Fixed Income

Tenor

Time remaining until maturity

Trustee

Financial institution representing an investor’s interest appointed by issuer

• ensure company meets obligations and payments

• takes action on behalf of bondholders

Floating Rate Notes

Variable market rate of interest + fixed margin

Bond indenture/ trust deed

Legal contract between bond issuer and bondholders

(Un)Secured Bond

Cash flows repaid from the operating cash flow of the company, with the added security of a legal claim when liquidating

Unsecured has no claim

Affirmative Covenants

Affirmative covenants are requirements the issuer must fulfill. These may include:

• Providing timely financial reports to bondholders

• Specifying the use of proceeds from the bond issue

• Granting bondholders the right to redeem at a premium if the issuer is acquired in a merger or takeover

Cross-default/ Pari Passu

• Cross-Default Clause:
  If the issuer defaults on any other debt, it is also considered a default on this bond.

• Pari Passu Clause:
  Ensures the bond has equal claim priority with the issuer’s other senior debt.

Negative Covenants

Negative covenants place restrictions on the issuer to protect bondholders by limiting risky actions. Examples include restrictions on:

• Asset sales and leasebacks

• Pledging the same collateral to multiple lenders

• Issuing more senior debt (negative pledge clause)

• New borrowings, share buybacks, or dividends — often subject to a financial ratio test (e.g., debt/EBITDA limits)

They prevent excessive risk-taking but shouldn’t overly restrict the issuer's flexibility.

Bullet Structure

Par paid back in a single payment at maturity

Partially Amortizing/Balloon Payment

Repayment of some principal at maturity.

Sinking fund provisions (pros/cons)

• Repayment of principal through a series of payments over the life of a bond issue

Pros: less credit risk cuz get periodic payments

Cons: receiving cash flows early and only behind able to reinvest them at lower yields (when interest rates fall due to reinvestment risk)

Waterfall structure

• pay bondholders in order of seniority

Floating-rate notes FRNs

• Periodic interest depending on prevailing market rate of interest at the time future coupon payments are made

  • Market reference rate → variable market rate

  • Add credit spread with basis points

Step-Up Coupon Bonds

Coupon rate increases over time according to a predetermined schedule

• leveraged loans/credit-linked note

  • if credit quality lowers

  • coupon increases

Leveraged/ Credit linked notes bonds

Both move with credit risk

• Leverage

  • Low starting credit quality issuer

• Credit linked

  • anyone can issue

Payment-in-kind bond PIK

Allows issuer to make the coupon payments by increasing the principal amount of the outstanding bonds

• paying bond interest with more bonds

Index-linked bond

Coupon payments or a principal value that is based on a specified published index

• Inflation-linked bonds (linkers) → increases cash flows with a specified inflation index

Inflation-indexed bonds

• Interest-indexed bonds

  • Coupon rate adjusted for inflation, while principal value remains unchanged

• Capital-indexed bonds

  • Treasury inflation-protected securities (TIPS)

  • coupon rate constant but principal value increased by inflation

  • PMT from new principal

Deferred coupon bond

coupon payments do not begin until a specified time after issuance

• often traded below par to provide investors with the yields they demand

Contingency provision

An action that may be taken if an event actually occurs

• embedded options

  • integral part of bond contract and are not a separate security

Callable, putable, convertible

Bermuda/ European/ American call provision

• Bermuda

  • Many specific dates to exercise

• European

  • One specific date to exercise

• America

  • From a date onwards can exercise

Convertible Bond terms

• Conversion price. This is the par amount per share at which the bond may be converted to common stock.

• Conversion ratio. This is equal to the par value of the bond divided by the conversion price. If a bond with a $1,000 par value has a conversion price of $40, its conversion ratio is 1,000 / 40 = 25 shares per bond.

• Conversion value. This is the market value of the shares that would be received upon conversion. A bond with a conversion ratio of 25 shares when the current market price of a common share is $50 would have a conversion value of 25 × $50 = $1,250.

Contingent convertible bonds CoCos

bonds that convert from debt to common equity automatically if a specific event occurs

• if bank equity falls below a given level → automatically converted to common stock

  • decrease liabilities

  • increase equity

  • meets min equity requirement

Eurobond

bonds issued outside the jurisdiction of any one country and can b issued in any currency

• global bond → eurobond in at least one domestic bond market and in eurobond market

• REFERRED TO THE CURRENCY THEY ARE DENOMINATED IN

• Old: bearer bond

• New: Registered Bonds

Global Bond

Similar to Eurobond but can be issued in multiple different countries

Sukuk bonds

the holder has an undivided ownership right in a particular asset and is therefore entitled to the return generated by that asset

Original issue discount (OID) bonds

ZCB and other bonds solder at significant discounts to par when issued

• tax liabilities even when no cash interest payment has been made

• a portion of the discount from par at issuance is treated as taxable interest income each year

• no capital gains but all in interest income

Bond Segments

• Type of issuer (or sector)

  • Governments, corporates, SPE

• credit quality

  • BBB or higher investment grade bonds

  • BB+ or lower “junk bonds”

• time to maturity

Issuer Credit Maturity Spectrum

Secured Corporate Bonds investment grade or high yield

High yield because lass reliable operating cash flows needs to offer security

Investor positioning in Credit/Maturity Spectrum

Fixed income index vs Equity index

• Fixed-income indexes have more constituents than equity indexes because companies issue many bonds, while they typically have only a few share classes.

