Bondistan — Fixed Income Primer

Ch 1

Bond Math — Time Value, Price & YTM

BLUF: A bond is worth the present value of all its future cashflows. Price and yield move inversely. YTM = IRR = the single discount rate that makes NPV of all cashflows equal the current market price.

Future Value & Compounding

FV = PV × [1 + (y/f)]^n DF = 1 / [1 + (y/f)]^n ← Discount Factor

y = annual yield · f = compounding frequency · n = number of periods

Example: $100 in 5Y, semi-annual, 5% yield → DF = 1/(1.025)^10 = 0.7811 → PV = $78.11

Bond Price = NPV of All Cashflows

Price = Σ [Coupon / (1+y)^t] + [Face / (1+y)^n]

When coupon = yield → price = par (100). Yield rises → price falls. Always.

Key identities: coupon = yield → par · yield > coupon → discount · yield < coupon → premium

Yield to Maturity (YTM) = IRR

The single constant discount rate applied to all future cashflows such that PV = market price. Assumes reinvestment of all coupons at YTM (rarely true in practice).

Clean vs Dirty Price

Dirty Price = Clean Price + Accrued Interest Accrued = Coupon × (Days since last coupon / Days in coupon period)

Bloomberg quotes clean price. You pay the dirty price at settlement.

Key Takeaways

Price ↑ when yield ↓ — always and in every market
YTM = IRR = the "true" yield blended across all cashflows
Discount factors are the building blocks — everything else follows
You pay dirty price; clean price is just the quote convention

Ch 2

Interest Rate Risk — Duration, Convexity & DV01

BLUF: Duration = speed of price change per 1% yield move. DV01 = that in dollars. Convexity explains why you gain more than you lose when yields move equally in either direction. It's why bonds have a curved price/yield relationship, not linear.

Macaulay Duration — The Breakeven Point

MacDur = Σ [t × PV(CF_t)] / Bond Price

Weighted average time until you receive your money back. Zero-coupon bond: MacDur = maturity. Coupon bond: MacDur < maturity (early coupons pull it forward).

Modified Duration — % Price Change per 1% Yield Move

ModDur = MacDur / (1 + y/f) ΔPrice% ≈ −ModDur × Δy

Example: ModDur = 7.5 · Rates rise 1% → price falls ~7.5% · Rates fall 1% → price rises ~7.5%

PV01 & DV01 — The Trader's Units

PV01 = Price × ModDur / 100 ← per $100 face per 1bp DV01 = PV01 × (Face / 100) ← total dollar P&L per 1bp

Example: $10MM face, Price=102, ModDur=6 → PV01=$6.12 → DV01=$612,000 per basis point

Convexity — Why the Relationship Is Curved

ΔPrice ≈ −ModDur × Δy + ½ × Convexity × (Δy)²

Yields fall: actual price gain > duration predicts (second-order bonus). Yields rise: actual price loss < duration predicts. Convexity is always positive for straight bonds — a gift to holders.

⚠ Negative convexity: Callable bonds and MBS — the upside is capped (bond gets called away when rates fall)

Day Count Conventions

Convention	Used For	Denominator
ACT/ACT	US Treasuries	Actual days in year
ACT/360	Money markets, most swaps, corporate	360
ACT/365	UK Gilts	365
30/360	US corporate bonds	Assumes 30-day months

Key Takeaways

Duration = speed; convexity = acceleration of price change
DV01 is how traders size and hedge positions — "P&L per basis point"
Convexity is a free gift for straight bond holders; negative convexity is a tax for MBS/callable holders
Day count matters — ACT/360 vs ACT/365 creates meaningful differences on large positions

Ch 3

Money Markets — T-Bills, SOFR, Repos & FRAs

BLUF: Money markets = the plumbing of finance. Short-term (<1Y) instruments where cash is parked, funded, and hedged. SOFR replaced LIBOR. Repo is the engine of leverage. OIS measures the market's Fed policy expectations.

Treasury Bills — Discount Basis Pricing

Price = 100 − [Discount Rate × (Days/360)]

Example: 90-day T-Bill at 2% → Price = 100 − (0.02 × 90/360) = 99.50 · True yield = (0.50/99.50) × (360/90) = 2.01% (higher than quoted 2%)

Key Benchmark Rates

Rate	Type	Use
SOFR	Secured overnight	New USD risk-free benchmark; repo-based; $1T+/day
EFFR (Fed Funds)	Unsecured overnight	Fed policy target; interbank; OIS floating leg
LIBOR	Historical panel	Retired June 2023; replaced by SOFR/SONIA/ESTR/TONAR
TED Spread	LIBOR − T-Bill	Bank credit risk gauge; spiked to 450bps in 2008

Repos (Repurchase Agreements) — Secured Lending

Cash borrower sells bonds to cash lender with agreement to buy them back at a higher price. Effectively: borrow cash using bonds as collateral.

