book

Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Name: Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools
Author: Frank J. Fabozzi
ISBN: 9780470078167

by Frank J. Fabozzi

August 2008

Beginner

896 pages

44h 17m

English

Wiley

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Copyright
About the Editor
Contributors
Preface
Guide to the Handbook of Finance
1. Risk Management
1. Risk and the French Connection
1.1. BLAISE PASCAL, THE NEUROTIC GENIUS1.2. GAMBLING INTO MATHEMATICS1.3. THE MAGIC OF THE MAGIC TRIANGLE1.4. THE MORAL AND THE MORALS OF THE STORY1.5. PASCAL'S WAGER1.6. THE ART OF THINKING1.7. SUMMARY
REFERENCES
2. Risk: Traditional Finance versus Behavioral Finance
2.1. WHAT IS RISK?2.2. THE DIFFERENT MEANINGS OF RISK2.3. WHAT IS THE DIFFERENCE BETWEEN RISK AND UNCERTAINTY?2.4. THE FINANCIAL PERSPECTIVE OF RISK FROM TWO SCHOOLS OF ACADEMIC THOUGHT2.5. WHAT IS TRADITIONAL FINANCE?2.5.1. The Basic Concepts of the Traditional Finance Perspective of Risk2.5.2. Modern Portfolio Theory2.5.3. Measures of Dispersion: Standard Deviation/Variance versus Semivariance2.5.4. The Capital Asset Pricing Model2.5.5. The "Great Beta Debate" in Academic Finance2.5.6. The Basic Viewpoint of Traditional Finance Researchers: The Objective (Quantitative) Nature of Risk2.6. WHAT IS BEHA VIORAL FINANCE?2.6.1. The Behavioral Finance Viewpoint of Risk2.6.2. The Basic Viewpoint of Behavioral Finance Researchers: The Subjective (Qualitative) Nature of Risk2.6.3. The Behavioral Finance Perspective: The Inverse (Negative) Relationship between Perceived Risk and Return2.7. SUMMARY2.8. ACKNOWLEDGMENTS
REFERENCES

3. Overview of Risk Management and Alternative Risk Transfer
3.1. RISK AND RETURN3.2. ACTIVE RISK MANAGEMENT3.2.1. Risk Management Processes3.2.2. Risk Management Techniques3.2.3. General Risk Management Considerations3.3. RISK CONCEPTS3.3.1. Expected Value and Variance3.3.2. Risk Aversion3.3.3. Risk Transfer and the Insurance Mechanism3.3.4. Diversification and Risk Pooling3.3.5. Hedging3.3.6. Moral Hazard, Adverse Selection, and Basis Risk3.3.7. Noninsurance Transfers3.4. OVERVIEW OF ART3.4.1. ART Background and Trends3.4.2. Product and Market Convergence
REFERENCES
4. Risk and Risk Management
4.1. FINANCIAL VERSUS NONFINANCIAL RISKS4.1.1. Financial Risks4.1.1.1. Market Risk4.1.1.2. Funding Risk4.1.1.3. Market Liquidity Risk4.1.1.4. Credit Risk4.1.1.5. Legal Risk4.1.2. Perils, Accidents, and Hazards4.1.2.1. Production Perils and Business Continuity Risks4.1.2.2. Operational Perils4.2. CORE VERSUS NONCORE RISKS4.3. RISK MANAGEMENT ALTERNATIVES4.3.1. Risk Retention and Risk Finance4.3.1.1. Funded and Unfunded Retentions4.3.1.2. Preloss versus Postloss Funding4.3.2. Risk Neutralization4.3.2.1. Risk Reduction, Prevention, and Control4.3.2.2. Risk Consolidation4.3.3. Risk Transfer4.3.3.1. Counterparties to Risk Transfer Agreements4.3.3.2. Types of Risk Transfer4.3.3.3. Limitation of Liability4.3.3.4. Funded versus Unfunded Risk Transfer Solutions4.4. SUMMARY
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5. Risk Management for Asset Management Firms
