Bond Value Depends on Market Rates

• Inverse relationship:
  • Market rate ↑ → Bond price ↓
  • Market rate ↓ → Bond price ↑

Bond Price vs Coupon Rate

Coupon vs Market Rate	Result
Coupon = Market Rate	Bond sells at par
Coupon > Market Rate	Bond sells at a premium
Coupon < Market Rate	Bond sells at a discount

Analogy:

A bond is like a fixed meal plan. If new restaurants offer better deals (higher rates), your old meal plan becomes less attractive → its “price” falls.

• Lower credit quality → higher risk → higher yield required → lower price
• Higher credit quality → lower yield → higher price
  LM1 – Fixed Income Securities -…

Analogy:

Loaning money to a friend with unstable income → you demand more interest.

• Supranational: IMF, World Bank
• Corporate: Public or private companies
• National Governments: U.S., Canada, etc.
• Non-Sovereign / Municipal: States, provinces
• Quasi-Government: Fannie Mae
• Special Purpose Entities (SPEs)

Term	Meaning
Perpetual Bond	No maturity date; pays coupons forever
Money Market Security	Maturity < 1 year
Capital Market Security	Maturity > 1 year
Tenor	Time left until maturity
Dual Currency Bond	Coupons in one currency, principal in another
Currency Option Bond	Investor chooses payment currency
Zero-Coupon Bond	No coupons; issued at discount

Analogy:

A zero-coupon bond is like buying a gift card today for less than its full value later.

Legal contract specifying:

• Issuer identity
• Source of repayment
• Collateral
• Credit enhancements
• Covenants

Affirmative (Do):

• Make timely payments
• Comply with regulations

Negative (Don’t):

• Don’t issue more debt
• Don’t sell major assets
• Don’t engage in mergers without permission

Analogy:

Covenants are like the rules your landlord gives you—some tell you what you must do, others what you must not do.

Internal Enhancements

• Excess spread
• Cash reserves
• Overcollateralization
• Credit tranching (seniority waterfall)
  • Senior tranches paid first
  • Lower tranches get higher yield

External Enhancements

• Surety bond (insurance company)
• Bank guarantee
• Letter of credit (bank backs payment)

Type	Collateral
Secured Bond	Specific assets
Unsecured / Debenture	General claim with no specific collateral
Equipment Trust Certificate	Equipment
Collateral Trust Bond	Securities / financial assets
Mortgage-Backed Security	Pool of mortgages

Bond Market Classifications

Term	Meaning
Domestic Bond	Issued by local firm, local currency
Foreign Bond	Foreign issuer, domestic currency
Eurobond	Issuer, market, currency all differ

Bearer vs Registered Bonds

• Bearer bonds: no ownership record
• Registered bonds: issuer keeps ownership records

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Bond Taxation

Component	Tax Treatment
Coupons	Taxed as ordinary income
Municipal Bonds	Usually tax-exempt
Capital Gains (selling early)	Taxed as capital gains
Zero-Coupon Bonds	Pay tax on imputed interest annually

1. Plain Vanilla / Bullet Bond

• Coupons + full principal at maturity

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2. Fully Amortizing Loan

• Equal payments containing interest + principal
• No remaining principal at maturity

Analogy:

Like a mortgage—part of every payment reduces principal.

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3. Sinking Fund Provision

• Issuer retires a portion each year
• Reduces credit risk

Floating-Rate Notes (FRNs)

• Coupon = reference rate (LIBOR/Prime) + spread
• Coupon for period set using reference rate at beginning of period

Type	Meaning
Inverse Floater	Coupon moves opposite reference rate
Step-Up Coupon	Coupon increases at set intervals
Credit-Linked Coupon	Lower credit rating → higher coupon
Payment-in-Kind (PIK)	Payments made with additional bonds
Index-Linked Bond	Coupon tied to inflation or other index

Callable Bonds (Issuer’s Option)

✔ Benefit issuer
✘ Negative for investors → higher yields

• Issuer can call after lockout period
• Call premium above par

Types

• American: Anytime after first call date
• European: Only on specific dates
• Bermuda: Specific periodic dates

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Putable Bonds (Bondholder’s Option)