GC (General Collateral) repo: any eligible bond; rates near risk-free.

Special repo: specific bond in high demand → lower repo rate (lender accepts less to obtain that specific bond — reveals which bonds are heavily shorted).

Haircut: bonds posted worth more than cash received (e.g., $100 bonds → $98 cash = 2% haircut).

OIS (Overnight Index Swap)

Swap where floating leg = overnight rate compounded daily. OIS rate = market's expectation for the AVERAGE overnight rate over the swap's term.

LIBOR-OIS spread: The interbank stress thermometer. Near zero normally; 350bps+ in the GFC.

Key Takeaways

T-Bills: discount pricing means the quoted rate understates true yield
SOFR = new USD risk-free rate; secured by Treasuries; $1T/day in volume
Repo = the leverage engine; special repos reveal short demand for specific bonds
OIS = purest measure of Fed policy expectations across the curve
LIBOR-OIS spread = stress gauge; "special" repo = short interest signal

Ch 4

The Yield Curve — Par, Spot, Forward; Carry, Rolldown & Trades

BLUF: Three yield curves exist — par (what you see), spot (what you should use to price), and forward (what the market implies for the future). Carry + rolldown are the passive returns from holding. Curve trades (steepener, flattener, butterfly) profit from changes in shape. All must be DV01-neutral.

Three Curves — Always in This Order on Normal Curve

Par Rate < Spot/Zero Rate < Forward Rate

Curve	Definition	Bloomberg
Par	Yield on bonds priced at 100 (coupon = yield)	WIR<GO>
Spot/Zero	Yield on zero-coupon bonds; derived via bootstrapping	ICVS<GO>
Forward	Implied rate for a future period; F(1y1y) = [(1+Z₂)² / (1+Z₁)] − 1	FWCM<GO>

Carry & Rolldown — The "Free Lunch"

Carry = Yield − Repo Rate ← earn on an upward-sloping curve Rolldown = ΔYield × Duration ← earn as bond shortens toward lower yield

Example: Hold 10Y bond for 1 year; it becomes a 9Y bond. If 9Y yield is 20bps below 10Y, you earn 20bps × duration in price appreciation from rolldown alone.

Curve Trades

Steepener: Long front end, short long end. Profits when long end sells off more than front end.

Flattener: Short front end, long long end. Profits when front end rises more than long end (Fed hikes).

Butterfly: Long belly, short wings (or vice versa). Isolates the curve shape vs parallel shift.

2s10s spread: 10Y − 2Y yield. Inversion (negative) historically signals recession.

DV01-Neutral Construction — Essential

Notional_short / Notional_long = DV01_long / DV01_short

Example: Long $100MM 2Y (DV01=$20k) + Short $X 10Y (DV01=$90k) → X = $100MM × (20/90) = $22.2MM to make the trade duration-neutral

Key Takeaways

Par < Spot < Forward — always on a normal (upward-sloping) curve
Carry + rolldown = compensation for duration risk, not a free lunch
Inverted 2s10s = historically reliable recession precursor
Every curve trade must be DV01-neutral to isolate shape exposure from parallel shift
Bloomberg: CARY<GO> (carry/rolldown), FWCM<GO> (forward rates), BFLY<GO> (butterfly)

Ch 5

Futures — Eurodollar, Treasury Note/Bond Futures & CTD

BLUF: Eurodollar futures price the short end (3M LIBOR); Treasury futures price longer maturities (standardized on a theoretical 6% coupon bond). Conversion Factors adjust each eligible bond to the standard. The futures short delivers the Cheapest-to-Deliver (CTD) bond — the one with the highest implied repo rate.

Eurodollar Futures

Price = 100 − Implied 3M LIBOR rate (e.g., 94.50 = 5.50% LIBOR)

DV01 = $25 per contract per 1bp. Organized in Packs (4 consecutive quarters) by color: White/Red/Green/Blue (WRGB).

Treasury Futures Contracts

Ticker	Contract	Eligible Maturity
`TU/ZT`	2Y T-Note	1Y9M to 2Y
`FV/ZF`	5Y T-Note	4Y2M to 5Y3M
`TY/ZN`	10Y T-Note	6Y6M to 10Y
`US/ZB`	T-Bond	15Y+
`WN/UB`	Ultra T-Bond	25Y+

Quoted in 32nds: 131-29 = 131 + 29/32 = 131.90625. Physically settled.

