Fixed Income Mathematics Analytical and Statistical Techniques

ISBN-10: 007146073X

ISBN-13: 9780071460736

Edition: 4th 2006 (Revised)

Authors: Frank J. Fabozzi
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Description: Despite their conservative nature, fixed income instruments are among the investment industry's most complex and potentially risky investments. This is a professional text for understanding the concepts and evaluative methodologies for bonds, mortgage-backed securities and other fixed income instruments.

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Book details

List price: $90.00
Edition: 4th
Copyright year: 2006
Publisher: McGraw-Hill Companies, The
Publication date: 1/6/2006
Binding: Hardcover
Pages: 600
Size: 6.50" wide x 9.50" long x 2.25" tall
Weight: 2.662
Language: English

Douglas J. Lucas is Executive Director and Head of CDO Research at UBS. He is also Chairman of The Bond Market Association's CDO Research Committee and ranked top three in CDO research in the Institutional Investor's fixed income analyst survey. Lucas has been involved in the CDO market for nearly two decades, having developed Moody's rating methodology for CDOs in 1989.LAURIE S. GOODMAN, PhD, is Managing Director and co-Head of Global Fixed Income Research at UBS. She manages U.S. Securitized Products and Treasury/Agency/Derivatives Research. Goodman has worked on Wall Street for over twenty years and is well regarded by the investor community, having won more #1 slots on the Institutional Investor All-American Fixed Income Team than any other analyst.FRANK J. FABOZZI, PhD, CFA, CPA, is an Adjunct Professor of Finance and Becton Fellow at Yale University's School of Management and a Fellow of the International Center for Finance. Fabozzi is the Editor of the Journal of Portfolio Management.