✔ Benefit investor
✘ Lower yields

• Holder can sell bond back at set price

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Convertible Bonds

• Bondholder converts to stock
• Conversion Ratio = Par Value / Conversion Price
• Conversion Value = #Shares × Stock Price

Benefits:

• Participate in equity upside
• Downside protection of bond
• Lower yield required

Topic	Key Concept
Bond Pricing	Inverse relation to market rates
Credit Quality	Lower credit = higher yield
Issuer Types	Governments, corporates, supranational
Key Definitions	Tenor, par, zero-coupon, dual currency
Indenture	Legal contract + covenants
Credit Enhancements	Internal & external protections
Collateral Types	Equipment, mortgages, financial assets
Tax Considerations	Interest taxed; muni interest exempt
Repayment Structures	Bullet, amortizing, sinking fund
Floating Rate Notes	Coupon resets with reference rate
Embedded Options	Calls, puts, convertibles

• Bond prices move opposite market yields.
• Higher credit risk → higher yield → lower price.
• Eurobonds differ by issuer, market, and currency.
• Zero-coupon bonds create imputed interest tax.
• Callable bonds favor issuer; putable & convertible favor investor.
• Sinking funds reduce credit risk.
• FRNs reset coupon using beginning-of-period reference rate.
• Collateral improves recovery rate.
• Tranching redistributes credit risk.

Bonds can be classified by:

• Type of issuer (government, non-sovereign, corporate, supranational)
• Credit quality (investment grade vs high yield)
• Maturity
• Currency denomination
• Coupon type (fixed, floating, inverse floater, zero)
• Geography
• Tax status

Analogy:

Bond classification is like categorizing music—by genre, region, tempo, and artist.

When banks lend to each other unsecured, the rate charged is the interbank offered rate (e.g., LIBOR).

Floating-Rate Notes (FRNs)

• Coupon = reference rate (e.g., 6-month LIBOR) + spread
• If coupon is semiannual → use 6-month LIBOR

Who Invests in Fixed Income?

• Central Banks
• Large Institutional Investors
• Retail investors (via Mutual Funds / ETFs)

Underwritten Offering

• Underwriter buys entire issue → bears risk of selling
• Syndicate = group of banks

Best-Efforts Offering

• Bank acts as broker only
• Issuer retains sales risk

Shelf Registration

• Issuer pre-registers future bond issues
• Can issue portions over time without reapplying

Auction

• Common for sovereign bonds
• Primary dealers bid

Analogy:

Underwriting is like a store buying inventory to resell; best efforts is like consignment—store only sells on your behalf.

Where previously issued bonds trade.
Most bonds trade OTC, not on exchanges.

Bid–Ask Spread

• Bid = dealer buys
• Ask = dealer sells
• Narrow spread → high liquidity

Settlement

• Government: T+1
• Corporate: T+2 or T+3

Sovereign Bonds

• Issued by national governments (e.g., T-bills, T-notes)
• High credit quality
• Repayment: taxation + ability to print money
• On-the-run securities = newest issues

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Non-Sovereign Bonds

• Issued by states, cities, provinces
• Repayment: local taxes or project revenue

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Quasi-Government / Agency Bonds

• Created by federal governments (e.g., Fannie Mae)
• Very high credit quality
• Paid from agency’s own cash flows

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Supranational Bonds

• Issued by entities like World Bank, IMF
• Extremely high credit quality

Bank Loans

Bilateral Loan

• One bank lends to a company

Syndicated Loan

• Several lenders provide funds

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Commercial Paper (CP)

Short-term financing (typically <270 days).
Used for working capital and as bridge financing.

Rolling Over

Issue new CP → pay off maturing CP.

US vs Euro CP

• US: discount basis
• Euro: add-on basis

Analogy:

Commercial paper is like using a low-interest credit line until your long-term mortgage is approved.

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Corporate Bonds

• Short-term: < 5 years
• Medium-term: 5–12 years
• Long-term: > 12 years

Principal Repayment Methods

• Term maturity: one lump sum
• Serial maturity: principal repaid on multiple dates
• Sinking fund: issuer retires portions but dates unknown to investors

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Medium-Term Notes (MTNs)

• Continuous issuance program
• Sold through an agent
• Can be short, medium, or long term

These redistribute risk.