Conversion Factor & Invoice Price

Invoice Price = Futures Price × CF + Accrued Interest CF ≈ Price of bond if YTM = 6%

Example: T 2⅝ 05/15/28, CF=0.8338, Futures=131-29 → Invoice = 131.90625 × 0.8338 = 109.9834

Cheapest-to-Deliver (CTD)

Gross Basis = Cash Price − Invoice Price (in 32nds) CTD = Bond with HIGHEST Implied Repo Rate

The futures short delivers the cheapest bond. Bloomberg DLV<GO> sorts by implied repo — top = CTD.

Rule: yields > 6% → longest eligible bond tends to be CTD; yields < 6% → shortest.

Key Takeaways

Eurodollar futures = $25 DV01; 100 − rate pricing; WRGB color packs
Treasury futures standardize all bonds to a theoretical 6% coupon via Conversion Factor
Invoice Price is what you pay/receive at delivery
CTD = highest implied repo rate = best cash-and-carry for the short
Bloomberg: DLV<GO> (CTD), FIHZ<GO> (horizon analysis)

Ch 6

Options on Futures — Greeks, MOVE Index & Vol Skew

BLUF: Options on Treasury futures give the right (not obligation) to buy/sell futures at a strike. MOVE = bond market's VIX — measures 1M normalized implied vol across tenors. Bond vol skew differs from equities and can reverse direction depending on the rate environment.

The Greeks

Greek	Measures	Sign for Long Options
Delta	Price change per unit futures move	Call: 0 to +1; Put: −1 to 0
Gamma	Rate of delta change; highest ATM near expiry	Positive (long)
Vega	Sensitivity to implied volatility	Positive (long)
Theta	Time decay; erodes option value daily	Negative (long)

MOVE Index — Bond Market's Fear Gauge

Merrill Lynch Option Volatility Estimate. 1-month normalized implied vol on US Treasuries, weighted across 2Y/5Y/10Y/30Y. Bloomberg: MOVE Index.

High MOVE = rate uncertainty, Fed path unclear. Low MOVE = complacency.

MBS holders hate high MOVE (prepayment uncertainty drives up option cost).

Bond vs Equity Vol Skew

Equities: Puts always more expensive than calls (left tail fear → negative skew, always).

Bonds: Skew direction FLIPS with the rate environment. In rising-rate environments: rate calls (bond puts) get more expensive. Near zero rates: floors are expensive. The "direction" of concern reverses — unlike equities.

Key Takeaways

Options on Treasury futures = right to buy/sell the future at a set price
MOVE = bond VIX; high = uncertainty; MBS managers watch this closely
Bond skew is not a one-way street — direction depends on rate level and direction of fear
Long straddle = long vol; buy when MOVE is low, expect a big move
Bloomberg: OVME<GO> (options valuation), OMON<GO> (options monitor)

Ch 7

Bootstrapping the Yield Curve

BLUF: Given par yields for each maturity, bootstrap the zero-coupon (spot) curve step by step — using each known zero rate to strip coupons off the next bond, leaving the last cashflow to solve for the next zero rate. Forward rates then follow mechanically. This is how the entire derivatives market is built.

Step-by-Step Bootstrapping

1Y T-Bill (zero coupon): Z₁ = 1.00% (direct — it's a zero) 2Y par bond (2% coupon): 100 = 2/(1+Z₁) + 102/(1+Z₂)² → solve: Z₂ = 2.01% 3Y par bond (4% coupon): 100 = 4/(1.01) + 4/(1.0201²) + 104/(1+Z₃)³ → solve: Z₃ = 4.098%

Pattern: use known zeros to discount interim coupons; the last cashflow is the only unknown.

Discount Factors

DF_n = 1 / (1 + Z_n)^n 1Y: DF = 1/1.01 = 0.990099 2Y: DF = 1/1.0201² = 0.960980 3Y: DF = 1/1.04098³ = 0.886488

Implied Forward Rates

F(1y1y) = [(1+Z₂)² / (1+Z₁)] − 1 = [1.0201² / 1.01] − 1 = 3.0301% Real example (ACT/360 day counts): F(3y7y) = [(1.013791^(3542/360)) / (1.004059^(1052/360))]^(360/2490) − 1 = 1.793%

The forward curve embeds the market's implied rate expectations for every future period.

The Three-Curve Hierarchy (Normal Curve)

Par Rate < Zero/Spot Rate < Forward Rate

Why: par rate blends all coupons (early low-rate ones drag it down); zero must compound purely at the long-end rate; forward must exceed zero to make their average equal the zero rate.

