indexes and trading
FI.4How companies and banks borrow
FI.5Government, agency and supranational borrowing
FI.6Pricing a bond from its yield
FI.7Yield conventions and spreads for fixed coupons
FI.8Floating-rate notes and money market yields
FI.9Spot, par and forward rate curves
FI.10Bond return sources and Macaulay duration
FI.11Modified duration, money duration and PVBP
FI.12Convexity and portfolio duration
FI.13Effective, key rate and empirical duration
FI.14Default risk, ratings and spreads
FI.15Assessing sovereign and municipal credit
FI.16Assessing corporate borrowers
FI.17How securitization works
FI.18Covered bonds, ABS and CDOs
FI.19Mortgage-backed securities and prepayment risk

FI.1Bond features and indenture covenants

A bond's basic features are the issuer, maturity, par value, coupon rate and frequency, and the currency of payment.
The indenture (trust deed) is the legal contract; a trustee acts for bondholders and monitors the issuer.
Affirmative covenants say what the issuer must do: pay interest and principal, keep collateral insured, report to bondholders.
Negative covenants restrict the issuer: limits on further debt, asset sales, liens and payouts to shareholders.
Security can be collateral (secured bonds) or the issuer's general credit (unsecured debentures); seniority sets the order of claims.

The situationAn indenture requires the issuer to file audited statements every year and bars it from pledging its plant as security for any new loan.
Step 1Filing statements is something the issuer must do: an affirmative covenant.
Step 2The ban on new pledges restricts the issuer: a negative covenant (a negative pledge).
Where questions turnQuestions turn on mistaking a restriction worded positively, such as 'maintain a maximum leverage ratio', for an affirmative covenant.
The takeawayAffirmative covenants oblige action; negative covenants restrict it, and negative covenants usually cost the issuer more.

Practise FI.1

FI.2Cash flow structures and embedded provisions

Principal can be repaid as a bullet at maturity, fully amortized over the life, or partially amortized with a balloon at maturity.
A sinking fund retires part of the issue each year, lowering credit risk but adding reinvestment risk for investors.
Floating-rate notes pay a reference rate plus a quoted margin; a cap protects the issuer, a floor protects the investor.
Contingency provisions that benefit the issuer: call options. Those that benefit investors: put options and conversion rights.
Callable bonds yield more than straight bonds; putable and convertible bonds yield less.
Domestic, foreign and Eurobonds differ by where and in what currency they are issued; tax rules (for example on original issue discount) change after-tax returns.

The situationA company can issue a 10-year bond at 5.0% straight or 5.6% if callable after year 3.
Step 1The call lets the issuer refinance if rates fall, which hurts investors.
Step 2Investors demand 60 basis points more to give up that upside.
Where questions turnCandidates mix up who owns the option: the issuer holds a call, the investor holds a put or a conversion right.
The takeawayOptions held by the issuer raise the yield; options held by the investor lower it.

Practise FI.2

FI.3Bond market segments, indexes and trading

Market segments are classified by issuer (sovereign, government-related, corporate, securitized), credit quality, maturity, currency and geography.
Investment grade is BBB- or Baa3 and above; below that is high yield.
Bond indexes are mostly weighted by market value of debt outstanding, so the largest borrowers get the largest weights.
Primary issuance is by auction (common for sovereigns), underwritten offerings, best-efforts offerings or private placements.
Most bonds trade over the counter through dealers; an issuer may have dozens of separate issues, so each trades less often than its shares.

The situationAn index of corporate bonds holds Issuer A with USD 40 billion outstanding and Issuer B with USD 10 billion, at similar prices.
Step 1Weights follow the market value of debt outstanding.
Step 2A has about four times B's weight.
Where questions turnBonds trade mostly over the counter, not on exchanges as equities do.
The takeawayA market-value index tilts toward the most indebted issuers, not the most creditworthy.

Practise FI.3

FI.4How companies and banks borrow

Short-term corporate funding: bank lines of credit, secured loans and factoring, and commercial paper.
Commercial paper is unsecured, short-dated debt from issuers with strong credit, usually backed by a bank line to cover rollover risk.
Banks also fund themselves with deposits, interbank loans, certificates of deposit and repos.
A repo is a sale of securities with an agreement to buy them back: the seller borrows cash; the buyer lends it.
The haircut (collateral value above the cash lent) protects the lender; it is larger for riskier collateral and longer terms.
Investment-grade issuers fund long-term with unsecured bonds and few covenants; high-yield issuers rely more on secured loans, covenants and call features.