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1. Capital-Protected Instruments

• Guarantee minimum payout
• Constructed by buying:
  • A zero-coupon bond (principal protection)
  • A call option (upside participation)

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2. Yield-Enhancing Instruments

Credit-Linked Notes (CLNs)

• Coupon increases due to credit event risk
• If credit event does not occur → redeemed at par
• If credit event occurs → redeemed below par

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3. Participation Instruments

• Returns linked to an index, stock, or reference rate

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4. Leveraged Instruments (Inverse Floaters)

$$\text{Coupon}=\text{Fixed Rate}-(L\times \text{Reference Rate})$$

• If reference rate ↑ → coupon ↓
• If L > 1 → leveraged exposure
• If L < 1 → de-leveraged

1. Retail Deposits

• Low-cost funding

2. Wholesale Funding

Includes:

• Interbank funds
• Central bank funds
• Certificates of deposit (CDs)

A repo = collateralized loan.
Borrower sells an asset today and agrees to repurchase later at a higher price.

Collateral: typically high-quality bonds

Higher collateral value → lower risk for lender.

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Repo Margin (Haircut)

$$\text{Repo Margin}=\frac{\text{MV of Collateral}-\text{Loan Amount}}{\text{MV of Collateral}}$$

Given in document as:$$\text{Loan Amount}\mathrm{/}\text{Market Value of Asset}$$

(both definitions measure level of protection)

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What Determines Repo Rate?

• Longer maturity → higher repo rate
• Higher collateral credit risk → higher repo rate
• If lender receives collateral → lower repo rate
• If market interest rates ↑ → repo rates ↑

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What Determines Repo Margin?

• Longer maturity → higher margin
• Higher collateral credit risk → higher margin
• High-quality borrower → lower margin
• High demand collateral → lower margin

Analogy:

Repos are like pawning an item—you give collateral and pay interest to buy it back later.

Section	Key Points
Classification	Issuer, quality, maturity, geography, taxes
Reference Rates	LIBOR/IBOR used for FRNs
Primary Market	Underwritten, best-efforts, shelf registration, auction
Secondary Market	Mostly OTC, bid–ask spread = liquidity
Issuer Types	Sovereign, non-sovereign, agency, supranational
Corporate Funding	Loans, CP, corporate bonds, MTNs
Structured Instruments	Capital protected, yield enhancing, participation, leveraged
Bank Funding	Retail deposits, wholesale funds
Repos	Collateralized loan; repo rate + haircuts

• FRNs use beginning-of-period reference rates.
• Underwriters bear risk; best-efforts offerings shift risk to issuer.
• Shelf registration speeds large, repeated bond issuance.
• Bid–ask spread is a direct measure of liquidity.
• Commercial paper = short-term funding; rolling over introduces liquidity risk.
• Serial maturity vs sinking fund: sinking fund dates unknown to investors.
• CLNs compensate investors for credit event risk.
• Repos behave like secured loans—haircuts protect lenders.
• High-demand collateral → lower repo margin.

Price–Yield Relationship

• Market yield ↑ → Bond price ↓
• Market yield ↓ → Bond price ↑
• Relationship is convex (curved, not linear).

Important Convexity Insight

• Price increase (when yields fall) is larger than price decrease (when yields rise).
• This asymmetry is good for investors.

Analogy:

Convexity is like a safety airbag—your losses are cushioned more than your gains are capped.

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Spot Rates & Present Value

• Spot rate = yield on a zero-coupon bond for a specific maturity.
• PV using spot rates = “no arbitrage price” — ensures pricing is internally consistent.

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Full Price, Flat Price & Accrued Interest

Bond price between coupon dates includes accrued interest.

Steps to compute selling price before coupon date:

1. Price bond as of most recent coupon date (PV).
2. Add accrued interest up to settlement.

Accrued Interest

$$AccruedInterest=FullPrice-FlatPrice$$

Given formula in notes:$$AccruedInterest=PV\times {(1+\frac{YTM}{n})}^t$$

Flat Price

$$FlatPrice=FullPrice-(Coupon\times \frac{\text{days since coupon}}{\text{days in period}})$$

Analogy:

Buying a bond mid-cycle is like buying a hotel room at noon—you pay the seller for the portion of the day they already “used.”

Used when a bond does not trade frequently.