Key Takeaways

Bootstrapping: iterate maturity by maturity, using known zeros to strip prior coupons
Zero rates are more precise for pricing — each cashflow discounted at its own rate
Forward rates = market-implied expectations embedded in today's spot curve
Derivation flow: Par → Spot/Zero → Forward → Forward Par
Bloomberg: FWCM<GO> (forward matrix), ICVS<GO> (curve builder), FWCV<GO> (horizon curve)

Ch 8

Corporate Bonds — Structure, Types & Trading

BLUF: Corporate bonds = company debt. Yield = risk-free + credit spread. Seniority determines who gets paid in bankruptcy. Callable bonds cap your upside. CoCos are high-yield but have binary risk (can wipe you out without warning).

Seniority Waterfall (Priority in Default)

Secured → Senior Unsecured → Senior Sub → Junior Sub → Hybrid/AT1 → Equity

If a company defaults, each layer is paid in full before the next gets anything. Senior secured = safest; equity = first to zero.

Bond Structures

Type	Description	Key Risk
Bullet	Fixed coupon, one maturity date	Pure duration + credit
Callable	Issuer can redeem early	Extension risk if not called; reinvestment risk if called
Puttable	Investor can sell back early	Reinvestment risk for investor (favorable)
Convertible	Bond + embedded equity call	Delta moves 0→1 as equity rises above conversion price
Perpetual	No maturity; coupon forever	Extension risk; issuer discretion on coupon
CoCo (AT1)	Converts/writes down at CET1 trigger	Binary: CET1 trigger → equity or zero

Bond Geography

Name	Currency	Issuer
Yankee	USD	Non-US in US market
Eurodollar	USD	Non-US in European market
Samurai	JPY	Non-Japanese in Japan
Bulldog	GBP	Non-UK in UK market

Key Takeaways

Seniority is everything in default — know your position in the waterfall before you buy
Callable bonds: higher yield, but capped upside (issuer calls when it hurts you most)
CoCos: attractive yield, but the trigger can wipe you out without market warning (Standard Chartered 2017)
Corporate bonds are OTC: check ALLQ<GO> for dealer axes; settlement T+2
Convertible delta ranges 0 to 1: when deep in-the-money, it trades like equity

Ch 9

Credit Risk — G-Spread, I-Spread, Z-Spread, OAS & ASW

BLUF: Credit spread = the extra yield you demand vs risk-free for owning a corporate bond. Four measures exist. Z-spread is most rigorous (uses the full curve). OAS strips out the option value from callable bonds. ASW is the only one you can actually trade.

Four Spread Measures Compared

Spread	Benchmark	Full Curve	Options	Tradeable
G-Spread	Government YTM	No	No	No
I-Spread	Swap YTM	No	No	No
Z-Spread	Zero swap curve	Yes	No	No
OAS	Zero swap curve	Yes	Yes (stripped)	No
ASW	SOFR/floating	Via discounting	No	Yes

Z-Spread — Most Rigorous Spread

Dirty Price = Σ [CF_t / (1 + Z_t + Z-spread)^t] Add a CONSTANT spread to EVERY point on the zero swap curve so NPV of all cashflows = dirty price

Delta Airlines example: Z-spread = 138.7bps → every zero swap rate shifted UP by 138.7bps. Graphically: the bond's discount curve = spot swap curve shifted up by 138.7bps.

OAS — Option-Adjusted Spread

OAS = Z-Spread − Option Value Boeing callable example: G-Spread = 128bps Z-Spread = 119.7bps OAS = 55.2bps Option value = 119.7 − 55.2 = 64.5bps ← cost of the call to investor

Uses stochastic rate tree (binomial). Higher vol assumption → option worth more → OAS smaller for callables.

For bullet bonds: OAS = Z-Spread always (no embedded option).

ASW — The Tradeable Spread

Buy corporate bond + enter fixed-to-float IRS (pay fixed coupon, receive SOFR/LIBOR + spread). The spread on the floating leg that makes NPV = 0 is the ASW.

What ASW MEANS: Bond + IRS = the bond's credit risk is now in the floating spread. It's the bond's credit risk expressed over the swaps curve, in tradeable form.

AAPL 1.4% 08/28 example: Bought at 99.591 → ASW = 30.3bps over SOFR. Bloomberg ASW<GO> vs manual SWPM build differ by ~0.03bps (cashflow date convention).

Key Takeaways

Z-spread: most rigorous; uses full curve; but assumes no rate volatility
OAS: Z-spread minus option value; correct for callable/puttable bonds
For bullet bonds: Z-spread = OAS (always)
ASW: only spread you can TRADE; how banks measure credit risk on funded positions
Z-spread − OAS = value of the embedded option in basis points
Extension risk: when an issuer fails to call → price drops sharply (market priced in the call)

Ch 10

Floating Rate Notes (FRNs)

BLUF: FRNs pay a variable coupon (benchmark + spread) that resets periodically. Very low interest rate duration (coupon resets protect price). But they ARE credit instruments — when credit conditions tighten, FRNs drop just like any other bond. FLOT was down 10%+ in March 2020.

