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• Advance Praise for Fixed Income Securities
• Foreword
• Preface
• Acknowledgments
• 1 A Primer on the Time Value of Money
• Nominal and Effective Rates of Interest
• Variables and Terms to Be Used and the Corresponding Symbols
• The Concept of Simple Interest
• The Concept of Compound Interest
• Properties of Simple and Compound Interest
• Effective Versus Nominal Rates of Interest
• A Symbolic Derivation of the Relationship Between Effective and Nominal Rates of Interest
• Computing Effective and Nominal Rates in Excel
• Principle of Equivalency of Interest Rates
• Continuous Compounding of Interest
• Using Excel to Compute the Effective Rate with Continuous Compounding
• Future Value of Cash Flows
• Computing the Future Value Using Excel
• Present Value of Cash Flows
• Computing Present Values of Cash Flows Using Excel
• The Internal Rate of Return of an Investment
• Pure and Mixed Cash Flows
• Descartes’ Rule of Signs and the IRR
• A Point About Effective Rates of Interest
• Level Annuities
• Present Value of a Level Annuity
• Future Value of a Level Annuity
• Relationship Between PVIFA and FVIFA for a Level Annuity
• Level Annuities Due
• Present Value of a Level Annuity Due
• Computation in Excel of the Present Value of an Annuity Due
• Future Value of an Annuity Due
• Computation of the Future Value of an Annuity Due in Excel
• Relationship Between PVIFA and FVIFA for Annuity Dues
• Perpetuities
• The Amortization Method of Loan Repayment
• Obtaining the Amortization Schedule Using Excel
• The Rationale for Why IPMT and PPMT Can Be Used with Two Different Sets of Parameters
• Amortization with a Balloon Payment
• Handling the Balloon Using Excel
• A Growing Annuity
• Present Value of a Growing Annuity
• Future Value of a Growing Annuity
• Growing Perpetuity
• Growing Annuity Due
• Present Value of a Growing Annuity Due
• Future Value of a Growing Annuity Due
• Growing Perpetuity Due
• Chapter Summary
• 2 An Introduction to Bonds
• The Leverage Effect
• Tax Shield Due to Interest Payments
• Variables Influencing the Bond Price
• Face Value
• Term to Maturity
• Coupon
• Yield to Maturity
• Valuation of a Bond
• Par, Premium, and Discount Bonds
• Influence of Variables on the Bond Price
• The Pull to Par Effect
• An Interesting Result about Bond Prices
• Eurobonds and Foreign Bonds
• Coupon Dates and Coupon Frequencies
• Zero Coupon Bonds
• Creating a Synthetic Zero Coupon Bond
• Price Quotes for Bonds
• Computation of the Bond Price Using Excel
• Different Bond Types
• Amortizing Bonds
• Bonds with Step-Up Coupons and Step-Down Coupons
• Payment-In-Kind (PIK) Bonds
• Treasury Securities
• Treasury Auctions
• Illustration of a Treasury Auction
• Security Identification
• Coupon Strips
• When Issued (WI) Trading
• Coupon Rolls
• Accounting for Bonds
• Issue of Discount Bonds
• Issue of Premium Bonds
• Risks Inherent in Bonds
• Credit Risk
• Moody’s Ratings Scale
• S&P’s Rating Scale
• Fitch’s Rating Scale
• Liquidity Risk
• Interest Rate Risk
• Inflation Risk
• Timing Risk
• Foreign Exchange Risk
• Chapter Summary
• 3 Bonds: Advanced Concepts
• Required Symbols for the Variables
• Day-Count Conventions
• The Actual/Actual Approach
• The Market Method for Bond Valuation
• The Treasury Method for Bond Valuation
• Accrued Interest
• The Impact of Time on the Dirty Price
• Computation of Price and Accrued Interest Using Excel
• Computation of the YTM Between Coupon Dates
• Other Day-Count Conventions
• The 30/360 NASD Approach
• 30/360 European Convention
• Actual/365 Convention
• Actual/360 Convention
• Comparison of Day-Count Conventions
• Additional Coupon-Related Excel Functions
• Valuing a Bond in the Final Coupon Period
• Yield Measures: An Introduction
• Current Yield of a Bond
• Simple Yield to Maturity
• Yield to Maturity of a Bond
• The Approximate Yield to Maturity Approach
• The Rationale for the AYM Approach
• The Realized Compound Yield
• The Horizon or Holding Period Return
• The Realized Compound Yield with Taxes
• Computing the YTM with Taxes
