Bloomberg - Fixed Income Securities And Derivatives Handbook Analysis And Valuation (Choudry, Cfa Level 2)

338 Pages·2006·25.25 MB·English

C O N T E N T S
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
PART ONE INTRODUCTION TO BONDS
1 The Bond Instrument 3
The Time Value of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Basic Features and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Present Value and Discounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Discount Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Bond Pricing and Yield: The Traditional Approach . . . . . . . . . . . . . . . . .15
Bond Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Bond Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Accrued Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
Clean and Dirty Bond Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
Day-Count Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

2 Bond Instruments and Interest Rate Risk 31
Duration, Modified Duration, and Convexity . . . . . . . . . . . . . . . . . . . . .31
Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
Properties of Macaulay Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
Modified Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41

3 Bond Pricing and Spot and Forward Rates 47
Zero-Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Bond Price in Continuous Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
Stochastic Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Coupon Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
Forward Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
Guaranteeing a Forward Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
The Spot and Forward Yield Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
Calculating Spot Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
Term Structure Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
The Expectations Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
Liquidity Premium Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Segmented Markets Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
4 Interest Rate Modeling 67
Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
Short-Rate Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
Ito’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
One-Factor Term-Structure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
Vasicek Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
Hull-White Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
Further One-Factor Term-Structure Models . . . . . . . . . . . . . . . . . . . . . . .73
Cox-Ingersoll-Ross (CIR) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
Two-Factor Interest Rate Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
Brennan-Schwartz Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
Extended Cox-Ingersoll-Ross Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
Heath-Jarrow-Morton (HJM) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .77
The Multifactor HJM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78
Choosing a Term-Structure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
5 Fitting the Yield Curve 83
Yield Curve Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84
Smoothing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
Cubic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
Non-Parametric Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
Spline-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88
Nelson and Siegel Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
Comparing Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92
PART TWO SELECTED CASH AND DERIVATIVE INSTRUMENTS
6 Forwards and Futures Valuation 95
Forwards and Futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
Cash Flow Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
Relationship Between Forward and Futures Prices . . . . . . . . . . . . . . . . . . .98
Forward-Spot Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99
The Basis and Implied Repo Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
7 Swaps 105
Interest Rate Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
Market Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
Swap Spreads and the Swap Yield Curve . . . . . . . . . . . . . . . . . . . . . . . . .109
Generic Swap Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112
Intuitive Swap Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112
Zero-Coupon Swap Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
Calculating the Forward Rate from Spot-Rate Discount Factors . . . . . . .113
The Key Principles of an Interest Rate Swap . . . . . . . . . . . . . . . . . . . . . .117
Valuation Using the Final Maturity Discount Factor . . . . . . . . . . . . . . . .118
Non–Plain Vanilla Interest Rate Swaps . . . . . . . . . . . . . . . . . . . . . . . . . .119
Swaptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122
Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122
Interest Rate Swap Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124
Corporate and Investor Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . .124
Hedging Bond Instruments Using Interest Rate Swaps . . . . . . . . . . . . . .127
8 Options 133
Option Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
Option Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137
Option Pricing: Setting the Scene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140
Limits on Option Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142
The Black-Scholes Option Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145
Pricing Derivative Instruments Using the Black-Scholes Model . . . . . . .145
Put-Call Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149
Pricing Options on Bonds Using the Black-Scholes Model . . . . . . . . . . .149
Interest Rate Options and the Black Model . . . . . . . . . . . . . . . . . . . . . . .152
Comments on the Black-Scholes Model . . . . . . . . . . . . . . . . . . . . . . . . .155
Stochastic Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156
Implied Volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156
Other Option Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157
9 Measuring Option Risk 159
Option Price Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159
Assessing Time Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159
American Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160
The Greeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161
Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161
Gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163
Theta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165
Vega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165
Rho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166
Lambda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168
The Option Smile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
Caps and Floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170