Steps

• Find comparable bonds (maturity, credit quality).
• Take average yields.
• Use linear interpolation to fill in missing yields.

Analogy:

Matrix pricing is like pricing a house by comparing it to nearby homes with similar characteristics.

Definitions

• Periodicity (n): number of coupon payments per year.
• YTM = APR = BEY = Stated Rate (annual).

Effective Annual Rate (EAR or EFF)

$$EFF=(1+\frac{YTM}{n}{)}^n-1$$

Equivalent Rates Across Compounding

$${(1+\frac{YTM}{n})}^n={(1+\frac{YTM}{m})}^m$$

• Coupon = Current LIBOR + Quoted Margin
• Discount Rate = LIBOR + Discount Margin
• If Quoted Margin = Discount Margin → trades at par.

Price Stability

FRNs are more stable than fixed-coupon bonds because their coupons reset with interest rates.

Analogy:

FRNs are like adjustable-rate mortgages—the payments change with the market, so the loan value stays close to par.

Short-term instruments:

• Commercial Paper
• T-Bills
• CDs

Yield Conventions

• Add-On Rate → PV in denominator
• Discount Rate → FV in denominator

Analogy:

Discount rates are like buying a $100 gift card for $98—price is quoted as discount from face value.

Yield Curve

Yields on coupon-bearing bonds at different maturities.

Spot Curve

Series of spot rates (zero-coupon yields).
Assumes no coupon.

Par Curve

YTM on bonds priced exactly at par for each maturity.

Forward Curve

Shows forward rates for future periods.

Definition

Interest rate on a loan starting in the future.
Example:
“1y2y = 3%”
→ One year from now, a 2-year loan will cost 3%.

Relationship Between Spot & Forward Rates

$$(1+S_4{)}^4=(1+S_1)(1+1y1y)(1+2y1y)(1+3y1y)$$

Simple Average Trick

Used for shortcuts if spot rates differ by small amounts.

Yield Spread

Difference between yields of two bonds.

Benchmark Spread

Bond yield – Benchmark yield.

G-Spread (Government Spread)

Bond yield – Government bond yield.

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Z-Spread

Spread added to each spot rate (not one yield) such that the present value equals market price.

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Option-Adjusted Spread (OAS)

Used for bonds with embedded options.

Relationship:

$$Z\text{-Spread}=OAS+\text{Option Value}$$

Option value:

• Positive for callable bonds
• Negative for putable bonds

Analogy:

OAS is like removing the cost or benefit of a “feature” to compare the true underlying value.

Topic	Summary
Price–Yield	Inverse & convex relationship
Accrued/Flat/Full Price	Adjusts for coupon timing
Matrix Pricing	Uses comparable bonds + interpolation
Periodicity	Converts YTM into effective rate
FRNs	LIBOR + margin; stable around par
Yield Curve Types	Yield, spot, par, and forward curves
Forward Rates	Rates on future loans
Spread Types	Yield spread, G-spread, Z-spread, OAS

• Bond prices are convex: price rises more when yields fall than they drop when yields rise.
• Use spot rates to get no-arbitrage prices.
• Flat price excludes accrued interest; full price includes it.
• Matrix pricing is essential for illiquid or newly issued bonds.
• FRNs stay near par because coupons adjust to market rates.
• Know difference between Yield Curve vs Spot Curve vs Par Curve vs Forward Curve.
• Z-spread > OAS for callable bonds (option value is positive).
• G-spread measures credit risk relative to government bonds.
• Forward rates link all spot rates through compounding identities.

Securitization = pooling many loans/assets and issuing securities backed by the pool.

Why it works

• Diversifies idiosyncratic risk (one default doesn’t stop all cash flows)
• Improves liquidity for investors
• Removes loans from bank balance sheets → frees capital
• Increases lending capacity → lowers borrowing costs

Who does what

• Seller/Originator: creates loans (e.g., mortgages)
• Special Purpose Entity (SPE/Trust/Issuer): holds assets; issues ABS
• Servicer: collects P&I from borrowers and passes through to investors

Analogy: Like turning many individual songs (loans) into a diversified playlist (ABS) that plays even if one song stops.