Preface
Acknowledgments
Introduction
Overview of the Book
Overview of Fixed Income Securities and Derivatives
General Features of Bonds
Bonds
Securitized Products
Preferred Stock
Interest-Rate Derivatives
Credit Derivatives
Summary
Time Value of Money
Future Value
Future Value of an Investment
Future Value of an Ordinary Annuity
Summary
Present Value
Present Value of a Single Amount to Be Received in the Future
Present Value for a Fractional Period
Properties of Present Value
Present Value of a Series of Future Values
Present Value of an Ordinary Annuity
Present Value When the Frequency Is More Than Once Per Year
Pricing Any Financial Instrument
Summary
Continuous Compounding
Yield (Internal Rate of Return)
Computing the Yield on Any Investment
Yield Calculation When There Is Only One Cash Flow
Annualizing Yields
Summary
Bond Pricing for Option-Free Bonds and Conventional Yield Measures
The Price of a Bond
Determining the Cash Flows
Determining the Required Yield
Pricing a Bond
Relationship between Required Yield and Price at a Given Time
Relationships among Coupon Rate, Required Yield, and Price
Time Path of a Bond
Analysis of Bond Price Changes
The Price of a Zero-Coupon Bond
Price Quotations
Determining the Price When the Settlement Date Falls between Coupon Periods
Price Buyer Pays and Price Quotes
Tax Treatment of Original-Issue Discount Coupon
Summary
Conventional Yield and Spread Measures for Bonds
Current Yield
Yield to Maturity
Yield to Call
Yield to Put
Yield to Worst
Portfolio Yield
Yield Spread Measures
Summary
The Yield Curve, Spot Rate Curve, and Forward Rates
A Bond is a Package of Zero-Coupon Instruments
The Yield Curve
The Spot Rate Curve
Pricing a Bond
Drawback of Traditional Yield Spread Analysis
Forward Rates
Summary
Return Analysis
Potential Sources of Dollar Return
Potential Sources of Dollar Return
Conventional Measures and the Three Potential Sources of a Bond's Dollar Return
Computation of the Interest-on-Interest Component of a Bond's Dollar Return
Bond Characteristics That Affect the Importance of the Interest-on-Interest Component
Tax Considerations
Summary and Investment Implications
Total Return
Another Look at the Drawbacks of the Yield to Maturity and Yield to Call
Computing the Total Return for a Bond Held to Maturity
Computing the Total Return for a Bond to Be Sold Prior to Maturity
Analyzing Callable Bonds With the Total Return
After-Tax Total Return to Maturity
Scenario Analysis
Application to Cheapest to Deliver for Futures Contract
Summary and Implications
Measuring Historical Performance
Portfolio Period Return
Averaging Subperiod Returns
Annualizing Returns
CFA Institute Performance Presentation Standards
Summary
Price Volatility for Option-Free Bonds
Price Volatility of Properties of Option-Free Bonds
A Closer Look at the Price/Yield Relationship for Option-Free Bonds
The Price Volatility Characteristics of Option-Free Bonds
Characteristics of a Bond That Affect Its Price Volatility
Measuring Price Volatility Using the Price Value of a Basis Point
Summary
Duration as a Measure of Price Volatility
Macaulay Duration
Link between Duration and Bond Price Volatility
Portfolio Duration
Approximating Duration
Applications
Spread Duration
Total Risk
Final Note on Duration
Summary
Combining Duration and Convexity to Measure Price Volatility
Estimating Price with Duration: A Graphical Depiction
Measuring Convexity
Percentage Price Change Due to Convexity
Percentage Price Change Due to Duration and Convexity
Convexity as a Measure of the Change in Dollar Duration
Summary of Properties of Convexity
Value of Convexity
Approximating Convexity: Effective Convexity
Summary
Duration and the Yield Curve
Duration and Nonparallel Yield-Curve Shifts
Types of Yield-Curve Shifts and Approaches to Measuring Yield-Curve Risk
Key Rate Durations
Level, Slope, and Curvature Durations
Yield-Curve Reshaping Durations
Summary
Analyzing Bonds With Embedded Options
Interest-Rate Models
Measuring Changes in Interest Rates
Historical Movements in Interest Rates
Arbitrage-Free versus Equilibrium Interest-Rate Models
One-Factor versus Multifactor Models
One-Factor Models: Normal versus Lognormal
Applying the Arbitrage-Free Interest-Rate Model
Summary
Call Options: Investment and Price Characteristics
What Is an Option?
Payoffs from Buying and Selling Options
The Intrinsic Value and Time Value of an Option
The Option Price
Sensitivity of the Theoretical Call Option Price to Changes in Factors
Duration of an Option
Summary
Valuation and Price Volatility of Bonds with Embedded Options
Price/Yield Relationship for a Callable Bond
The Components of a Bond with an Embedded Option
Traditional Valuation Methodology
Lattice Model for Valuing Bonds with Embedded Options
Option-Adjusted Spread
Price Volatility of Bonds with Embedded Options
Summary
Credit Risk
Credit Risk Concepts and Measures for Corporate Bonds
Types of Credit Risk
Rating Transition Table
Measuring Default Rates
Recovery Rate and Loss Given Default
Approaches to Credit Risk Modeling
Financial Ratios Used in Traditional Credit Analysis
Analyzing Securitized Products
Measures Used for Securitized Products
Structured Finance Transactions and Securitization
Illustration of a Securitization
Amortizing versus Nonamortizing Assets
Information Used in the Underwriting Process
Description of the Pool of Assets
Prepayment Measures
Defaults and Delinquencies
Summary
Description of Pool of Assets for CSFB Manufactured Housing Pass-Through Certificates, Series 2002-MH3 at the Cut-Off Date
Composition of the Receivables Pool for Toyota Auto Receivables 1996-A Grantor Trust $722,335,000 6.30% Asset Backed Certificates, Class A
Composition and Historical Performance of the Sears Portfolio for Sears Credit Account Master Trust II
Cash Flow Characteristics of Amortizing Loans
Residential Fixed-Rate, Level-Payment, Fully Amortizing Mortgage Loans
Residential Adjustable-Rate Mortgages
Other Loan Types
Cash Flow Characteristics of Mortgage-Backed Securities
The Prepayment Option and the Cash Flow
Overview of Agency Mortgage-Backed Securities
Cash Flow for an Agency CMO and Stripped MBS
Cash Flow for Credit-Sensitive MBS
Summary
Prepayment Models for Mortgage-Backed Securities
Agency Prepayment Models
Nonagency MBS Prepayment Models
Summary
Basics of MBS Structuring
Overview of Structuring
Structuring for Agency CMOs
Agency Mortgage Strips
Credit-Sensitive CMOs
Summary
Analysis of Agency Mortgage-Backed Securities
Static Cash Flow Model
Monte Carlo Simulation Model
Market-Based Approaches to Duration Estimation for Agency MBS
Total Return
General Approach to ABS Valuation
Summary
Statistical and Optimization Techniques
Basics of Probability Theory and Statistics
Basic Concepts in Probability Theory
Basic Rules of Probability Theory
Random Variable and Probability Distribution
Discrete versus Continuous Probability Distribution
Describing a Probability Distribution Function
Discrete Probability Distributions Used in Credit Risk Modeling
Continuous Probability Distributions
Two Applications to Risk Measurement
Summary
Regression Analysis
The Simple Linear Regression Model
Multiple Linear Regression Model
Nonlinear Regressions
Applications of Regression Analysis
Summary
Statistical Techniques for Credit Scoring and Risk Factor Identification
Statistical Techniques for Credit Scoring Models
Principal Component Analysis
Summary
Tracking Error and Multifactor Risk Models
Tracking Error
Multifactor Risk Models
Summary
Simulation
Monte Carlo Simulation
Steps for Monte Carlo Simulation
Illustration of the Steps of Monte Carlo Simulation
Application to a Mortgage-Backed Securities Portfolio
Summary
Optimization Models
Mathematical Programming
Types of Mathematical Programming Models
Applications
Summary
Index
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