  • Use sampling techniques to buy a representative subset of the index.

  • This aims to closely match the index’s performance while keeping costs and complexity down.

• Bonds mature and are issued frequently, causing higher turnover in bond indexes compared to equity indexes.

• Broad bond indexes are heavily weighted toward government (sovereign) bonds, and their composition shifts with changes in issuance trends like maturity and credit quality.

Debut Issuer

An issuer that is offering its first ever–bond is referred to as a debut issuer and is typically a growing and maturing firm that is replacing bank loans in its capital structure with the proceeds from the bond issue.

Distressed debt profit

A distressed debt investor might buy the debt from other institutions that are prohibited from owning securities with low credit ratings, and aims to profit from the issuer's fortunes reversing, higher–than–expected recovery rates in liquidation, or value-enhancing restructuring of the issuer.

Private Placement

Newly issued debt BUT for specific investors

• mainly for newer companies with less predictable cash flows

Bank lines of credit

• Uncommitted Line: Bank may refuse to lend; flexible; no fees except interest; may be unsecured.

• Committed Line: Bank must lend for a set time; commitment fee (~50bps); renewal risk at maturity.

  • Regulators requires banks to holder higher reserves

• Revolving Line ("Revolver"): Most reliable; longer-term; restrictive covenants; similar fees/rates to committed lines.

Syndicates can be formed for committed/revolving to minimize capital requirement

Factoring

Actual transfer of credit granting and collection of receivables to a lender at a discount from their face value

• Discount depends on creditworthiness of firm’s customers and collection costs

• usually sold to a third party

Bridge financing

Temporary debt until permanent financing can be secured

Rollover risk

Risk that a company will not be able to sell new CP to replace maturing paper

• Backup lines of credit

  • liquidity enhancement where lenders agree to provide funds to make repayments if needed

Checking accounts/Operational Deposits/Saving deposits

• Checking account

  • provide transaction services and immediate availability of funds

  • no interest

• Operational deposits

  • larger customers who require cash management, custody, and clearing services

• Savings deposits

  • stated term and interest rate

(Non)negotiable CDs

Nonnegotiable CANNOT be sold before maturity, and early withdrawals of funds incurs a penalty

Central bank funds market

Excess reserves lent to other banks at central bank funds rate

Asset-backed commercial paper

1. Financial institution transfers collateral to an SPE in return for cash

2. SPE sells ABCP to investors

Funding for financial institutions

• Checking account

• Operational deposits

• Saving deposits

• CD

• interbank fund

  • REPOS

• Central bank funds market

Repurchase agreement

One party sells a security to a counterparty with the commitment to buy it back at a later date at higher price

• Repo rate

  • interest rate implied by the difference between the 2 prices

Purchase price/ initial margin/ variation margin

• Purchase price

  • amount to receive for the collateral

• Initial margin

  • amount of collateral needed for lender

• Variation margin

  • change in MV of collateral leads to more/less collateral

General collateral repo

collateral using specific security of general type of security

• Any high-quality securities

Regular collateral

• Specific security the lender wants

Main uses of repurchase agreements

• Borrowers: Financial institutions use repos to finance securities holdings.

• Lenders: Banks/investors use repos to earn short-term interest on extra cash.

• Central banks: Use repos to control money supply (lend to ease, borrow to tighten).

• Short sellers: Hedge funds use repos to borrow securities, sell short, and profit if prices fall.

Repo Risks and Mitigation

• Default risk: Borrower fails to repurchase at the end.

• Collateral risk: Value of collateral drops in case of default.

• Margining risk: Incorrect or untimely margin calculations.

• Legal risk: Issues with enforceability of contracts.

• Netting & settlement risk: Problems with payment netting or settling cash and collateral.

Mitigation:

• Tri-party repos (using a third-party intermediary like a custodian or clearinghouse) improve efficiency and collateral management but don't reduce credit risk.

• Bilateral repos are directly between two parties, without a third party.

Public vs private accounting

Public sector accounting relies more on cash transactions and less on accruals (e.g., depreciation, unfunded liabilities) than private sector accounting.
When assessing government financial statements, an analyst should consider an "economic balance sheet" that includes:

• Implied assets (e.g., expected future tax revenues)

• Implied liabilities (e.g., promised future expenditures)
  in addition to the reported financial assets and liabilities.