The situationA dealer sells bonds worth USD 10.2 million and borrows USD 10.0 million overnight at a repo rate of 3.6% (360-day basis).
Step 1Haircut = (10.2 - 10.0)/10.2 = about 2%.
Step 2Interest = 10,000,000 x 0.036 x 1/360 = USD 1,000.
Step 3Repurchase price = USD 10,001,000.
Where questions turnThe party that sells the security in a repo is the borrower of cash, not the lender.
The takeawayThe repo is a collateralized loan whose cost is the repo rate and whose protection is the haircut.

Practise FI.4

FI.5Government, agency and supranational borrowing

Sovereigns borrow in their own currency (local) and sometimes in foreign currency; local currency debt is usually rated higher.
Sovereign bonds are mostly sold at regular public auctions, often through primary dealers.
Non-sovereign governments (states, provinces, cities) issue general obligation bonds backed by taxes and revenue bonds backed by a project.
Quasi-government agencies may carry an explicit or implied state guarantee; supranationals are owned by several member countries.
Government debt is issued on a regular calendar in benchmark sizes, which makes the newest issues (on-the-run) the most liquid.

The situationA city issues bonds to build a toll bridge, repayable only from tolls.
Step 1Repayment depends on one project's cash flows, not the city's taxes.
Step 2That makes it a revenue bond, analysed much like a business.
Where questions turnSupranationals are owned by many countries; agencies belong to a single government.
The takeawayThe source of repayment, taxes or project income, defines the type of non-sovereign bond.

Practise FI.5

FI.6Pricing a bond from its yield

Price = the sum of each cash flow discounted at the yield per period: PV = C/(1 + r) + C/(1 + r)^2 + ... + (C + FV)/(1 + r)^N.
Coupon above yield: premium; coupon below yield: discount; coupon equal to yield: par.
Price and yield move inversely and the relation is convex; for the same coupon, a longer bond is more sensitive to yield.
Between coupon dates: full price = PV at the last coupon date x (1 + r)^(t/T); flat price = full price - accrued interest, where accrued = coupon x t/T.
With constant yield, a premium or discount bond's price moves toward par as maturity nears (pull to par).
Matrix pricing estimates the yield of a rarely traded bond from the yields of traded bonds with similar credit, coupon and maturity.

The situationA 3-year bond with a 5% annual coupon yields 6%.
Step 1PV of coupons: 5/1.06 + 5/1.06^2 = 4.717 + 4.450 = 9.167.
Step 2PV of final payment: 105/1.06^3 = 88.160.
Step 3Price = 97.33.
Where questions turnQuoted (flat) prices exclude accrued interest; the buyer pays the full price.
The takeawayBecause the coupon is below the yield, the bond trades at a discount to par.

Practise FI.6

FI.7Yield conventions and spreads for fixed coupons

Yields must be compared on the same periodicity: convert with (1 + APR_m/m)^m = (1 + APR_n/n)^n.
Effective annual yield of a semiannual bond = (1 + y/2)^2 - 1.
Current yield = annual coupon / flat price; it ignores reinvestment and the move to par.
Yield-to-call and yield-to-worst (the lowest of yield-to-maturity and each yield-to-call) matter for callable bonds.
G-spread: over an interpolated government yield. I-spread: over the swap rate. Z-spread: a constant spread over every point on the government spot curve.
Option-adjusted spread = Z-spread minus the value of the embedded option in spread terms; for a callable bond OAS is below the Z-spread.

The situationA semiannual bond yields 6.00% stated annually; an investor wants the annual-pay equivalent.
Step 1Semiannual rate = 3.00%.
Step 2Annual equivalent = 1.03^2 - 1 = 6.09%.
Where questions turnQuestions turn on comparing yields with different compounding without converting them first.
The takeawayThe same return is stated as a higher rate when compounding is less frequent.

Practise FI.7

FI.8Floating-rate notes and money market yields

An FRN pays a reference rate plus a quoted margin, reset each period; its price stays near par on reset dates.
The discount (required) margin is the spread the market now demands; if it is above the quoted margin the FRN trades at a discount, if below at a premium.
Money market instruments are quoted on a discount rate basis (based on face value) or an add-on rate basis (based on price).
Discount basis: PV = FV x (1 - days/year x DR). Add-on basis: PV = FV/(1 + days/year x AOR).
To compare, restate on a common basis such as the bond equivalent yield: an add-on rate on a 365-day year.