5.1. IMPORTANCE OF CLIENT RISK REPORTING5.2. RISK MANAGEMENT IN DETAIL5.2.1. Value at Risk5.2.1.1. Style VaR and Cornish-Fisher5.2.1.2. Incremental VaR5.2.1.3. Beyond VaR5.2.2. Factor Models and Risk Management5.2.2.1. Explicit Factor Models5.2.2.2. Implicit Factor Models5.2.2.3. Hybrid or Multi-Index Model5.2.3. Growing Importance of the Compliance Function5.2.4. Credit Risk Approaches5.2.4.1. Merton Model5.2.4.2. Reduced-Form Model5.3. SUMMARY
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6. Catastrophe and Risk
6.1. NATURE OF CATASTROPHE6.1.1. Definition6.1.2. Frequency6.1.3. Vulnerability6.1.4. Measuring Severity6.2. SCOPE OF IMPACT6.3. CATASTROPHE AND THE RISK MANAGEMENT FRAMEWORK6.4. SUMMARY
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7. Overview of Enterprise Risk Management
7.1. THE BENEFITS OF ERM7.2. THE CHIEF RISK OFFICER7.2.1. The Role of the CRO7.2.2. The Ideal CRO7.3. COMPONENTS OF ERM7.3.1. Corporate Governance7.3.2. Line Management7.3.3. Portfolio Management7.3.4. Risk Transfer7.3.5. Risk Analytics7.3.6. Data and Technology Resources7.3.7. Stakeholder Management7.4. SUMMARY
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8. Model Risk
8.1. MODELS AND MODEL RISK8.2. SOURCES OF MODEL RISK8.2.1. Incorrect Model Specification8.2.2. Incorrect Model Application8.2.3. Implementation Risk8.2.4. Endogenous Model Risk8.2.5. Other Sources of Model Risk8.3. MANAGING MODEL RISK8.3.1. Some Guidelines for Risk Managers8.3.2. Some Institutional Guidelines8.4. SUMMARY
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9. Back-Testing Market Risk Models
9.1. STATISTICAL BACK-TESTING9.2. EXCEEDANCE-BASED STATISTICAL APPROACHES9.2.1. Binomial (Kupiec) Approach9.2.2. A Normal Approximation9.2.3. Tests of Independence9.2.4. Conditional Testing (Christoffersen) Approach9.2.5. Strengths and Limitations of Exceedance-Based Approaches9.3. STATISTICAL BACK-TESTING OF VaRs AT MULTIPLE CONFIDENCE LEVELS9.3.1. Testing Uniformity9.3.2. Applying the Berkowitz Transformation and Testing for Standard Normality9.3.3. Tests Applied to Truncated Distributions9.4. USING BACK-TESTS FOR DIAGNOSTIC PURPOSES9.5. RANKING ALTERNATIVE MODELS9.6. SUMMARY
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10. Risk Measures and Portfolio Selection
10.1. DESIRABLE FEATURES OF INVESTMENT RISK MEASURES10.1.1. Basic Features of Investment Risk Measures10.1.2. Intertemporal Dependence and Correlation with Other Sources of Risk10.2. ALTERNATIVE RISK MEASURES FOR PORTFOLIO SELECTION10.3. DISPERSION MEASURES10.3.1. Mean Standard Deviation10.3.2. Mean Absolute Deviation10.3.3. Mean Absolute Moment10.3.4. Gini Index of Dissimilarity10.3.5. Mean Entropy10.3.6. Mean Colog10.4. SAFETY-FIRST RISK MEASURES10.4.1. Classical Safety First10.4.2. Value at Risk10.4.3. Conditional Value at Risk/Expected Tail Loss10.4.4. MiniMax10.4.5. Lower Partial Moment10.4.6. Power Conditional Value at Risk10.5. SUMMARY
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11. Statistical Models of Operational Loss