Credit Tranching (Waterfall Structure)

• Investors split into tranches by payment priority
• Senior tranches paid first (lower risk, lower yield)
• Subordinated/equity tranches absorb losses first (higher risk, higher yield)
• Does not reduce risk—redistributes it

Analogy: Stadium seating—front rows (senior) see the show first; back rows (subordinated) take the bumps.

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Time Tranching

• Principal paid sequentially: Level 1 → Level 2 → Level 3
• Changes timing risk, not total cash received

• Mortgage: loan secured by real estate collateral
• Non-recourse: lender can seize collateral only
• Recourse: lender can also pursue borrower’s other assets

Key terms

• Loan-to-Value (LTV) = Loan / Market value (lower is safer for lender)
• Avg maturity: ~30 years
• Rates: fixed, adjustable, indexed, convertible
• Amortization:
  • Fully amortizing: principal paid over life; none due at maturity
  • Partially amortizing: some principal due at maturity
  • Interest-only: all principal due at maturity

• When rates fall, borrowers refinance → early principal return
• Lenders dislike losing high-rate loans; may impose prepayment penalties
• Lockout period: no prepayments allowed

Risks

• Contraction risk: faster-than-expected principal (reinvest at lower rates)
• Extension risk: slower-than-expected principal (stuck at lower coupons)

Issuers

1. Government National Mortgage Association (GNMA) — fully government-backed
2. GSEs: FNMA & FHLMC (government-sponsored)
3. Private issuers (Non-Agency) — no government guarantee; often need credit enhancement

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Mortgage Pass-Through Securities

• Pool of mortgages → payments passed through to investors
• Borrowers may pay 7%; after servicing/fees, investors receive pass-through rate

Single-Month Mortality (SMM)

$$SMM=\frac{\text{Prepayment for the month}}{\text{Beg. mortgage balance}-\text{Scheduled principal}}$$

Conditional Prepayment Rate (CPR)

• Annualized SMM

PSA Benchmark

• PSA > 100: faster prepayments → higher contraction risk
• PSA < 100: slower prepayments → higher extension risk

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RMBS Structures to Manage Prepayment Risk

Sequential-Pay

• Early tranches get principal first
• Senior: highest contraction risk
• Last: highest extension risk

Planned Amortization Class (PAC)

• PAC tranches: predictable cash flows; lowest contraction/extension risk
• Support tranches: absorb variability; highest risk

Analogy: Shock absorbers—support tranches take the bumps so PACs ride smoothly.

• Backed by income-producing real estate
• Loans typically non-recourse

Key metrics

• LTV = Loan / Property value (lower is safer)
• Debt Service Coverage (DSC) = NOI / Debt service (higher is better)

Tranching

• Equity/subordinated absorbs losses first

Call protection (prepayment control)

• Structure-level: sequential tranches
• Loan-level: penalties, lockouts, points, yield maintenance, defeasance

Auto-Loan ABS

• Collateral: car loans (amortizing)
• Prepayments from sale, repossession, trade-ins
• Always include credit enhancement (tranching, reserves, excess spread, overcollateralization)

Credit Card ABS

• Collateral: non-amortizing credit card receivables
• Lockout/reinvestment period: investors receive finance charges/fees; principal is reinvested
• After lockout, principal distributed

Collateralized Debt Obligations (CDOs)

• Backed by pools of ABS (e.g., MBS)
• CMO: backed by MBS
• Collateral manager actively manages pool
• Tranches: senior, mezzanine, subordinated

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Covered Bonds (Compare to ABS)

Backed by asset pools (CM, RM, public assets) but four key differences:

1. Dual recourse: claim on collateral and issuer assets
2. On-balance-sheet: no SPE
3. Dynamic pool: underperformers replaced
4. No extension risk; redemption regimes stabilize cash flows on default

Analogy: ABS = sealed box sold off; Covered bonds = secured loan you can still chase the borrower for.