10 Credit Derivatives 173
Credit Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175
Credit Risk and Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175
Applications of Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177
Credit Derivative Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178
Credit Default Swap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178
Credit Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179
Credit-Linked Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180
Total Return Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181
Investment Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
Capital Structure Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
Exposure to Market Sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
Credit Spreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184
Funding Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185
Credit-Derivative Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .186
Pricing Total Return Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .187
Asset-Swap Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .187
Credit-Spread Pricing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188
11 The Analysis of Bonds with Embedded Options 189
Understanding Option Elements Embedded in a Bond . . . . . . . . . . . . .189
Basic Options Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190
Option Valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191
The Call Provision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192
The Binomial Tree of Short-Term Interest Rates . . . . . . . . . . . . . . . . . . .193
Arbitrage-Free Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194
Options Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196
Risk-Neutral Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .197
Recombining and Nonrecombining Trees . . . . . . . . . . . . . . . . . . . . . . . .198
Pricing Callable Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200
Price and Yield Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205
Measuring Bond Yield Spreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206
Price Volatility of Bonds with Embedded Options . . . . . . . . . . . . . . . . .207
Effective Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .207
Effective Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208
Sinking Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .209
12 Inflation-Indexed Bonds 211
Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211
Choice of Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211
Indexation Lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .213
Coupon Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214
Type of Indexation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214
Index-Linked Bond Cash Flows and Yields . . . . . . . . . . . . . . . . . . . . . . .216
TIPS Cash Flow Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217
TIPS Price and Yield Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217
Assessing Yields on Index-Linked Bonds . . . . . . . . . . . . . . . . . . . . . . . . .221
Which to Hold: Indexed or Conventional Bonds? . . . . . . . . . . . . . . . . .222
Analysis of Real Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .223
Indexation Lags and Inflation Expectations . . . . . . . . . . . . . . . . . . . . . . .223
An Inflation Term Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .225
13 Hybrid Securities 227
Floating-Rate Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228
Inverse Floating-Rate Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .231
Hedging Inverse Floaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233
Indexed Amortizing Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .234
Advantages for Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .236
Synthetic Convertible Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237
Investor Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238
Interest Differential Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .238
Benefits for Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .240
14 Securitization and Mortgage-Backed Securities 241
Reasons for Undertaking Securitization . . . . . . . . . . . . . . . . . . . . . . . . . .242
Market Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .242
Securitizing Mortgages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .244
Growth of the Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .244
Types of Mortgages and Their Cash Flows . . . . . . . . . . . . . . . . . . . . . . .245
Mortgage Bond Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248
Types of Mortgage-Backed Securities . . . . . . . . . . . . . . . . . . . . . . . . . . .249
Cash Flow Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250
Prepayment Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250
Prepayment Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254
Collateralized Mortgage Securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .255
Sequential Pay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .257
Planned Amortization Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .258
Targeted Amortization Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260
Z-Class Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .261
Interest-Only and Principal-Only Classes . . . . . . . . . . . . . . . . . . . . . . . .261
Nonagency CMO Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264
Credit Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264
Commercial Mortgage-Backed Securities . . . . . . . . . . . . . . . . . . . . . . . .265
Issuing a CMBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .265
Types of CMBS Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .266
Evaluation and Analysis of Mortgage-Backed Bonds . . . . . . . . . . . . . . .267
Term to Maturity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .268
Calculating Yield and Price: Static Cash Flow Model . . . . . . . . . . . . . . .268
Bond Price and Option-Adjusted Spread . . . . . . . . . . . . . . . . . . . . . . . .270
Effective Duration and Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .271
Total Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272
Price-Yield Curves of Mortgage Pass-Through, PO, and IO Securities . .274
15 Collateralized Debt Obligations 279
CDO Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281
Conventional CDO Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .281
Synthetic CDO Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283
Motivation Behind CDO Issuance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284
Balance Sheet–Driven Transactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .285
Investor-Driven Arbitrage Transactions . . . . . . . . . . . . . . . . . . . . . . . . . .285
Analysis and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286
Portfolio Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286
Cash Flow Analysis and Stress Testing . . . . . . . . . . . . . . . . . . . . . . . . . . .286
Originator’s Credit Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .287
Operational Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .287
Review of Credit-Enhancement Mechanisms . . . . . . . . . . . . . . . . . . . . .288
Legal Structure of the Transaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288