11.1. OPERATIONAL RISKS11.1.1. Definitions of Operational Risks11.1.2. Frequency and Severity11.1.3. Probability-Impact Diagrams11.1.4. Data Considerations11.1.4.1. Scorecards11.1.4.2. External Data11.2. BAYESIAN ESTIMATION11.2.1. Bayesian Estimation of Loss Severity Parameters11.2.1.1. Estimating the Mean and Standard Deviation of a Loss Severity Distribution11.2.1.2. Bayesian Estimation of Loss Probability11.2.1.3. Estimating the Loss Probability Using Internal Data Combined with (a) External Data and (b) Scorecard Data11.3. INTRODUCING THE ADVANCED MEASUREMENT APPROACHES11.3.1. A General Framework for the Advanced Measurement Approach11.3.2. Functional Forms for Loss Frequency and Severity Distributions11.3.3. Comments on Parameter Estimation11.3.4. Comments on the 99.9th Percentile11.4. ANALYTIC APPROXIMATIONS TO UNEXPECTED ANNUAL LOSS11.4.1. A Basic Formula for the ORR11.4.2. Calibration: Normal, Poisson, and Negative Binomial Frequencies11.4.2.1. ORR for Two Risk Types11.4.3. The ORR with Random Severity11.4.3.1. Comparison of Bayesian and Classical Estimates of ORR11.4.4. Inclusion of Insurance and the General Formula11.5. SIMULATING THE ANNUAL LOSS DISTRIBUTION11.5.1. Comparison of ORR from Analytic and Simulation Approximations11.6. AGGREGATION AND THE TOTAL LOSS DISTRIBUTION11.6.1. Aggregation of Analytic Approximations to the ORR11.6.2. Comments on Correlation and Dependency11.6.3. The Aggregation Algorithm11.6.4. Aggregation of Annual Loss Distributions under Different Dependency Assumptions11.6.5. Specifying Dependencies11.7. SUMMARY
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12. Risk Management in Freight Markets with Forwards and Options Contracts
12.1. FREIGHT FORWARD AGREEMENTS12.1.1. FFA Contract Specification12.1.2. Freight Options Market12.2. FREIGHT RATE DYNAMICS12.2.1. Freight Market Equilibrium Theory12.2.2. Modeling Forward Freight Rate Dynamics12.3. MODELING OF FREIGHT RATE DERIVATIVES12.3.1. Theoretical Framework12.3.2. Deriving FFA from Spot Price12.3.3. Freight Rate Options12.3.4. Spot Freight Rate Dynamics12.3.5. The Black Model for Freight Rate Options12.3.6. Lognormal Approximation for FFA Dynamics when t < T112.3.7. Exemplifications12.4. MONTE CARLO SIMULATION12.4.1. Option Pricing12.4.2. Empirical Results12.5. SUMMARY
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13. Fixed Income Risk Modeling
13.1. MODELING FRAMEWORK13.2. INTEREST RATE RISK13.3. SPREAD RISK—THE CONVENTIONAL APPROACH13.3.1. Swap Spread Factors13.4. DETAILED CREDIT SPREAD FACTORS13.4.1. Emerging Markets Spread Factors13.5. EMPIRICAL CREDIT RISK13.6. IMPLIED PREPAYMENT RISK13.7. IMPLIED VOLATILITY RISK13.8. SPECIFIC RISK13.9. CURRENCY RISK13.10. GLOBAL MODEL INTEGRATION13.10.1. Coping with Incomplete Return Series13.10.2. Global Integration13.11. THE MODEL IN ACTION13.12. SUMMARY
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14. Effective Duration and Convexity
14.1. EFFECTIVE DURATION AND EFFECTIVE CONVEXITY—AN EXAMPLE14.1.1. Straight Bond14.1.2. Callable Bond14.1.3. Putable Bond14.2. PUTTING IT ALL TOGETHER14.3. SUMMARY
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15. Duration Estimation for Bonds and Bond Portfolios
15.1. DURATION15.2. DOLLAR DURATION15.3. MODIFIED DURATION, MACAULAY DURATION, AND EFFECTIVE DURATION15.4. SPREAD DURATION FOR FIXED-RATE BONDS15.5. DURATION OF A FLOATING-RATE SECURITY15.6. PORTFOLIO DURATION15.6.1. Contribution to Portfolio Duration15.7. SUMMARY
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16. Yield Curve Risk Measures