ABS Structures & Risks

Structure	What It Does	Who Bears Risk
Credit tranching	Prioritizes losses	Subordinated first
Time tranching	Changes timing	Later tranches
Sequential-pay RMBS	Early principal to seniors	Seniors: contraction
PAC RMBS	Stabilizes cash flows	Support tranches

ABS Types

Type	Collateral	Key Risk
RMBS	Home mortgages	Prepayment
CMBS	Commercial property loans	Property cash flow
Auto ABS	Auto loans	Collateral depreciation
Credit Card ABS	Receivables	Revolving balances
CDO	ABS pools	Manager & correlation
Covered Bonds	Asset pool + issuer	Issuer credit

• Securitization redistributes risk via tranching; it doesn’t eliminate it.
• Prepayment risk creates contraction/extension risk; PACs mitigate it using support tranches.
• SMM → CPR → PSA quantify prepayments; PSA > 100 implies faster prepay.
• CMBS emphasize LTV and DSC; call protection is central.
• Auto ABS always use credit enhancement; Credit Card ABS have reinvestment periods.
• Covered bonds differ from ABS by dual recourse, on-balance-sheet assets, dynamic pools, and no extension risk.

Total bond return comes from three sources:

1. Coupon & Principal Payments

• Regular coupon income
• Principal repayment at maturity

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2. Reinvestment Income

Income earned from reinvesting coupon payments.

• Bond pricing assumes coupons are reinvested at the YTM
• If rates change → actual return differs from YTM

When rates rise:

• Coupons reinvested at higher rates
• Actual return > YTM

When rates fall:

• Coupons reinvested at lower rates
• Actual return < YTM

Analogy:
Reinvestment risk is like getting monthly paychecks—your total savings depend on where you reinvest that cash.

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3. Capital Gains / Losses (Market Price Risk)

Occurs if bond is sold before maturity.

• Carrying value = PV of remaining cash flows discounted at YTM at issuance
• If market yields rise:
  • Market price < carrying value
  • Investor sells at a loss
  • Actual return < YTM
• If market yields fall:
  • Market price > carrying value
  • Capital gain

Holding Period	Dominant Risk
Short-term	Market price risk
Long-term (before maturity)	Reinvestment risk
Held to maturity	Reinvestment risk only

Key rule:

• If held to maturity → market price risk disappears

Analogy:
Selling early exposes you to resale value (market risk); holding long exposes you to what you earn along the way (reinvestment risk)

Duration measures how sensitive a bond’s price is to interest rate changes.

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Macaulay Duration

• Weighted average time (years) to receive cash flows

$$D_{Mac}=\sum (Weigh{t}_t\times Tim{e}_t)$$

• Interpreted as the bond’s effective maturity

Analogy:
Macaulay duration is the bond’s “center of gravity” for cash flows.

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Modified Duration

$$D_{Mod}=\frac{D_{Mac}}{1+YTM}$$

• Approximates % price change for a 1% change in yield

$$\mathrm{\%}\mathrm{\Delta }P\approx -D_{Mod}\times \mathrm{\Delta }YTM$$

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Approximate Modified Duration

Uses prices from yield up/down scenarios instead of formulas.
Useful when cash flows are complex.

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Effective Duration

• Used for bonds with embedded options
• Accounts for cash flow changes due to yield movements
• Uses shifts in the benchmark yield curve

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Key Rate Duration

• Used when yield curve shifts are not parallel
• Measures sensitivity to one specific spot rate
• All other spot rates held constant

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Money Duration (Dollar Duration)

$$\text{Money Duration}=D_{Mod}\times \text{Full Price}$$

• Measures $ change in price for a 1% yield change

$$\mathrm{\Delta }P\approx -(\text{Money Duration})\times \mathrm{\Delta }YTM$$

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Price Value of a Basis Point (PVBP)

$$PVBP=\frac{V_{-}-V_{+}}{2}$$

• Measures price change for a 1 bp (0.01%) change in yield

• Price–yield relationship is convex, not linear
• Duration underestimates price increases and overestimates price decreases
• Convexity corrects this error

Rule:

• Price increase (rates ↓) > price decrease (rates ↑)

Analogy:
Convexity is like shock absorbers—it softens losses more than it limits gains.