FRN Structure & Valuation

Coupon = Benchmark Rate + Spread Duration ≈ 0 to next reset date (~0.25 for quarterly) Huarong example (3M LIBOR + 185bps, quarterly, ACT/360): Coupon = (0.12888% + 1.85%) / 4 × (92/360) = 0.5057% → $5,057.14 per $1MM notional

Quoted Margin (QM) = at issuance. Discount Margin (DM) = secondary market equivalent. DM > QM → discount; DM < QM → premium.

In Advance vs In Arrears

Type	When benchmark is set	Duration
In Advance (common)	Start of coupon period	Slightly higher (~next reset date)
In Arrears (rarer)	End of coupon period	Near zero

FRNs Are Credit Instruments

Rates rise → coupon goes up → price stays near par ✓
Credit conditions tighten → DM widens → price drops ✗

March 2020 — FLOT ETF: Traded at 10%+ discount to NAV. Not because rates moved. Credit spreads blew out. IG FRNs looked "safe" from rate risk but got hammered by credit risk. The lesson: low duration ≠ low risk.

Key Takeaways

FRN duration ≈ 0 to next reset; they absorb rate moves through coupon adjustment
FRNs are credit instruments: DM spread is what you're buying, not rate exposure
March 2020 FLOT collapse proves: low duration does NOT mean low risk
Day count (ACT/360 vs ACT/365) changes coupon meaningfully — verify before booking
Bloomberg: YASN<GO> for OAS on floaters

Ch 11

TIPS — Treasury Inflation-Protected Securities

BLUF: TIPS protect real value by growing the principal with CPI. Fixed coupon RATE on floating PRINCIPAL. But TIPS do NOT give extra return when inflation rises — they maintain purchasing power. BEI = Nominal yield − TIPS yield = the constant inflation rate at which both perform equally. It is NOT an inflation forecast.

TIPS Mechanics

Adjusted Principal = Face × Index Ratio Index Ratio = Reference CPI / Base CPI Coupon = Fixed Rate × Adjusted Principal × day count fraction CPI lag: ~3 months. Mid-month dates: linear interpolation. Example (settle 08/27/2021): Aug 1 ref CPI = May 2021 = 269.195 Sep 1 ref CPI = July 2021 = 271.696 Interpolated = 269.195 + (2.501 × 29/31) = 271.535 Index Ratio = 271.535 / 268.021 = 1.01311

Deflation floor: principal cannot fall below par at maturity.

What TIPS Do NOT Protect Against

TIPS protect real value. They still expose you to:

Real yield movements (GDP growth expectations, Fed policy, credit quality)
If real yields RISE → TIPS price falls, just like any bond

TIPS = a bet on REAL RATES falling, not on inflation accelerating.

Breakeven Inflation (BEI) & Inflation Swaps

BEI = Nominal Yield − TIPS Real Yield 5Y5Y Forward Inflation Swap (Fed watches this): = [(1+10Y ZC)^10 / (1+5Y ZC)^5]^(1/5) − 1 = [(1.025343)^10 / (1.027248)^5]^(1/5) − 1 = 2.344% Bloomberg: FWISUSS55 Index

BEI is NOT an inflation forecast. It includes the inflation risk premium and TIPS illiquidity discount. BEI typically understates true inflation expectations.

Key Takeaways

TIPS: fixed rate on growing principal; principal floors at par at maturity (deflation protection)
BEI = nominal − real; NOT a forecast; it's the equilibrium inflation rate for equal returns
TIPS are real-rate instruments: real yields rise → TIPS price falls
Long breakevens (long TIPS + short nominals) = bet actual inflation exceeds BEI
5Y5Y forward inflation swap = what the Fed watches for long-run inflation expectations
Bloomberg: SWIL<GO> (inflation projections), SWPM-ILFX (ZC inflation swap)

Ch 12

Mortgage-Backed Securities (MBS)

BLUF: $11.5T market; only Treasuries trade more. Agency MBS has no credit risk (GSE-guaranteed) but massive prepayment risk. You're short a call option to every homeowner. This creates negative convexity — you underperform in rallies (prepayments) AND in sell-offs (extension). You only win when rates are range-bound.

MBS Structure & Key Terms

Term	Definition
Factor	Remaining principal as % of original (starts at 1.0)
WAC	Weighted Average Coupon (underlying mortgage rate)
WALA	Weighted Average Loan Age (months)
LTV	Loan-to-Value ratio (80% = standard conforming)
Day Delay	~1.5 months between borrower payment and investor receipt
TPO	Third-party origination = more refi-aggressive pools

Prepayment Measures

CPR: % of remaining balance that prepays per year PSA: Standard benchmark curve - Month 1-30: CPR grows from 0% by 0.2%/month → reaches 6% CPR at month 30 - Month 30+: stays flat at 6% CPR - 150 PSA in month 31 = 150% × 6% = 9% CPR FNCI 2.5 current speeds: - Base: 392 PSA (very fast — low rate environment) - +100bps: 148 PSA (much slower — refi math breaks down)

Negative Convexity — The MBS Curse

Rates fall: Homeowners refi → MBS pays at par → price capped. You get cash back at the worst time (low rates).