16.1. DURATION, CONVEXITY, AND NONPARALLEL YIELD CURVE SHIFTS16.2. CASH-FLOW DISTRIBUTION ANALYSIS VERSUS A BENCHMARK16.3. KEY RATE DURATION16.4. SLOPE ELASTICITY MEASURE16.5. YIELD CURVE RESHAPING DURATION16.6. ANALYSIS OF LIKELY YIELD CURVE SHIFTS16.7. SUMMARY
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17. Improving Guidelines for Interest Rate and Credit Derivatives
17.1. FUTURES AND FORWARD CONTRACTS17.2. DURATION AND FUTURES POSITIONS17.3. GUIDELINES FOR INTEREST RATE FUTURES17.4. WHAT ABOUT LEVERAGE?17.5. APPLICATION TO OTHER INTEREST RATE DERIVATIVE INSTRUMENTS17.6. CREDIT DEFAULT SWAP GUIDELINES17.7. LOAN GUIDELINES17.8. SUMMARY
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18. Modeling Portfolio Credit Risk
18.1. QUANTIFYING PORTFOLIO CREDIT RISK18.1.1. Key Observations18.2. CREDIT RISK UNDER DEFAULT MODE18.2.1. Default Correlation18.2.2. Relationship to Loss Correlation18.2.3. Estimating Default Correlation18.2.4. Key Observations18.3. ESTIMATING ASSET RETURN CORRELATION18.3.1. Remarks18.3.2. Factor Models18.3.3. Approximate Asset Return Correlations18.4. CREDIT RISK UNDER MIGRATION MODE18.4.1. Computing Joint Migration Probabilities18.4.2. Computing Joint Credit Loss18.4.3. Portfolio Credit Risk18.5. SUMMARY
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19. The Basics of Cash-Market Hedging
19.1. THE MECHANICS OF HEDGING19.1.1. Identifying the Sources of Price Risk19.1.2. Balancing Risk and Return19.1.3. Choosing a Hedge Instrument19.1.4. Determining the Appropriate Hedge Position Using DVBP19.1.5. The Hedge Ratio19.1.6. Adjusted Hedge Ratio19.1.7. 10-Year Treasury-Note Equivalent19.2. HEDGING A NONCALLABLE BOND19.2.1. Yield-Spread Risk19.2.2. Cost of Carry19.2.2.1. Long Carry19.2.3. Short Carry19.2.4. Net Carry19.2.4.1. Negative Carry: A Treasury "Goes on Special"19.2.5. Incorporating Carry into a Hedge19.3. HEDGING SECURITIES WITH OFF-THE-RUN MATURITIES19.4. HEDGING OPTION-EMBEDDED BONDS19.4.1. Option-Embedded Corporate Bonds19.4.2. Mortgage Pass-Through Securities19.5. Hedging Considerations for Option-Embedded Notes19.6. SUMMARY
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20. Hedging Fixed Income Securities with Interest Rate Swaps
20.1. CHARACTERIZING INTEREST RATE SWAPS20.1.1. Swaps as Financed Bond Positions20.2. PRICING OF INTEREST RATE SWAPS20.2.1. Interest Rate Sensitivity of a Swap20.2.2. DVBP of a Swap20.2.3. Hedging with Interest Rate Swaps20.2.4. Hedge Ratio20.2.5. Corporate Bond Hedge20.2.6. Mortgage-Backed Security Hedge20.2.7. Swaps versus Other Hedge Instruments20.3. SUMMARY
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21. Yield Curve Risk Management
21.1. SINGLE-FACTOR YIELD CURVE MODELS21.1.1. Mathematical Framework21.1.2. Yield-to-Maturity Approach21.1.3. Other Single-Factor Models21.1.4. Single-Factor Yield Curve Management21.1.5. Single (and Multi)Factor Yield Curve Management Failure21.1.6. Single-Factor Yield Curve Management: The Time Dynamic21.1.7. Is There a "Best" Single-Factor Model?21.2. MULTIFACTOR YIELD CURVE MODELS21.2.1. Mathematical Framework21.2.2. Multifactor Models21.2.3. Relationships Between Single- and Multifactor Models21.2.4. Is There a "Best" Multifactor Model?21.2.5. Multifactor Yield Curve Management I21.2.6. Multifactor Yield Curve Management II21.2.7. Additional Considerations for Multifactor Models21.3. SUMMARY