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Yield Volatility Drivers

• Duration (first-order sensitivity)
• Convexity (curvature adjustment)
• Yield changes must occur for volatility to matter

Yield to Maturity

• YTM ↑ → Duration ↓
• Bond prices less sensitive to yield increases than decreases

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Coupon Rate

• Higher coupon → lower duration
• Zero-coupon bond:
  • Duration = maturity
• Coupon bond:
  • Duration < maturity

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Time to Maturity

• Longer maturity → higher duration
• Longer discounting horizon increases sensitivity

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Embedded Options

• Callable or putable bonds → lower duration
• Options stabilize price movements

Portfolio Duration

Weighted Average Duration

$$D_{Portfolio}=\sum w_i{D}_i$$

• Works only for parallel yield curve shifts
• Not reliable with options or floating rates

Key Immunization Result

If:$$\text{Investment Horizon}=D_{Mac}$$

→ Market price risk and reinvestment risk cancel out
→ Actual return = YTM

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Duration Gap

$$DG=D_{Mac}-\text{Investment Horizon}$$

DG	Interpretation
DG > 0	Selling too early
DG < 0	Holding too long

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$$YTM=\text{Government Benchmark Yield}+\text{Credit Spread}$$

• GBY changes due to:
  • Inflation expectations
  • Real interest rates
• Credit spread changes due to:
  • Issuer credit quality
  • Liquidity

Analytical Duration

• Formula-based
• Assumes gov yields & credit spreads not correlated

Empirical Duration

• Statistical, based on historical prices
• Captures real-world behavior

Key insight:

• For high-yield bonds, empirical duration < analytical duration
• Empirical may better estimate price sensitivity in downturns

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Duration Measures:

Measure	Best Used For
Macaulay	Timing of cash flows
Modified	% price sensitivity
Effective	Bonds with options
Key Rate	Non-parallel shifts
Money Duration	Dollar price impact
PVBP	Small yield changes

Risk Dominance by Horizon

Holding Period	Dominant Risk
Short	Market price risk
Long (pre-maturity)	Reinvestment risk
To maturity	Reinvestment risk

• YTM assumes coupons are reinvested at YTM—this is rarely true.
• Selling before maturity introduces market price risk.
• Duration measures interest rate sensitivity, not return.
• Modified duration estimates % price change; money duration estimates $ change.
• Convexity improves duration estimates for large yield changes.
• If horizon = Macaulay duration → interest rate risk is immunized.
• Yield changes come from benchmark rates + credit spreads.
• Empirical duration may better capture high-yield bond behavior.

Credit Risk

Risk that a borrower fails to meet contractual obligations.

Credit risk has two components:

1. Default Risk

• Probability that the borrower defaults

2. Loss Severity

• Amount the lender loses if default occurs
• Equivalent to:

$$\text{Loss Severity}=1-\text{Recovery Rate}$$

• Recovery Rate: proportion of investment recovered after default

Effective Loss

$$\text{Effective Loss}=\text{Default Risk}\times \text{Loss Severity}$$

Analogy:
Default risk is whether your car crashes; loss severity is how badly damaged it is.

Yield Spread

$$\text{Yield Spread}=\text{Risky Bond Yield}-\text{Risk-Free Yield}$$

Spread Risk

Risk that the spread widens, lowering bond prices.

Main Drivers of Spread Risk

• Credit migration (downgrade) risk
• Market liquidity risk

Analogy:
Spreads are like insurance premiums — when risk rises, premiums widen.

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Credit Migration / Downgrade Risk

• Credit rating deteriorates
• Bond becomes riskier
• Required yield increases → price falls

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Market Liquidity Risk

• Less liquid bonds require higher yields
• Leads to wider spreads, even if credit quality is unchanged

Bondholders are ranked by seniority, determining recovery in default.

Hierarchy (Highest → Lowest Seniority)

1. First Lien / Senior Secured
2. Second Lien / Secured
3. Senior Unsecured
4. Senior Subordinated
5. Subordinated
6. Junior Subordinated

• Higher seniority → higher recovery, lower yield
• Lower seniority → lower recovery, higher yield

Pari Passu

• Investors within the same rank are treated equally

⚠️ Important CFA nuance:

• In bankruptcy, ranks may not always be strictly respected
• Courts or negotiations may alter recoveries

Analogy:
Think of liquidation as slicing a pie — those at the front of the line get served first.

What Ratings Are Based On

• Typically based on issuer’s senior unsecured debt
• Individual bond issues may be rated differently → Notching

Notching

• Adjusting ratings up/down for specific issues
• More common for lower-rated issuers

Structural Subordination

Occurs when:

• Subsidiaries must pay their own debt first
• Only excess cash flows to the parent company
• Parent company bonds may be riskier than subsidiary debt

Analogy:
The parent company gets leftovers after subsidiaries eat first.

