Fixed Income Securities: Valuation, Risk, and Risk Management

841 Pages·2010·7.04 MB·English

by  Pietro Veronesi

Fixed Income
Securities
VALUATION, RISK, AND RISK MANAGEMENT
Pietro Veronesi
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FIXED INCOME SECURITIES
Valuation, Risk, and Risk Management
Pietro Veronesi
UniversityofChicago
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LibraryofCongressCataloging-in-PublicationData:
Veronesi,Pietro.
Fixedincomesecurities:valuation,risk,andriskmanagement/PietroVeronesi.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-10910-6(cloth)
1. Fixed-incomesecurities. 2. Riskmanagement. I. Title.
HG4650.V472010
658.15(cid:2)5–dc22
2009043712
10 9 8 7 6 5 4 3 2 1
To Tommaso
Gabriele,
Sofia,
and Micaela
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CONTENTS
Preface xix
Acknowledgments xxxiii
PART I BASICS
1 ANINTRODUCTIONTOFIXEDINCOMEMARKETS 3
1.1 Introduction 3
1.1.1 TheComplexityofFixedIncomeMarkets 6
1.1.2 NoArbitrageandtheLawofOnePrice 7
1.2 TheGovernmentDebtMarkets 9
1.2.1 ZeroCouponBonds 11
1.2.2 FloatingRateCouponBonds 11
1.2.3 TheMunicipalDebtMarket 14
1.3 TheMoneyMarket 14
1.3.1 FederalFundsRate 14
1.3.2 EurodollarRate 14
1.3.3 LIBOR 14
1.4 TheRepoMarket 15
1.4.1 GeneralCollateralRateandSpecialRepos 16
1.4.2 WhatiftheT-bondIsNotDelivered? 18
1.5 TheMortgageBackedSecuritiesMarketandAsset-BackedSecurities
Market 21
v
vi CONTENTS
1.6 TheDerivativesMarket 23
1.6.1 Swaps 23
1.6.2 FuturesandForwards 25
1.6.3 Options 25
1.7 RoadmapofFutureChapters 26
1.8 Summary 28
2 BASICSOFFIXEDINCOMESECURITIES 29
2.1 DiscountFactors 29
2.1.1 DiscountFactorsacrossMaturities 30
2.1.2 DiscountFactorsoverTime 31
2.2 InterestRates 32
2.2.1 DiscountFactors,InterestRates,andCompounding
Frequencies 34
2.2.2 TheRelationbetweenDiscountsFactorsand
InterestRates 38
2.3 TheTermStructureofInterestRates 38
2.3.1 TheTermStructureofInterestRatesoverTime 40
2.4 CouponBonds 42
2.4.1 FromZeroCouponBondstoCouponBonds 43
2.4.2 FromCouponBondstoZeroCouponBonds 45
2.4.3 ExpectedReturnandtheYieldtoMaturity 47
2.4.4 QuotingConventions 50
2.5 FloatingRateBonds 52
2.5.1 ThePricingofFloatingRateBonds 52
2.5.2 Complications 54
2.6 Summary 57
2.7 Exercises 57
2.8 CaseStudy: OrangeCountyInverseFloaters 61
2.8.1 Decomposing Inverse Floaters into a Portfolio of Basic
Securities 61
2.8.2 CalculatingtheTermStructureofInterestRatesfromCoupon
Bonds 62
2.8.3 CalculatingthePriceoftheInverseFloater 62
2.8.4 LeveragedInverseFloaters 64
2.9 Appendix: Extracting the Discount Factors Z(0,T) from Coupon
Bonds 65
2.9.1 BootstrapAgain 66
2.9.2 Regressions 67
2.9.3 CurveFitting 67
2.9.4 CurveFittingwithSplines 70
CONTENTS vii
3 BASICSOFINTERESTRATERISKMANAGEMENT 73
3.1 TheVariationinInterestRates 73
3.1.1 TheSavingsandLoanDebacle 75
3.1.2 TheBankruptcyofOrangeCounty 75
3.2 Duration 75