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2. Interest Rate Modeling
22. The Concept and Measures of Interest Rate Volatility
22.1. BASIC DEFINITIONS AND FIRST FINDINGS22.2. A DIFFUSIVE MODEL FOR RANDOMNESS22.2.1. A Brief Excursion to Brownian Motion22.3. MEAN REVERSION AND MARKET STABILITY22.4. THE RATE DISTRIBUTION22.5. INTEREST RATE JUMPS22.6. SUMMARY22.7. ACKNOWLEDGMENTS
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23. Short-Rate Term Structure Models
23.1. THE CONCEPT OF SHORT-RATE MODELING23.1.1. The Arbitrage-Free Inter-Rate Relationship23.1.2. Consistency with the Initial Yield Curve23.1.3. Consistency with European Option Values23.2. SINGLE-FACTOR SHORT-RATE MODELS23.2.1. The Hull-White Model23.2.2. The Cox-Ingersoll-Ross Model23.2.3. The Squared Gaussian (SqG) Model (also known as Quadratic Model)23.2.4. The Black-Karasinski Model23.2.5. The Flesaker-Hughston Model23.2.6. Other Single-Factor Models23.2.7. Calibration Issues23.3. WHICH MODEL IS BETTER?23.3.1. Measuring Volatility Skew23.3.2. Using Volatility Index23.4. ADDING A SECOND FACTOR TO SHORT-RATE MODELS23.5. THE CONCEPT OF AFFINE MODELING23.5.1. The Jump-Diffusion Case23.6. SUMMARY23.7. ACKNOWLEDGMENTS
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3. Credit Risk Modeling and Analysis
24. Credit Risk
24.1. CREDIT DEFAULT RISK24.1.1. Credit Ratings24.1.2. Factors Considered in Rating Corporate Bond Issues24.1.3. Factors Considered in Rating Sovereign Debt24.1.4. Bankruptcy and Creditor Rights in the United States24.1.4.1. The Bankruptcy Process24.1.4.2. Absolute Priority: Theory and Practice24.1.5. Default and Recovery Rates24.1.6. Counterparty Risk24.2. CREDIT SPREAD RISK24.2.1. Fundamental Factors that Affect Credit Spreads24.2.1.1. Macro Fundamentals24.2.1.2. Micro Fundamentals24.3. DOWNGRADE RISK24.3.1. Rating Migration (Transition) Table24.4. CREDIT RISK TRANSFER MECHANISMS24.5. SUMMARY
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25. Credit Risk Modeling Using Structural Models
25.1. COMPLEXITIES IN CREDIT RISK MODELING25.2. OVERVIEW OF CURRENT MODELS25.3. THE BLACK-SCHOLES-MERTON MODEL25.3.1. Implications of BSM Model25.4. GESKE COMPOUND OPTION MODEL25.5. BARRIER STRUCTURAL MODELS25.6. ADVANTAGES AND DRAWBACKS OF STRUCTURAL MODELS25.7. SUMMARY
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26. Credit Risk Modeling Using Reduced-Form Models
26.1. THE POISSON PROCESS26.2. THE JARROW-TURNBULL MODEL26.3. THE CALIBRATION OF JARROW-TURNBULL MODEL26.3.1. Transition Matrix26.4. THE DUFFIE-SINGLETON MODEL26.5. GENERAL OBSERVATIONS ON REDUCED-FORM MODELS26.6. OTHER MODELS26.6.1. Spread-Based Models26.6.2. Hazard Models26.7. SUMMARY
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27. The Credit Analysis of Municipal Bonds