Expected Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .289
PART THREE SELECTED MARKET TRADING CONSIDERATIONS
16 The Yield Curve, Bond Yield, and Spot Rates 293
Practical Uses of Redemption Yield and Duration . . . . . . . . . . . . . . . . .293
The Concept of Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .294
Yield Comparisons in the Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .296
Measuring a Bond’s True Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297
Implied Spot Rates and Market Zero-Coupon Yields . . . . . . . . . . . . . .300
Spot Yields and Coupon-Bond Prices . . . . . . . . . . . . . . . . . . . . . . . . . . .300
Implied Spot Yields and Zero-Coupon Bond Yields . . . . . . . . . . . . . . .304
Determining Strip Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307
Strips Market Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308
Strips Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309
Case Study: Treasury Strip Yields and Cash Flow Analysis . . . . . . . . . .311
17 Approaches to Trading 315
Futures Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316
Yield Curves and Relative Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .320
Determinants of Government Bond Yields . . . . . . . . . . . . . . . . . . . . . . .320
Characterizing the Complete Term Structure . . . . . . . . . . . . . . . . . . . . .323
Identifying Relative Value in Government Bonds . . . . . . . . . . . . . . . . . .323
Hedging Bond Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326
Simple Hedging Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326
Hedge Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327
Summary of the Derivation of the Optimum-Hedge Equation . . . . . .329
Appendix: The Black-Scholes Model in Microsoft Excel. . . . . . . . . . . 331
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
P A R T O N E
Introduction to Bonds
Part One describes fi xed-income market analysis and the basic
concepts relating to bond instruments. The analytic building
blocks are generic and thus applicable to any market. The analy-
sis is simplest when applied to plain vanilla default-free bonds;
as the instruments analyzed become more complex, additional
techniques and assumptions are required.
The fi rst two chapters of this section discuss bond pricing and
yields, moving on to an explanation of such traditional interest
rate risk measures as modifi ed duration and convexity. Chapter 3
looks at spot and forward rates, the derivation of such rates from
market yields, and the yield curve. Yield-curve analysis and the
modeling of the term structure of interest rates are among the
most heavily researched areas of fi nancial economics. The treat-
ment here has been kept as concise as possible. The References
section at the end of the book directs interested readers to acces-
sible and readable resources that provide more detail.
11
C H A P T E R 1
The Bond Instrument
Bonds are the basic ingredient of the U.S. debt-capital market,
which is the cornerstone of the U.S. economy. All evening televi-
sion news programs contain a slot during which the newscaster
informs viewers where the main stock market indexes closed that day and
where key foreign exchange rates ended up. Financial sections of most
newspapers also indicate at what yield the Treasury long bond closed. This
coverage refl ects the fact that bond prices are affected directly by economic
and political events, and yield levels on certain government bonds are fun-
damental economic indicators. The yield level on the U.S. Treasury long
bond, for instance, mirrors the market’s view on U.S. interest rates, infl a-
tion, public-sector debt, and economic growth.
The media report the bond yield level because it is so important to the
country’s economy—as important as the level of the equity market and
more relevant as an indicator of the health and direction of the economy.
Because of the size and crucial nature of the debt markets, a large number
of market participants, ranging from bond issuers to bond investors and
associated intermediaries, are interested in analyzing them. This chapter
introduces the building blocks of the analysis.
Bonds are debt instruments that represent cash fl ows payable during
a specifi ed time period. They are essentially loans. The cash fl ows they
represent are the interest payments on the loan and the loan redemption.
Unlike commercial bank loans, however, bonds are tradable in a secondary
market. Bonds are commonly referred to as fi xed-income instruments. This
term goes back to a time when bonds paid fi xed coupons each year. That is
3
4 Introduction to Bonds
no longer necessarily the case. Asset-backed bonds, for instance, are issued
in a number of tranches—related securities from the same issuer—each of
which pays a different fi xed or fl oating coupon. Nevertheless, this is still
commonly referred to as the fi xed-income market.
In the past bond analysis was frequently limited to calculating gross
redemption yield, or yield to maturity. Today basic bond math involves
different concepts and calculations. These are described in several of the
references for chapter 3, such as Ingersoll (1987), Shiller (1990), Neftci
(1996), Jarrow (1996), Van Deventer (1997), and Sundaresan (1997).
This chapter reviews the basic elements. Bond pricing, together with the
academic approach to it and a review of the term structure of interest rates,
are discussed in depth in chapter 3.
In the analysis that follows, bonds are assumed to be default-free. This
means there is no possibility that the interest payments and principal re-
payment will not be made. Such an assumption is entirely reasonable for
government bonds such as U.S. Treasuries and U.K. gilt-edged securities.
It is less so when you are dealing with the debt of corporate and lower-
rated sovereign borrowers. The valuation and analysis of bonds carrying
default risk, however, are based on those of default-free government secu-
rities. Essentially, the yield investors demand from borrowers whose credit
standing is not risk-free is the yield on government securities plus some
credit risk premium.
The Time Value of Money
Bond prices are expressed “per 100 nominal”—that is, as a percentage
of the bond’s face value. (The convention in certain markets is to quote
a price per 1,000 nominal, but this is rare.) For example, if the price of
a U.S. dollar–denominated bond is quoted as 98.00, this means that for
every $100 of the bond’s face value, a buyer would pay $98. The principles
of pricing in the bond market are the same as those in other fi nancial mar-
kets: the price of a fi nancial instrument is equal to the sum of the present
values of all the future cash fl ows from the instrument. The interest rate
used to derive the present value of the cash fl ows, known as the discount
rate, is key, since it refl ects where the bond is trading and how its return is
perceived by the market. All the factors that identify the bond—including
the nature of the issuer, the maturity date, the coupon, and the currency
in which it was issued—infl uence the bond’s discount rate. Comparable
bonds have similar discount rates. The following sections explain the tra-
ditional approach to bond pricing for plain vanilla instruments, making
certain assumptions to keep the analysis simple. After that, a more formal
analysis is presented.