Rates rise: Homeowners stay → loan extends → duration increases at the worst time ("extend-o-matic").

Only range-bound rates reward MBS holders with carry and no convexity headwind.

CMOs & IO Strips

Sequential CMO: All principal flows to Tranche A first → B → C. A = shortest, most protected.

PAC (Planned Amortization Class): Pays off within a specific window across a PSA collar/band. "Busts" outside band.

IO Strips (Interest-Only): NEGATIVE DURATION. Rates rise → fewer prepayments → more interest payments → IO price RISES. Used as duration hedge.

"Prepayment risk cannot be created or destroyed — only redistributed."

Key Takeaways

Agency MBS = no credit risk; 100% prepayment risk (you're short a call to every borrower)
Negative convexity: MBS underperforms in both rallies AND sell-offs — only wins in range
MOVE matters: high vol = expensive optionality = MBS OAS looks cheap but option cost is high
Payups: premium pools (LLB, NY geo) prepay slower → worth paying a premium over TBA
IO strips have negative duration — useful as a duration hedge for MBS portfolios
CPR measures speed; PSA normalizes to a standard ramping curve

Ch 13

Interest Rate Swaps (IRS)

BLUF: A swap exchanges fixed cashflows for floating ones with no principal exchange. The quoted swap rate IS the fixed coupon that makes the swap worth zero at inception. Post-GFC dual-curve stripping uses SOFR to discount and the swap curve to imply forwards. $466.5T notional globally.

Comparative Advantage — Why Swaps Exist

Company	Fixed Rate	Floating Rate
A	5%	LIBOR + 100
B	6%	LIBOR + 175

A borrows fixed (advantage), B borrows floating (advantage). Via a swap: A ends up paying LIBOR+15 (saves 85bps); B ends up paying 5.85% fixed (saves 15bps). Both parties win by exploiting comparative advantage.

6 Parts of a Par Vanilla Swap

Fixed Leg: 1. Fixed coupon (the swap rate; e.g., 1.5% S/A) 2. Day count stripping (ACT/365, 30/360, etc.) 3. Fixed NPV = PV of all fixed cashflows Floating Leg: 4. Floating index (SOFR, 3M LIBOR, EURIBOR) 5. Floating NPV = PV of implied forward rates 6. Swap Premium = Fixed NPV − Floating NPV = 0 at inception

KEY TAKEAWAY: "The swap rate you see quoted daily is the fixed coupon rate required to ensure the premium = 0. That is why the swap curve is called a par swaps curve."

Dual Curve Stripping (Post-GFC)

Era	Forward Rates	Discount Rate
Pre-2008	LIBOR swap curve	LIBOR (same curve)
Post-2008	LIBOR/swap curve (Bloomberg curve 23)	SOFR/OIS (Bloomberg curve 490)

LCH shifted to SOFR discounting October 2020. Rationale: LIBOR reflects bank credit risk; SOFR is truly risk-free.

XVAs — The Hidden Costs of Bilateral OTC Swaps

XVA	Adjusts For
CVA	Counterparty credit risk (expected loss if they default)
DVA	Your own default risk (controversial)
FVA	Cost of funding uncollateralized exposure
MVA	Initial margin cost
KVA	Regulatory capital (RWA) cost

Key Takeaways

Payer = pays fixed = long duration (benefits from rates rising)
Receiver = receives fixed = short duration (benefits from rates falling)
Swap rate = par coupon — at inception, NPV = 0 for both sides
Dual curve: forward rates from swap curve; discount from SOFR
DV01 of swap ≈ DV01 of fixed leg; use to duration-hedge bond portfolios
Dodd-Frank: most eligible swaps must clear via CCP (LCH, CME)

Ch 14

Other Swap Types — OIS, ASW, TRS, Basis Swaps & XCCY

BLUF: OIS bets on the Fed's overnight rate path. ASW converts fixed bond cashflows to tradeable floating spreads. TRS gives synthetic total return on any asset (Archegos mechanism). Basis swaps exchange floating rates across tenors — pricing the value of funding certainty. XCCY swaps exchange rates across currencies — the basis measures global USD demand (deeply negative = foreign investors desperate for dollars).