27.1. GENERAL OBLIGATION BONDS27.1.1. Debt Burden27.1.2. Budgetary Soundness27.1.3. Tax Burden27.1.4. Overall Economy27.2. RED FLAGS FOR THE GENERAL OBLIGATION BOND ANALYST27.3. REVENUE BONDS27.3.1. Limits of the Basic Security27.3.2. Flow-of-Funds Structure27.3.3. Rate, User Charge, or Dedicated Revenue and Tax Covenants27.3.4. The Priority of Pledged Revenue Claims27.3.5. Additional-Bonds Test27.3.6. Other Relevant Covenants and Issues27.4. ANALYSIS BY TYPE OF REVENUE BOND27.4.1. Airport Bonds27.4.2. Hospital Bonds27.4.3. Public Power Bonds27.4.4. Highway and Bridge Bonds27.4.5. Water and Sewer Bonds27.5. RED FLAGS FOR THE REVENUE BOND ANALYST27.6. SPECIAL SECURITY STRUCTURES27.6.1. Refunded Bonds27.6.1.1. Pure versus Mixed Escrow Funds27.6.1.2. Two Major Types of Refunded Bonds27.6.1.3. Determining the Safety of the Refunded Bonds27.6.2. Tax and Bond Anticipation Notes27.6.2.1. Reasons for Issuance27.6.2.2. Security behind Tax and Revenue Anticipation Notes27.6.2.3. Information Needed before Buying Tax or Revenue Anticipation Notes27.6.3. Lease-Rental Bonds27.6.4. Industrial Revenue Bonds27.6.5. FHA-Insured Mortgage Hospital Bonds27.6.5.1. What Are FHA Mortgage–Insured Hospital Bonds?27.6.5.2. What Is the Credit Risk?27.6.5.3. What Is the "Prudent Man" Evaluation Approach?27.7. SUMMARY
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4. Valuation
28. Introduction to Valuation
28.1. A PHILOSOPHICAL BASIS FOR VALUATION28.2. GENERALITIES ABOUT VALUATION28.2.1. Myth 1: Since Valuation Models Are Quantitative, Valuation Is Objective28.2.1.1. The Biases in Equity Research28.2.2. Myth 2: A Well-Researched and Well-Done Valuation Is Timeless28.2.3. Myth 3: A Good Valuation Provides a Precise Estimate of Value28.2.4. Myth 4: The More Quantitative a Model, the Better the Valuation28.2.5. Myth 5: To Make Money on Valuation, You Have to Assume that Markets Are Inefficient28.2.6. Myth 6: The Product of Valuation Is What Matters; The Process of Valuation Is Not Important28.3. THE ROLE OF VALUATION28.3.1. Valuation and Portfolio Management28.3.1.1. Fundamental Analysts28.3.1.2. Franchise Buyer28.3.1.3. Chartists28.3.1.4. Information Traders28.3.1.5. Market Timers28.3.1.6. Efficient Marketers28.3.2. Valuation in Acquisition Analysis28.3.3. Valuation in Corporate Finance28.4. SUMMARY
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29. Applied Equity Valuation: Discounted Cash Flow Method
29.1. DIVIDEND DISCOUNT MODEL29.1.1. Stocks that Currently Pay No Dividend29.2. CONSTANT-GROWTH DDM29.3. NONCONSTANT-GROWTH DDM29.4. INTUITION BEHIND THE DDM29.5. COMPLICATIONS IN IMPLEMENTING THE DDM IN THE REAL WORLD29.5.1. Expected Growth of Dividends29.5.2. Appropriate Expected Required Rate of Return29.5.3. Expected Future Selling Price29.5.4. Reinvestment of Profits/Internal Financing that Support Growth29.6. ADAPTING TO THE COMPLICATIONS: THE EARNINGS PER SHARE APPROACH29.7. FREE CASH FLOW DCF MODEL—TOTAL FIRM VALUATION29.7.1. Difference between Cash Flow and Free Cash Flow29.8. CALCULATING FCF29.9. USING THE CASH-FLOW STATEMENT TO ARRIVE AT OCF AND FCF29.9.1. Adjustments for Changes in Net Working Capital29.9.2. Adjustments for Investment in New Fixed Assets29.9.3. Adjustments for Depreciation and Other Noncash Expenses29.9.4. Financial Adjustments29.10. VALUING THE TOTAL FIRM29.11. ESTIMATING TOTAL FIRM VALUE USING THE FCF MODEL29.12. SUMMARY
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30. Applied Equity Valuation: Relative Valuation Method