The situationA 180-day bill of face 100 is quoted at a 4.00% discount rate (360-day year).
Step 1Price = 100 x (1 - 0.04 x 180/360) = 98.00.
Step 2Bond equivalent yield = (2/98) x 365/180 = 4.14%.
Where questions turnDiscount rates are computed on face value, not on the price paid, so they understate the investor's yield.
The takeawayA discount rate understates the return, because it is based on face value and a 360-day year.

Practise FI.8

FI.9Spot, par and forward rate curves

A spot rate is the yield on a zero-coupon bond for one maturity; a bond's price can be found by discounting each cash flow at its own spot rate.
A par rate is the coupon that makes a bond priced off the spot curve trade at par.
A forward rate is the rate for a future period implied by spot rates: (1 + S2)^2 = (1 + S1)(1 + f(1,1)).
Spot rates are geometric averages of the forward rates before them.
Upward-sloping spot curve: forward curve above it and par curve slightly below it; downward-sloping: the reverse; flat: all three equal.

The situationThe 1-year spot rate is 3% and the 2-year spot rate is 4%.
Step 1(1.04)^2 = 1.0816.
Step 21.0816 / 1.03 = 1.0501.
Step 3The 1-year rate one year forward = 5.01%.
Where questions turnA forward rate is not the average of two spot rates; it is the marginal rate that links them.
The takeawayRising spot rates imply forward rates above the spot rates.

Practise FI.9

FI.10Bond return sources and Macaulay duration

A fixed-rate bond's return comes from coupons, reinvestment of coupons, and the gain or loss on sale or redemption.
If yields rise, reinvestment income rises but the sale price falls; if yields fall, the reverse.
Macaulay duration is the weighted average time to receive the cash flows, weighted by each cash flow's share of the price.
When the horizon equals Macaulay duration, the two effects offset for a small one-time parallel shift.
Duration gap = Macaulay duration - investment horizon: a positive gap leaves price risk dominant; a negative gap leaves reinvestment risk dominant.

The situationA 2-year bond with a 10% annual coupon is priced at par.
Step 1PV of year 1 cash flow = 9.09; PV of year 2 = 90.91.
Step 2MacDur = (1 x 9.09 + 2 x 90.91)/100 = 1.91 years.
Where questions turnA short-horizon investor faces price risk, not reinvestment risk, when yields rise.
The takeawayDuration is shorter than maturity whenever coupons arrive before the final payment.

Practise FI.10

FI.11Modified duration, money duration and PVBP

Modified duration = Macaulay duration / (1 + yield per period); %price change approx. -ModDur x change in yield.
Approximate modified duration = (PV- - PV+)/(2 x PV0 x change in yield), from prices with the yield shifted down and up.
Money duration = ModDur x full price (in currency); PVBP is the price change for a 1 basis point move: ModDur x full price x 0.0001.
Duration rises with maturity (usually), and falls with a higher coupon or a higher yield.
A zero-coupon bond's Macaulay duration equals its maturity.

The situationA position of USD 2,000,000 par at a full price of 98.00 has modified duration 4.50.
Step 1Market value = 1,960,000.
Step 2Money duration = 4.50 x 1,960,000 = 8,820,000.
Step 3PVBP = 8,820,000 x 0.0001 = USD 882.
Where questions turnUsing Macaulay instead of modified duration, or par instead of full price, overstates the price change.
The takeawayPVBP turns duration into a currency amount per basis point.

Practise FI.11

FI.12Convexity and portfolio duration

Duration is a straight-line estimate; convexity captures the curvature of the price-yield relation.
%price change approx. -ModDur x dy + 0.5 x Convexity x dy^2; with positive convexity the adjustment is always added.
A bond with more convexity gains more when yields fall and loses less when they rise.
Portfolio duration and convexity are market-value-weighted averages of the holdings' figures.
That average assumes a parallel shift; it fails for twists and is less exact for callable bonds and large moves.

The situationA bond has modified duration 6.50 and convexity 60; its yield rises 100 basis points.
Step 1Duration effect = -6.50 x 0.01 = -6.50%.
Step 2Convexity effect = 0.5 x 60 x 0.0001 = +0.30%.
Step 3Estimate = -6.20%.
Where questions turnThe convexity term uses the squared yield change, so it never changes sign with the direction of the move.
The takeawayPositive convexity makes a price fall smaller than duration alone predicts.