3.2.1 DurationofaZeroCouponBond 77
3.2.2 DurationofaPortfolio 78
3.2.3 DurationofaCouponBond 79
3.2.4 DurationandAverageTimeofCashFlowPayments 80
3.2.5 PropertiesofDuration 82
3.2.6 TraditionalDefinitionsofDuration 83
3.2.7 TheDurationofZeroInvestmentPortfolios: DollarDuration 84
3.2.8 DurationandValue-at-Risk 86
3.2.9 DurationandExpectedShortfall 89
3.3 InterestRateRiskManagement 90
3.3.1 CashFlowMatchingandImmunization 91
3.3.2 ImmunizationversusSimplerInvestmentStrategies 93
3.3.3 WhyDoestheImmunizationStrategyWork? 96
3.4 Asset-LiabilityManagement 97
3.5 Summary 98
3.6 Exercises 99
3.7 CaseStudy: The1994BankruptcyofOrangeCounty 103
3.7.1 Benchmark: WhatifOrangeCountywasInvestedinZero
CouponBondsOnly? 104
3.7.2 TheRiskinLeverage 105
3.7.3 TheRiskinInverseFloaters 105
3.7.4 TheRiskinLeveragedInverseFloaters 106
3.7.5 WhatCanWeInferabouttheOrangeCountyPortfolio? 107
3.7.6 Conclusion 108
3.8 CaseAnalysis: TheEx-AnteRiskinOrangeCounty’sPortfolio 108
3.8.1 TheImportanceoftheSamplingPeriod 109
3.8.2 Conclusion 110
3.9 Appendix: ExpectedShortfallundertheNormalDistribution 111
4 BASICREFINEMENTSININTERESTRATERISKMANAGEMENT 113
4.1 Convexity 113
4.1.1 TheConvexityofZeroCouponBonds 116
4.1.2 TheConvexityofaPortfolioofSecurities 118
4.1.3 TheConvexityofaCouponBond 118
4.1.4 PositiveConvexity: GoodNewsforAverageReturns 120
4.1.5 ACommonPitfall 121
viii CONTENTS
4.1.6 ConvexityandRiskManagement 122
4.1.7 ConvexityTradingandthePassageofTime 126
4.2 SlopeandCurvature 127
4.2.1 ImplicationsforRiskManagement 129
4.2.2 FactorModelsandFactorNeutrality 130
4.2.3 FactorDuration 132
4.2.4 FactorNeutrality 134
4.2.5 EstimationoftheFactorModel 136
4.3 Summary 137
4.4 Exercises 138
4.5 CaseStudy: FactorStructureinOrangeCounty’sPortfolio 142
4.5.1 FactorEstimation 142
4.5.2 FactorDurationoftheOrangeCountyPortfolio 142
4.5.3 The Value-at-Risk of the Orange County Portfolio with
MultipleFactors 144
4.6 Appendix: PrincipalComponentAnalysis 145
4.6.1 BenefitsfromPCA 149
4.6.2 TheImplementationofPCA 150
5 INTERESTRATEDERIVATIVES:FORWARDSANDSWAPS 153
5.1 ForwardRatesandForwardDiscountFactors 154
5.1.1 ForwardRatesbyNoArbitrage 157
5.1.2 TheForwardCurve 158
5.1.3 ExtractingtheSpotRateCurvefromForwardRates 161
5.2 ForwardRateAgreements 162
5.2.1 TheValueofaForwardRateAgreement 164
5.3 ForwardContracts 167
5.3.1 ANoArbitrageArgument 169
5.3.2 ForwardContractsonTreasuryBonds 170
5.3.3 TheValueofaForwardContract 171
5.4 InterestRateSwaps 171
5.4.1 TheValueofaSwap 175
5.4.2 TheSwapRate 175
5.4.3 TheSwapCurve 176
5.4.4 TheLIBORYieldCurveandtheSwapSpread 178
5.4.5 TheForwardSwapContractandtheForwardSwapRate 179
5.4.6 PaymentFrequencyandDayCountConventions 181
5.5 InterestRateRiskManagementusingDerivativeSecurities 182
5.6 Summary 184
5.7 Exercises 184
5.8 CaseStudy: PiVeCapitalSwapSpreadTrades 189
5.8.1 SettingUptheTrade 191