30.1. THE BASIC PRINCIPLES OF RELATIVE VALUATION30.2. STEPS IN RELATIVE VALUATION30.2.1. Choose Similar (Comparable or Like-Kind) Firms30.2.2. Choose Bases for Multiples30.2.3. Determine an Appropriate Multiple30.2.4. Project Bases for the Valued Firm30.2.5. Value the Firm30.3. SELECTING COMPARABLE FIRMS TO ESTIMATE AVERAGE MULTIPLES30.4. CRITERIA MOST OFTEN USED FOR THE SELECTION OF COMPARABLE FIRMS30.4.1. Industry Classification30.4.2. Technology30.4.3. Clientele30.4.4. Size30.4.5. Risk Class30.5. DCF AND RV METHODS30.5.1. When DCF Valuation Works Best30.5.2. When RV Works Best30.5.3. The Link between RV and DCF30.5.4. Problems with Price/X Ratios (e.g., the P/E Ratio)30.5.5. The Need for Sensitivity Analysis in Both DCF and RV—"What If" and Simulation30.6. SUMMARY
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31. Dividend Discount Models
31.1. DIVIDEND MEASURES31.2. DIVIDENDS AND STOCK PRICES31.3. BASIC DIVIDEND DISCOUNT MODELS31.4. THE FINITE LIFE GENERAL DIVIDEND DISCOUNT MODEL31.4.1. Assuming a Constant Discount Rate31.4.2. Required Inputs31.4.3. Assessing Relative Value31.5. CONSTANT GROWTH DIVIDEND DISCOUNT MODEL31.6. MULTIPHASE DIVIDEND DISCOUNT MODELS31.6.1. Two-Stage Growth Model31.6.2. Three-Stage Growth Model31.7. STOCHASTIC DIVIDEND DISCOUNT MODELS31.7.1. Binomial Stochastic Model31.7.1.1. Binomial Additive Stochastic Model31.7.1.2. Binomial Geometric Stochastic Model31.7.2. Trinomial Stochastic Models31.7.2.1. Trinomial Additive Stochastic Model31.7.2.2. Trinomial Geometric Stochastic Model31.7.3. Applications of the Stochastic DDM31.7.3.1. Advantages of the Stochastic DDM31.8. EXPECTED RETURNS AND DIVIDEND DISCOUNT MODELS31.9. SUMMARY
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32. Equity Analysis Using Traditional and Value-Based Metrics
32.1. OVERVIEW OF TRADITIONAL METRICS32.1.1. Growth Rates32.1.2. Return on Equity and the Dupont Formula32.1.3. ROE and Leverage32.1.4. Financial Risk Considerations32.2. PRICE RELATIVES32.2.1. Stock Analysis Using Price Multiples32.2.2. Price Multiples: Comparables versus Forecasted Fundamentals32.2.3. Price Relatives Using Common Factors32.3. FUNDAMENTAL STOCK RETURN32.4. REQUIRED RETURN: THE MISSING LINK32.5. TRADITIONAL CAVEATS32.6. OVERVIEW OF VALUE-BASED METRICS32.6.1. Background32.6.2. Basic EVA32.6.3. EVA Spread32.6.4. Return on Capital Decomposition32.6.5. WACC Issues32.6.5.1. Target Capital Structure32.6.5.2. Estimating the Cost of Equity32.6.5.3. Cash-Flow Return on Investment32.6.6. Residual Income32.6.7. Role of EVA Momentum32.6.8. Valuation Considerations32.6.8.1. Identifying Good Stocks32.6.8.2. Residual Income Valuation32.6.9. VBM Caveats32.6.10. Case Study: Equity Analysis Template32.7. SUMMARY32.8. APPENDIX: CASE STUDY32.8.1. Coca-Cola: Integrated Traditional and VBM Analyses
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33. The Franchise Factor Approach to Firm Valuation
33.1. INTRODUCTION33.2. BACKGROUND33.2.1. Historical Data Observations33.3. KEY FINDINGS33.4. FORMULATION OF THE BASIC MODEL33.5. P/E MYOPIA: THE FALLACY OF STABLE P/Es33.5.1. P/E Orbits for High-Growth Stocks33.5.2. P/E Orbits for Low-Growth Stocks33.5.3. The Stable P/E33.5.4. Two-Phase P/E Orbits33.5.5. The Franchise Factor Model and P/E Orbits33.5.5.1. FV Growth, FV Decay, and FV Bubbles33.5.5.2. Franchise Valuation under Q-Type Competition33.5.5.3. Franchise Labor33.6. SUMMARY