Practise FI.12

FI.13Effective, key rate and empirical duration

Effective duration and convexity use model prices after shifting the benchmark curve, so cash flows may change with rates.
They are the right measures for bonds with embedded options and mortgage-backed securities, whose cash flows depend on rates.
EffDur = (PV- - PV+)/(2 x PV0 x dCurve); EffCon = (PV- + PV+ - 2 x PV0)/(dCurve^2 x PV0).
Callable bonds show negative effective convexity when rates are low; putable bonds show more positive convexity.
Key rate durations measure sensitivity to shifts at single maturities and capture non-parallel shifts; they sum to effective duration.
Empirical duration is estimated from observed price changes; it can be lower than analytical duration for credit-risky bonds because spreads often narrow when government yields rise.

The situationA callable bond is priced at 100.00, at 101.50 when the curve falls 25 basis points and at 98.70 when it rises 25 basis points.
Step 1EffDur = (101.50 - 98.70)/(2 x 100 x 0.0025).
Step 2= 2.80/0.50 = 5.60.
Where questions turnYield-based duration assumes fixed cash flows, which fails for callable and prepayable bonds.
The takeawayThe call caps price gains, so effective duration falls as rates drop toward the call level.

Practise FI.13

FI.14Default risk, ratings and spreads

Credit risk has two components: probability of default (PD) and loss given default (LGD = exposure x (1 - recovery rate)).
Expected loss = PD x LGD; a yield spread of about PD x LGD (as a rate) just covers expected losses.
Ratings group issuers and issues by credit quality; notching rates issues of one issuer differently by seniority.
Ratings are stable but can lag market spreads, miss event risk and be wrong.
Spreads widen in downturns and narrow in expansions, react to market liquidity and supply, and vary with issuer leverage and earnings.

The situationA bond has a 2% annual default probability and a 40% expected recovery rate.
Step 1LGD = 1 - 0.40 = 60%.
Step 2Expected loss = 0.02 x 0.60 = 1.2% a year.
Where questions turnRecovery rate and loss given default are complements; questions often swap them.
The takeawayA spread of about 120 basis points would only just cover expected losses, before any risk premium.

Practise FI.14

FI.15Assessing sovereign and municipal credit

Sovereign analysis weighs institutions and politics, economic strength, fiscal position, monetary flexibility and external position.
A sovereign's ability to pay is backed by taxes; willingness to pay matters because creditors cannot seize its assets.
Local currency debt is usually rated above foreign currency debt, since the government controls its own currency.
Reserve currency status and an independent central bank support creditworthiness.
General obligation bonds rely on taxing power; revenue bonds rely on a project's income and are judged by debt service coverage.

The situationA country has high debt to GDP, a floating currency and reserve currency status, and most of its debt is in its own currency.
Step 1Local currency debt can be serviced through taxes or money creation.
Step 2Reserve status keeps demand for its bonds strong.
Where questions turnQuestions confuse the higher-rated local currency debt with the riskier foreign currency debt.
The takeawayHigh debt alone does not mean low creditworthiness; currency control and institutions matter.

Practise FI.15

FI.16Assessing corporate borrowers

Qualitative factors: business model, industry, competitive position, management, governance; the four Cs are capacity, collateral, covenants and character.
Profitability and cash flow: EBITDA, funds from operations, free cash flow.
Coverage: EBITDA / interest expense; higher is stronger. Leverage: debt / EBITDA and debt / capital; lower is stronger.
Seniority runs: first lien secured, second lien, senior unsecured, subordinated, then preferred and common equity.
Recovery rates are higher for senior secured debt; the absolute priority rule is not always followed in reorganizations.
Agencies may notch a high-yield issuer's subordinated debt further below the issuer rating than an investment-grade issuer's.

The situationA company has EBITDA of USD 240 million, interest of USD 40 million and debt of USD 900 million.
Step 1Coverage = 240/40 = 6.0x.
Step 2Leverage = 900/240 = 3.75x.
Where questions turnQuestions swap coverage (EBITDA over interest) and leverage (debt over EBITDA).
The takeawayTwo ratios, coverage and leverage, give a first view of capacity to repay.