• The Portfolio Yield for Bonds
• The Weighted Average Approach
• The IRR Approach
• The Taxable Equivalent Yield (TEY)
• Sinking Fund Provisions
• Serial Bonds
• Yield to Average Life
• Yield to Equivalent Life
• Chapter Summary
• 4 Yield Curves and the Term Structure
• Analyzing the Yield Curve
• Spot Rates of Interest
• The Relationship Between Spot Rates and the YTM
• Yield Curve versus the Term Structure
• Required Symbols
• Bootstrapping to Obtain Spot Rates
• Practical Difficulties with Bootstrapping
• Coupon Yield Curves and Par Bond Yield Curves
• Deducing a Par Bond Yield Curve
• Implied Forward Rates of Interest
• Fitting the Yield Curve
• Interpolation
• Polynomial Models of the Yield Curve
• Regression Models of the Yield Curve
• The Nelson-Siegel Model of the Yield Curve
• Interpretation of the Nelson-Siegel Model
• Theories of the Term Structure
• The Pure or Unbiased Expectations Hypothesis
• The Liquidity Preference Theory (LPT)
• The Expectations Hypothesis versus the LPT: A Mathematical Analysis
• The Money Substitute Hypothesis
• The Market Segmentation Hypothesis
• The Preferred Habitat Theory
• Features of the Debt Market and Theories of the Term Structure
• Chapter Summary
• 5 Duration, Convexity, and Immunization
• A Mathematical Definition of Duration
• A Useful Excel Function
• Duration of a Bond When the Settlement Date Is Between Two Coupon Dates
• A Concise Formula for the Duration on a Coupon Date
• The Case of a Par Bond
• Duration of a Level Annuity
• Duration of a Perpetuity
• The Rationale Behind Duration
• Factors Influencing Duration
• Term to Maturity
• Coupon
• Yield to Maturity
• Accrued Interest
• Coupon Frequency
• Percentage Price Change and Duration
• Duration of Annuities Due and Perpetuities Due
• Dollar Duration
• Computing Duration and Modified Duration with Excel
• Modified Duration
• Approximating Duration
• The Concept of Effective Duration
• Duration as a Center of Gravity
• Portfolio Duration
• Bond Convexity
• Approximating the Price Change of a Bond for a Given Change in Yield
• Dispersion of a Bond
• Convexity of a Zero Coupon Bond
• Dispersion as an Expected Value
• Portfolio Convexity and Dispersion
• Properties of Convexity
• The Impact of Duration
• The Irrelevance of the Face Value
• Dollar Convexity
• Approximate Convexity
• Convexity of Annuities and Perpetuities
• Perpetuities
• Immunization of a Bond Portfolio
• A Point on Long-Dated Treasury Bonds
• Chapter Summary
• Appendix 5.1 Derivation of a Concise Formula for Duration
• Appendix 5.2 Duration of Annuities and Perpetuities
• Appendix 5.3 Duration and Interest Rate Sensitivity
• Appendix 5.4 Convexity of Annuities and Perpetuities
• Appendix 5.5 Proof of Single-Period Immunization
• 6 The Money Market
• Risk Factors in the Money Market
• Supervision of the Money Market
• Key Dates in Money Market Transactions
• Roll Conventions in the Event of Market Holidays
• The End/End Rule
• The Interbank Market
• Types of Loans in the Inter-bank Market
• LIBOR
• Interest Computation Methods
• Money Market Forward Rates
• Term Money Market Deposits
• Federal Funds
• Treasury Bills
• Re-openings of T-bills
• Discount Rates and T-bill Prices
• The Money Market Yield of a T-bill
• The Bond Equivalent Yield of a T-bill
• Holding Period Return for an Investor
• Concept of a Tail in a T-bill Transaction
• T-bill Related Computations Using Excel
• Repurchase Agreements
• Repo Rates
• Margins in Repo Transactions
• The Federal Reserve and Repos
• Negotiable Certificates of Deposit (CDs)
• Required Symbols
• Term Certificates of Deposit
• NCDs vs. Money Market Time Deposits
• The Effective Cost of a CD
• Commercial Paper
• Letters of Credit (LCs)
• Yankee Paper
• Credit Rating
• Moody’s Rating Scale
• S&P’s Rating Scale
• Fitch’s Rating Scale
• Bills of Exchange
• Chapter Summary
• 7 Floating Rate Bonds
• Call and Put Provisions in Floating Rate Bonds
• Caps and Floors for the Coupon Rate
• Symbols: An Important Note of Caution
• Valuation of a Floating Rate Bond
• Variations on the Floating Rate Feature
• Inverse Floating Rate Bonds