Analyst considerations forecasting government debt

• The government's fiscal policy (e.g., tax cuts, spending increases to manage the business cycle)

• The cyclicality and inflation sensitivity of revenues and spending

• Debt features (e.g., floating rates, inflation indexing)

• Any guarantees of non-sovereign debt

Nonsovereign Debt

Issued by states, provinces, counties, and entities created to fund and provide services

Agency/ quasi-government bonds

Issued by national governments ENTITY FOR SPECIFIC PURPOSES

• infrastructure

• mortgage

General Obligation bonds

Local and regional government authorities may issue debt for public

Revenue bonds

Debt for specific project

• repayment from revenue of project

Supranational bond

Issued by international institutions (World Bank, IMF) to promote economic cooperation, trade or economic growth.

Auction debt workflow

• Noncompetitive bids: Guaranteed allocation at the auction's final price.

• Competitive bids: Set the price; ranked by highest price (lowest yield) first.

• Cut-off yield: Yield of the lowest-price successful competitive bid.

• Single-price auction: All pay the cut-off price.

• Multiple-price auction: Winners pay the price they bid.

What are the roles of primary dealers in sovereign bond markets?

Primary dealers:

• Submit competitive bids in government debt auctions

• Submit bids on behalf of third parties

• Act as counterparties to the central bank in open market operations (buying/selling securities)

How do noneconomic investors affect sovereign bond yields?

Noneconomic investors (e.g., central banks, foreign governments, regulated institutions):

• Buy government bonds for purposes like monetary policy, reserves, or regulation compliance

• Their demand lowers sovereign bond yields compared to non-sovereign issuers

Direct/ Indirect risk

• Direct

  • Direct currency exposure of holding foreign denominated debt

• Indirect

  • Risk exposure from default

  • Need to raise bond currency through international transactions

Types of day count methods

• actual/actual convention

  • actual number of days between coupon payments and actual number of days between the last coupon date and the settlement date

  • government bonds

• 30/360 convention

  • assumes each month has 30 days and year has 360 days

  • corporate bonds

Flat/Full Price

• Flat/ Clean/ Quoted

  • bond’s quoted price

  • imagine the previous price at previous payment

• Full/ Dirty/ Invoice

  • sum of its flat price and accrued interest

Flat = Full - accrued interest

Price and specific bond features

1. At a point in time, a decrease (increase) in a bond's YTM will increase (decrease) its price. That is, there is an inverse relationship between yield and price.

2. Other things equal, the price of a bond with a lower coupon rate is more sensitive to a change in yield than is the price of a bond with a higher coupon rate.

3. Other things equal, the price of a bond with a longer maturity is more sensitive to a change in yield than is the price of a bond with a shorter maturity.

4. The percentage decrease in value when the YTM increases by a given amount is smaller than the increase in value when the YTM decreases by the same amount (the price-yield relationship is convex).

Constant-yield price trajectory

“Pull to par”

Matrix pricing

Estimating required YTM of bonds that are currently not traded, or infrequently

Periodicity

Number of bond coupon payments per year

Street convention/ True Yield

• Street convention

  • Bond yields calculated using the stated coupon payment dates

• True Yield

  • Yield calculated using the actual coupon payment dates

  • payments can be paid later due to weekends or holidays

    • True Yield are usually slightly lower

Current Yield/ Income Yield/ Running Yield

Looks at bond’s annual interest income

• does not consider capital gains or losses or reinvestment income

Yield to Call/ Yield to Worse

Yield up to the callable date for callable bonds

• Yield to Call

  • Yield up to a call date

• Yield to Worse

  • Lowest yield of the Yield to Calls

Option Adjusted Price/Yield

Straight bond = Callable bond value + call option

• Straight bond price can reflect option adjusted yield

• useful to compare the yields of bonds with various embedded options

G-Spread

Yield spread in bp over a government bond

Interpolated spreads (I-spread)

Extra return of a bond in excess of the interbank market reference rates (MRRs) used in swap contracts

Quoted/ Required/ Discount Margin/ Deficiency

• Quoted Margin

  • fixed margin above MRR in coupon

  • Quoting FRNs

• Required/Discount

  • margin required to price FRN at par

    • Valuing FRNs

• Deficient

  • Bond traded at discount DM > QM

Reset Frequency FRNs

Allows price of bonds to adjust more object thus more fluctuations

Add-on-Yield/ Discount Yield

• Add-on-Yield

  • Annualized interest over period

• Discount Yield

  • Annualized discount from par

Bond-Yield Equivalent

Add-On Yield in 365 day term

Par Yields

Reflect the coupon rate that a HYPOTHETICAL bond at each maturity would need to have to be priced at par, given a specific spot curve.