Practise FI.16

FI.17How securitization works

Securitization pools loans or receivables and sells them to a special purpose entity (SPE), which issues securities backed by the pool.
Parties: the originator (seller), the SPE (issuer), the servicer, the trustee and the investors.
The SPE is bankruptcy remote, so investors depend on the pool rather than the originator's credit.
Benefits: frees originators' capital and funding, gives investors tailored risk exposures, turns illiquid loans into tradable securities.
Risks include complexity, poor underwriting when originators do not keep risk, and the opacity seen in 2007 to 2008.

The situationA bank sells USD 500 million of auto loans to an SPE that issues three tranches of securities.
Step 1The bank receives cash and can lend again.
Step 2The servicer collects payments and passes them to the trustee for investors.
Where questions turnThe servicer and the SPE play different roles; the SPE owns the assets, the servicer collects the cash.
The takeawaySecuritization separates the assets from the originator and redistributes their cash flows.

Practise FI.17

FI.18Covered bonds, ABS and CDOs

Covered bonds are issued by banks, secured by a dynamic cover pool, stay on the balance sheet and give dual recourse to the issuer and the pool.
Internal credit enhancement: subordination, overcollateralization, excess spread and reserve accounts. External: guarantees and letters of credit.
Subordination (tranching) allocates losses from the most junior tranche up, protecting senior tranches.
Auto loan ABS are amortizing; credit card ABS are non-amortizing during a lockout period, then pay down principal.
A CDO repackages bonds or loans into senior, mezzanine and equity tranches; its manager aims to earn more on the collateral than the funding cost.

The situationA deal has a pool of 100, a senior tranche of 80, a mezzanine of 15 and an equity tranche of 5; the pool loses 8.
Step 1Equity absorbs the first 5 and is wiped out.
Step 2Mezzanine absorbs the next 3.
Step 3The senior tranche loses nothing.
Where questions turnCovered bond pools are dynamic and give recourse to the issuer; ABS pools are usually static with recourse only to the pool.
The takeawayTranching moves credit losses to junior investors in return for higher expected yields.

Practise FI.18

FI.19Mortgage-backed securities and prepayment risk

Prepayment risk is the uncertainty in when mortgage principal is repaid: contraction risk when rates fall and prepayments speed up, extension risk when rates rise and they slow.
Residential mortgages vary by maturity, rate type (fixed, adjustable), amortization, prepayment penalties and whether lenders have recourse to the borrower.
A pass-through passes the pool's interest and principal, less fees, to investors pro rata; investors bear all prepayment risk.
A collateralized mortgage obligation (CMO) splits the cash flows into tranches; sequential-pay tranches get principal in order, and PAC tranches with support tranches give more predictable cash flows.
Commercial MBS are backed by income-producing property loans, often non-recourse with balloon payments and strong call protection (lockouts, penalties, defeasance); credit analysis uses debt service coverage and loan-to-value.

The situationMortgage rates fall from 6% to 4% and many borrowers refinance a pool backing a pass-through.
Step 1Principal comes back earlier than expected.
Step 2Investors must reinvest it at lower rates, and the security's price rises less than an option-free bond's.
Where questions turnContraction risk goes with falling rates and extension risk with rising rates; questions swap them.
The takeawayFalling rates create contraction risk, which limits the upside of mortgage securities.

Practise FI.19

Key terms

Indenture: The legal contract stating a bond's terms, covenants and remedies.
Flat price: The quoted bond price, which excludes accrued interest.
Full price: Flat price plus accrued interest; what the buyer pays.
Spot rate: The yield on a zero-coupon bond for one maturity.
Forward rate: The interest rate for a future period implied by today's spot rates.
Macaulay duration: The weighted average time to receive a bond's cash flows.
Modified duration: The approximate percentage price change for a 1% change in yield.
PVBP: The price change in currency for a 1 basis point change in yield.
Convexity: The curvature of the price-yield relation, improving the duration estimate.
Effective duration: Duration from model prices after shifting the benchmark curve; used for bonds with options.
Loss given default: The share of exposure lost if the issuer defaults: one minus the recovery rate.
Z-spread: A constant spread over the spot curve that makes discounted cash flows equal the price.
Haircut: The amount by which repo collateral value exceeds the cash lent.
Covered bond: A bank bond secured by a dynamic cover pool, with recourse to the bank and the pool.

After this guide: You should be able to price a bond from its yield or from spot rates, convert yields, estimate price changes with duration and convexity, and explain credit risk and securitization structures.

Practise Fixed Income

Built to the topics and weights CFA Institute publishes for the 2027 Level I curriculum. The module names, explanations, worked examples and traps are ExamDragon's own. Every source this path is built on.