• Deleveraged Floating Rate Bonds
• Dual-Indexed Floating Rate Bonds
• Range Notes
• Variations on the Principal Repayment Feature
• Floaters, Inverse Floaters, and Plain Vanilla Bonds
• A More General Relationship for an Inverse Floater
• Duration of a Floating Rate Bond
• Convexity of a Risk-Free Floating Rate Bond
• Comparison with a Zero Coupon Bond
• Margin Measures for Floaters
• Simple Margin
• Adjusted Simple Margin
• Adjusted Total Margin
• The Discount Margin
• Inflation Indexed Bonds
• Principal Linkers or P-Linkers
• Analysis
• Coupon Linkers or C-Linkers
• Valuing a Risky Floater
• Pricing Equation
• Duration of a Risky Floater
• Chapter Summary
• Appendix 7.1 Duration of a Risky Floater
• Appendix 7.2 Duration of a Risky Perpetual Floater
• 8 Mortgage Loans
• Important Mortgage-Related Terms
• Risks in Mortgage Lending
• Default Risk
• Liquidity Risk
• Interest Rate Risk
• Prepayment Risk
• The Role of the Mortgage Rate in Prepayments
• Negative Amortization
• Other Mortgage Structures
• Adjustable Rate Mortgages (ARMs)
• Option to Change the Maturity
• Features of ARMs
• Variations on the ARM Structure
• Interest Rate Caps
• Example of Interest Rate Caps
• Payment Caps
• Graduated Payment Mortgages
• Growing Equity Mortgages
• A Comparison of the Three Mortgage Structures
• Year 1
• Year 2
• Year 3
• Year 4
• Year 5
• Year 6
• Year 7
• Year 8
• Mortgage Servicing
• Income for the Servicer
• Mortgage Insurance
• Sale of Mortgage Loans
• The Average Life of a Mortgage Loan
• Prepayments of Principal
• Single Month Mortality (SMM)
• Analysis of a Loan with Prepayments
• Relationship between Cash Flows with and without Prepayments
• Conditional Prepayment Rate (CPR)
• An Equal Principal Repayment Loan
• Weighted Average Coupon (WAC) and Weighted Average Maturity (WAM)
• Chapter Summary
• 9 Mortgage-Backed Securities
• Cash Flows for a Pass-Through Security
• Cash Flow Yield of a Pass-Through Security
• Symbols Required for the Exposition
• Collateralized Mortgage Obligations
• Extension Risk and Contraction Risk for Mortgage-backed Securities
• Accrual Bonds
• Creating Floating Rate Tranches
• Notional Interest-Only Tranches
• Interest-Only and Principal-Only Strips
• Planned Amortization Class (PAC) Bonds
• Analysis of the SMM = 15% Scenario
• Chapter Summary
• 10 A Primer on Derivatives
• Futures and Forwards: Comparisons and Contrasts
• The Role of the Clearinghouse in a Futures Trade
• Margins for Futures Trades
• Marking to Market of Futures Contracts
• The Settlement Price for Futures Contracts
• Movements in the Margin Account
• Offsetting of Futures Contracts
• Spot-Futures Convergence of Prices
• Delivery in the Case of Futures Contracts
• Cash Settlement of Futures Contracts
• Valuation of Futures and Forwards
• The Case of Assets Making Payouts
• Conversion Factors When There Are Multiple Deliverable Grades
• Multiplicative Adjustment of the Futures Price
• Additive Adjustment of the Futures Price
• Hedging Using Futures Contracts
• Hedging and Ex-Post Regret
• Hedging and the Case of Cash-Settled Contracts
• Perfect Hedges Using Futures Contracts
• The Importance of Terminating the Hedge on the Expiration Date
• The Importance of Hedging an Integer Multiple of the Contract Size
• Choosing an Expiration Month for Hedging
• Speculation Using Futures Contracts
• Introduction to Options
• Common Terms Associated with Options
• Exercise Price
• Expiration Date
• Option Premium
• Notation
• Exercising Call and Put Options
• Payoffs and Profits: A Symbolic Representation
• Moneyness of the Option
• Call Options
• Put Options
• Intrinsic Value and Time Value of Options
• The Absence of Arbitrage and Its Implications for Option Prices
• Non-Negative Option Premia
• Non-Negative Time Value of American Options
• Lower Bound for Call Options
• Lower Bound for Put Options
• Put-Call Parity for European Options
• Option Premia at Expiration
• Proof
• Variables of Interest for Option Valuation
• The Current Stock Price
• The Exercise Price
• Dividends
• Volatility
• Time to Maturity
• Riskless Rate of Interest