OIS (Overnight Index Swap)

IRS where floating leg = overnight rate (EFFR in USD, ESTR in EUR, SONIA in GBP, TONAR in JPY) compounded daily. Paid as single annual lump sum. OIS rate = market expectation for AVERAGE overnight rate over the swap term.

No principal exchange. Used to bet on Fed policy: pay fixed OIS if you think Fed will hike.

ASW (Asset Swap) — Deep Mechanics

Step 1: Buy bond at market (e.g., 99.591) Step 2: Enter SWPM — pay 1.4% fixed, receive LIBOR + spread Step 3: At par (premium=0): spread = 24.326bps Step 4: Factor in bond's 0.409 premium → spread = 30.293bps Step 5: ASW<GO> confirms: 30.3bps (tiny difference = cashflow date conventions) Par-Par ASW: bond premium factored into fixed leg at par; credit risk lives in the floating spread.

What ASW means: Bond + IRS = credit risk now in the floating spread. ASW = bond's credit risk over swaps curve, in tradeable form.

TRS (Total Return Swap)

Receive total return of an asset (capital gain + income); pay floating financing rate (e.g., LIBOR+75bps). No principal exchange. Synthetic exposure without owning the asset.

Archegos mechanism: Used TRS on media stocks → enormous synthetic levered positions → margin calls → fire sale. TRS works on any asset: equities, bonds, indices, commodities.

Basis Swaps — Pricing Funding Certainty

3M vs 6M LIBOR basis: receive 3M LIBOR + spread, pay 6M LIBOR KEY TAKEAWAY: "The guarantee of 6M funding today is more valuable than 3M today + another 3M in 3 months time." Lehman 2008: 3M-6M basis hit 40bps+ (no one would commit to 3M funding) Normal times: ~1-2bps (excess liquidity → low certainty premium)

Basis swaps price the value of LONGER-TERM funding certainty. The post-Lehman spike shows why the 3-month gap matters in stress.

XCCY (Cross Currency Basis Swap)

Exchange principals in 2 currencies at spot + exchange floating rates + re-exchange principals at maturity at ORIGINAL spot FX rate EUR/USD XCCY solver (1Y): 0 spread both legs → EUR leg NPV > USD leg NPV (EUR rates negative → EUR "costs" more to earn) Solve EUR spread for NPV=0 → EUR spread = −7.852bps → EUR holder gives up 7.85bps below EURIBOR to access USD 2016 extreme: EUR/USD XCCY → −48bps (massive EUR demand for USD) 5Y EUR/USD XCCY with -48bps basis: → Implies EUR investors pay a 2% premium on a 5Y swap from day one

Practical trade (March 2020, JPY-USD basis −57bps): Buy JGB at −0.22% yield → XCCY ASW → earn 1.1299% USD fixed. When domestic US 1Y bills yield 0.1654% — massive pickup.

Bloomberg: XCCY<GO> — global cross-currency basis spreads. Deeply negative = strong foreign USD demand.

Global XCCY Basis Spreads (vs USD, 5Y, Sep 2021)

Currency	Spread	Interpretation
JPY	−26.25bps	Japanese investors pay to get USD
KRW	−71bps	Very strong Korean demand for USD
EUR	−6.50bps	EUR investors pay modest premium for USD
AUD	+16.50bps	USD investors pay to get AUD (rare)
CHF	−5.50bps	CHF investors pay to get USD

Key Takeaways

OIS = bet on Fed policy path; OIS rate = implied average overnight rate
ASW = tradeable credit risk measure; the only spread you can actually transact
TRS = synthetic total return; no ownership needed; Archegos used it for massive leverage
Basis swaps: price the VALUE OF CERTAINTY — 6M funding > two 3M rollovers
XCCY deeply negative = foreign investors desperate for USD (flight to dollar safety)
XCCY value = f(USD swap rates, foreign swap rates, FX forward rates) — three drivers

Ch 15

Appendix — The Cheapest-to-Deliver Bond

BLUF: Treasury futures shorts must deliver an actual bond. They choose the one that maximizes their cash-and-carry profit — the CTD. CTD = bond with highest Implied Repo Rate. Bloomberg DLV<GO> sorts it for you. Invoice Price = Futures Price × CF + Accrued. The CF normalizes every eligible bond to the theoretical 6% convention.