What period bond basis are yield curves quoted as?

Semiannual

• US treasury bonds pay semiannually

Taxation/Illiquidity

Can cause distortions from realistic intrinsic price

Par yield curves vs Spot curves vs Forward Curves

Par yield curves are less reactive/slower than spot

Spot curves are less reactive/slower than forward curves

Curve Type	Based On	Main Use	Typical Behavior
Spot Curve	Zero-coupon (spot) rates	Pricing, discounting	Smooth; lags forward curve
Par Curve	YTMs of par-priced bonds	Yield benchmarks	Close to spot; slightly below/above
Forward Curve	Implied future short-term rates	Rate forecasting	Most volatile; leads spot curve
Yield Curve	YTMs of coupon bonds	General interest rate reference	Varies; depends on bond data

Yield volatility

relationship between yield volatility and time to maturity

Which curves with an arbitrageur use?

Spot curve

• SPECIFIC discount rates for each individual cash flow

Macaulay Duration

average time it takes for you to get your money back (from a bond) in present value terms.

Bond Return Scenarios – YTM, Reinvestment, and Holding Periods

• Hold to maturity, YTM unchanged:
  ✅ Return = Original YTM (e.g., 5%)

• Sell before maturity, YTM unchanged:
  ✅ Return = Original YTM

• Hold to maturity, reinvestment rate increases:
  ✅ Return > Original YTM (e.g., 5.09%)

• Sell shortly after purchase, YTM increases:
  ❌ Return < Original YTM (e.g., 3.07%)

• Hold long-term, reinvestment rate decreases:
  ❌ Return < Original YTM (e.g., 4.96%)

Duration Gap

Duration Gap = Macaulay Duration – Investment Horizon

It tells investors how aligned your bond’s cash flows are with when you actually need the money.

Situation	Duration Gap	Main Risk	Explanation
Duration > Horizon	Positive duration gap	Price Risk	You might sell early, and price drops will hurt you more.
Duration < Horizon	Negative duration gap	Reinvestment Risk	Coupons come early, but you may have to reinvest at lower rates later.
Duration = Horizon	Zero duration gap	Balanced / Immunized	Price and reinvestment effects cancel out. Stable return.

Modified Duration

ModDur = MacDur/ (1 + YTM)

Estimate for the % change in a bond’s price given 1% change in YTM

ModDur = 3.5 → if +0.5%, then price decrease ~1.75%

Money Duration

Estimate $ change given change in interest rates

Price Value of a Basis Point (PVBP)

Money change in the full price of a bond when its YTM changes by one bp

Longer Maturity: Factors and its effect on duration/ interest rate risk

Usually increases duration and risk (but not always for discount bonds_

Time Passes: Factors and its effect on duration/ interest rate risk

Duration decreases gradually, jumps up slight at coupon dates

Higher coupon: Factors and its effect on duration/ interest rate risk

Decrease duration and risk

• ZCB

  • Highest duration for given maturity and YTM

Floating-rate note (FRN): Factors and its effect on duration/ interest rate risk

Low price risk; duration ~~ time to next reset

Higher YTM: Factors and its effect on duration/ interest rate risk

Decreases duration (flatter price-yield curve)

Limitation of portfolio duration and convexity to estimate value changes?

Assumes parallel shift in yield curve — the YTM of every bond in the portfolio changes by the same amount

Key Rate/ Partial Duration

Impact of nonparallel shift measurement

Sensitivity of the value of bond or portfolio to changes in the benchmark yield for a specific maturity, holding other yields constant.

• Sum of all key durations = effective duration

Shaping Risk

Effect of a nonparallel shift in the yield curve on a bond portfolio

• using KDRs

Bottom-Up Credit Analysis Factors

• Capacity. The borrower's ability to make their debt payments on time.

• Capital. Other resources available to the borrower that reduce reliance on debt.

• Collateral. The value of assets pledged to provide the lender with security in the event of default.

• Covenants. The legal terms and conditions the borrowers and lenders agree to as part of a bond issue.

• Character. The borrower's integrity (e.g., management for a corporate bond) and their commitment to make payments under their debt obligations.

Top-Down Credit Analysis

• Conditions. The general economic environment that affects all borrowers' ability to make payments on their debt.

• Country. The geopolitical environment, legal system, and political system that apply to the debt.

• Currency. Foreign exchange fluctuations and their impact on a borrower's ability to service foreign-denominated debt.

Illiquid or Insolvent

• Illiquid

  • Unable to raise cash to service debt

• Insolvent

  • Assets of an issuer fall below the value of its debt

Recovery Rate/ Loss Severity

• Recovery Rate

  • proportion of a claim an investor will recover if the issuer defaults

• Loss Severity

  • Unrecoverable proportion