• The Binomial Model of Option Valuation
• The One Period Binomial Model
• The Two-Period Case
• The Binomial Model for European Puts
• Using the Binomial Model: The Case of European vs. American Puts
• Valuing a European Put Using the Binomial Model
• Valuing an American Put Using the Binomial Model
• The Black-Scholes Formula for Valuing Options
• Put-Call Parity and Option Pricing Models
• Interpretation of N(d1) and N(d2)
• Chapter Summary
• 11 The Valuation of Interest Rate Options
• Short Rates
• Issues in the Valuation of Interest Rate Derivatives
• Equilibrium Models of the Term Structure
• Arbitrage-Free Term Structure Models
• The Ho-Lee Model
• The Hull-White Model
• The Black-Derman-Toy Model
• The Binomial Tree Approach to the Term Structure
• Some Insights into the Ho-Lee Model
• Calibrating the Ho-Lee Model
• Arrow-Debreu Securities
• Calibrating the Black-Derman-Toy Model
• An Issue with Recombination
• An Issue with Calibration
• Valuation of a Plain Vanilla Bond
• Valuation of a Zero Coupon Bond
• Valuing a European Call
• Valuing an American Put
• Caps, Floors, and Collars
• Caps and Floors: A Detailed Perspective
• Interest Rate Collars
• Captions and Floortions
• Chapter Summary
• 12 Interest Rate Forwards and Futures
• Forward Rate Agreements (FRAs)
• Determining the Contract Rate
• Using Short Rates to Determine the FRA Rate
• Eurodollar Futures
• Calculating Profits and Losses on ED Futures
• Locking in a Borrowing Rate
• Locking in a Lending Rate
• Cash-and-Carry Arbitrage
• Reverse Cash-and-Carry Arbitrage
• The No-Arbitrage Pricing Equation
• Hedging an N-day Loan Using ED Futures
• A More General Argument
• Using ED Futures to Create a Fixed Rate Loan
• Stack and Strip Hedges
• FRAs vs. ED Futures: An Important Point
• Federal Funds
• Fed Funds Futures
• T-Note and T-Bond Futures
• T-Bond Contracts
• Conversion Factors
• Calculating the Invoice Price for a T-Bond
• The Cheapest-to-Deliver (CTD) Bond
• The Cheapest-to-Deliver Bond Prior to Expiration
• Risk in an Arbitrage Strategy Due to Multiple Deliverable Grades
• Seller’s Options
• The Delivery Process
• The Wild Card Option
• The Quality Option
• The End-of-Month Option
• Hedging
• Hedging the Cheapest-to-Deliver Bond: A Naive Approach
• The Conversion Factor Approach
• Hedging a Portfolio Other Than the CTD Bond
• Changing the Duration of a Portfolio of Bonds
• Chapter Summary
• Appendix 12.1 Duration-Based Hedge Ratio
• Appendix 12.2 Required Number of Contracts to Change the Duration
• 13 Bonds withEmbedded Options
• Callable Bonds
• Yield to Call
• Relationship between the Yield to Call and the Yield to Maturity
• The Approximate Yield to Call Approach
• Reinvestment Assumption
• Concept of the Yield to Worst
• Valuation of a Callable Bond
• Putable Bonds
• Valuation of a Putable Bond
• Pricing the Callable and Putable Bonds Using the BDT Model
• The Callable Bond and the BDT Model
• Valuation of the Putable Bond
• Yield Spreads for Callable Bonds
• The Traditional Yield Spread
• The Static Spread
• The Option-Adjusted Spread
• Convertible Bonds
• Changes in the Conversion Ratio
• Pros and Cons of a Convertible Issue: The Issuer’s Perspective
• Concept of Break-Even
• Liquid Yield Option Notes (LYONs)
• Exchangeable Bonds
• Valuing a Convertible Bond with Built-in Call and Put Options
• Chapter Summary
• 14 Interest Rate Swaps and Credit Default Swaps
• Interest Rate Swaps
• Contract Terms
• Key Dates in a Swap Contract
• The Swap Rate
• Risk
• Quoted Swap Rates
• Comparative Advantage and Credit Arbitrage
• The Role of Banks in the Swap Market
• Valuing an Interest Rate Swap
• Valuing a Swap at an Intermediate Stage
• Terminating a Swap
• Motives for the Swap
• Speculation
• Hedging a Liability
• Hedging an Asset
• Equivalence with FRAs
• Determining the Fixed Rate
• Forward-Start Swaps
• Amortizing Swaps
• In-Arrears Swaps
• Extendable and Cancelable Swaps
• Swaptions
• Credit Default Swaps
• Valuation of a CDS
• Using Default Probabilities to Determine the Swap Rate
• Chapter Summary
• Appendix A
• Goal Seek
• Solver
• Bibliography
• Subject Index