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Limitations of Credit Ratings (Very Testable)

• Ratings are dynamic
• Agencies can make mistakes
• Credit risk is hard to predict
• Ratings lag market prices

Key exam insight:
Markets usually react before rating agencies.

1. Capacity (Ability to Pay)

Industry Structure

Analyzed using Porter’s Five Forces:

• Supplier power
• Customer power
• Barriers to entry
• Level of competition
• Threat of substitutes

Industry Fundamentals

• Cyclicality
• Growth prospects
• Published statistics (ratings, research, news)

Company Fundamentals

• Competitive position
• Management quality
• Strategy & execution
• Financial ratios

Analogy:
Capacity asks: Does the borrower have the engine to keep going?

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2. Collateral

Assets backing the loan.

• Should be high quality
• Collateral value > loan amount
• Tangible assets (land, equipment) preferred over goodwill

Analogy:
Collateral is your parachute — better quality means safer landing.

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3. Covenants

Restrictions imposed to protect lenders.

Affirmative Covenants

Borrower must do:

• Make timely payments
• Maintain insurance

Negative Covenants

Borrower must not do:

• Excessive M&A
• Exceed maximum D/E ratio

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4. Character

Qualitative assessment of management:

• Reputation & integrity
• Track record
• Accounting conservatism
• Past treatment of bondholders
• Signs of fraud

Analogy:
Character answers: Can we trust them?

Profitability Measures

• Higher profitability → stronger debt servicing ability

Leverage Ratios

• Measure debt burden
• Higher leverage → higher credit risk

Coverage Ratios

• Measure ability to service debt from cash flow
• Higher is better

$$YTM=\text{Risk-Free Rate}+\text{Expected Inflation}+\text{Maturity Premium}+\text{Yield Spread}$$

$$\text{Yield Spread}=\text{Liquidity Premium}+\text{Credit Spread}$$

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Five Factors Affecting Yield Spreads

1. Credit Cycle
   • Bottom of cycle → fear → wider spreads
2. Economic Conditions
   • Weak economy → higher default risk → wider spreads
3. Funding Availability
   • Scarce funding → higher borrowing costs
4. Issuer Financial Performance
   • Poor performance → wider spreads
5. Demand & Supply
   • Low demand → falling prices → wider spreads

High-Yield (Junk) Bonds

• Higher yields compensate for higher risk

Six Key Factors to Analyze

1. Liquidity (cash, WC, operating CF, credit lines)
2. Earnings projections
3. Debt structure
4. Debt ratios & priority of claims
5. Corporate structure
6. Covenants

Change of Control Puts

• Bondholders can sell bond back to issuer if acquisition occurs

Key insight:
High-yield analysis resembles equity analysis.

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Sovereign Debt

Analyze using five-factor framework:

1. Institutional
   • Government stability, corruption risk
2. Economic
   • GDP growth, income sources
3. External
   • International liquidity & investment flows
4. Fiscal
   • Tax capacity and spending control
5. Monetary
   • Effectiveness of monetary policy

⚠️ Also assess willingness to pay, not just ability.

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Non-Sovereign Debt

Municipal Bonds

General Obligation Bonds

• Backed by taxing power
• Analyze:
  • Employment
  • Income levels
  • Demographics

Revenue Bonds

• Backed by project revenue
• Focus on coverage ratios

Credit Risk Components

Component	Meaning
Default Risk	Probability of default
Loss Severity	Loss given default
Effective Loss	Expected credit loss

4 C’s of Credit

C	Focus
Capacity	Ability to pay
Collateral	Asset backing
Covenants	Lender protection
Character	Management integrity

Yield Spread Drivers

Factor	Effect
Economic weakness	Spreads widen
Liquidity decline	Spreads widen
Downgrades	Spreads widen

• Credit risk = default risk × loss severity
• Higher seniority → higher recovery, lower yield
• Credit ratings lag markets and can be wrong
• Structural subordination increases parent-level risk
• Covenants materially affect bond risk
• Yield spreads reflect credit + liquidity risk
• High-yield bond analysis is closer to equity analysis
• Sovereign analysis includes willingness, not just ability