The Mechanics — Invoice Price & Gross Basis

Invoice Price = Futures Price × CF + Accrued Interest Gross Basis = Cash Price − Invoice Price (in 32nds) Example (TYU1, Sep 2021): Futures price: 131-29 = 131.90625 T 2⅝ 05/15/28: CF = 0.8338 Invoice = 131.90625 × 0.8338 = 109.9834 Cash bond: 110-24¼ = 110.7578 Gross Basis = (110.7578 − 109.9834) × 32 = 24.78 (32nds)

Implied Repo Rate — The CTD Selector

Cash-and-Carry: Buy cash bond + sell futures → deliver at expiry Implied Repo = annualized money market return from this trade FIHZ<GO> example (T 2⅝ 05/15/28): Buy at 110-24.25 on 06/21/21 Deliver at Invoice Price on 09/30/21 (101 days) MMKT return: 0.047% annualized = Implied Repo Rate CTD = Bond with HIGHEST Implied Repo = most profitable cash-and-carry Bloomberg DLV<GO> sorts all eligible bonds by implied repo → top = CTD

CTD Rule of Thumb

Rate Environment	CTD Tends To Be
Yields > 6% (futures convention)	Longest duration eligible bond
Yields < 6%	Shortest duration eligible bond

CTD can SWITCH as rates move → creates switching risk in futures positions.

Key Takeaways

Invoice Price = what the futures buyer pays for the delivered bond
Gross Basis = cash price − invoice price (in 32nds); the short's "profit" on delivery
Implied Repo = annualized cash-and-carry return; CTD = bond with highest implied repo
DLV<GO> sorts deliverables by implied repo — top = CTD today
CTD drives futures pricing; when CTD changes, the futures reprices
Net Basis = Gross Basis − Carry = fairest value measure of the basis

BB

Bloomberg Terminal Quick Reference

BLUF: Key Bloomberg screens from throughout the book. Organized by function.

Screen	Function	Chapter
`YAS<GO>`	Yield & Spread Analysis (Z-spread, OAS, duration)	9
`ALLQ<GO>`	All Quotes — dealer axes for corporates	8
`GC<GO>`	G-Spread calculator	9
`SWPM<GO>`	Swap Pricing/Manager — build any swap type	13, 14
`ASW<GO>`	Asset Swap Spread calculator (quick)	9, 14
`ICVS<GO>`	Curve Builder — construct custom yield curves	7, 13
`FWCM<GO>`	Forward Rate Matrix — all forward rates	4, 7
`FWCV<GO>`	Forward Curve horizon (shift to future date)	7
`CARY<GO>`	Carry & Rolldown analysis	4
`BFLY<GO>`	Butterfly trade structure	4
`DLV<GO>`	Cheapest-to-Deliver screen (sorted by implied repo)	5, 15
`FIHZ<GO>`	Fixed Income Horizon Analysis (hold period return)	15
`OVME<GO>`	Options Valuation Manager	6
`OMON<GO>`	Options Monitor	6
`MOVE Index`	Bond market volatility index (bond's VIX)	6
`OSA<GO>`	OAS Analysis	9
`YASN<GO>`	OAS for floating rate notes	10
`SWIL<GO>`	Inflation projections	11
`FWISUSS55`	5Y5Y Forward Inflation Swap (Fed's favorite)	11
`TBA<GO>`	TBA (To Be Announced) MBS market	12
`TBPF<GO>`	TBA pricing and factors	12
`XCCY<GO>`	Cross-Currency Basis Spreads (global)	14
`WIR<GO>`	World Interest Rates (par curve comparison)	4
`WBF<GO>`	World Bond Futures	5
`VCUB<GO>`	Vol Cube	6
`SECF<GO>`	Security Finder (bond search)	8
`PRPL<GO>`	Principal/Price lookup	9
`CCRV<GO>`	Credit Curve builder	9

∑

Formula Sheet

Concept	Formula
Future Value	`FV = PV × [1 + (y/f)]^n`
Discount Factor	`DF = 1 / [1 + (y/f)]^n`
Bond Price	`P = Σ [CF_t / (1+y)^t]`
Modified Duration	`ModDur = MacDur / (1 + y/f)`
% Price Change	`ΔP% ≈ −ModDur × Δy`
PV01	`Price × ModDur / 100`
DV01	`PV01 × (Face / 100)`
T-Bill Price	`P = 100 − [disc_rate × days/360]`
Carry	`Yield − Repo Rate`
Forward Rate	`F(1y1y) = [(1+Z₂)² / (1+Z₁)] − 1`
Index Ratio (TIPS)	`Reference CPI / Base CPI`
Breakeven Inflation	`BEI = Nominal Yield − TIPS Real Yield`
5Y5Y Forward Inflation	`[(1+Z₁₀)^10 / (1+Z₅)^5]^(1/5) − 1`
Invoice Price (Futures)	`Futures Price × CF + Accrued`
Gross Basis	`(Cash Price − Invoice Price) × 32 (in 32nds)`
DV01-Neutral Ratio	`N_short / N_long = DV01_long / DV01_short`
OAS	`Z-Spread − Option Value`
PSA (after mo 30)	`N PSA = N × 6% CPR`