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34. IPO Valuation
34.1. LITERATURE REVIEW ON IPO VALUATION34.2. ESTIMATION OF INTRINSIC IPO VALUE34.3. COMPARABLE FIRM METHOD TO ESTIMATING INTRINSIC VALUE34.3.1. Choosing Matching Firms34.3.2. Calculating Comparable Firm Multiples34.3.3. Empirical Evidence34.4. REGRESSION METHOD TO ESTIMATING INTRINSIC VALUE34.4.1. Independent Variables34.4.2. Empirical Evidence34.5. SUMMARY
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35. The Valuation of Private Firms
35.1. THE STANDARD OF VALUE35.2. WHAT IS BEING VALUED?35.3. VALUATION METRICS35.3.1. The Asset-Based Method35.3.2. The Income Method35.3.3. Market Method: The Method of Comparables35.4. THE RELATIONSHIP BETWEEN A FIRM'S STAGE OF BUSINESS DEVELOPMENT AND THE VALUATION APPROACH35.5. VALUING A PRIVATE FIRM35.5.1. Overview of Tentex and Defining Cash Flow for Valuation Purposes35.5.2. Compensation of Officers and Employee Family Members and Friends35.5.3. Discretionary Expenses35.5.4. The Fair Value of Tentex Based on Discounted Free Cash Flow to the Firm35.5.5. Valuing Tentex: Discounted Free Cash Flow35.5.6. Valuing Tentex Using Market Multiples35.6. THE COST OF CAPITAL35.6.1. The Cost of Equity35.6.2. The Cost of Debt35.7. DISCOUNT FOR LACK OF LIQUIDITY35.8. SUMMARY
REFERENCES
36. General Principles of Bond Valuation
36.1. GENERAL PRINCIPLES OF BOND VALUATION36.1.1. Estimating Cash Flows36.1.2. Determining the Appropriate Interest Rate or Rates36.1.3. Discounting the Expected Cash Flows36.1.4. Determining a Bond's Value36.1.4.1. Valuing a Zero-Coupon Bond36.1.4.2. Valuing a Bond between Coupon Payments36.1.5. The Price/Discount Rate Relationship36.1.6. Time Path of Bond36.2. ARBITRAGE-FREE BOND VALUATION36.2.1. Theoretical Spot Rates36.2.1.1. Par Rates36.2.1.2. Bootstrapping the Spot Rate Curve36.2.2. Valuation Using Treasury Spot Rates36.2.3. Reason for Using Treasury Spot Rates36.2.4. Stripping and Arbitrage-Free Valuation36.2.5. Credit Spreads and the Valuation of Non-Treasury Securities36.3. SUMMARY
REFERENCES
37. Yield Curves and Valuation Lattices
37.1. THE INTEREST RATE LATTICE37.1.1. Determining the Value at a Node37.2. CALIBRATING THE LATTICE37.3. USING THE LATTICE FOR VALUATION37.4. SUMMARY
REFERENCES
38. Using the Lattice Model to Value Bonds with Embedded Options, Floaters, Options, and Caps/Floors
38.1. FIXED-COUPON BONDS WITH EMBEDDED OPTIONS38.1.1. Valuing a Callable Bond38.1.2. Valuing a Putable Bond38.2. FLOATING-COUPON BONDS WITH EMBEDDED OPTIONS38.2.1. Valuing Capped Floating-Rate Bonds38.2.2. Callable Capped Floating-Rate Bonds38.3. VALUING CAPS AND FLOORS38.4. VALUATION OF TWO MORE EXOTIC STRUCTURES38.4.1. Valuing a Step-Up Callable Note38.4.2. Valuing a Range Note38.5. VALUING AN OPTION ON A BOND38.6. EXTENSIONS38.6.1. Option-Adjusted Spread38.6.2. Effective Duration and Effective Convexity38.7. SUMMARY
REFERENCES
39. Valuing Mortgage-Backed and Asset-Backed Securities
39.1. CASH-FLOW YIELD ANALYSIS39.2. ZERO-VOLATILITY SPREAD39.3. VALUATION USING MONTE CARLO SIMULATION AND OAS ANALYSIS39.3.1. Simulating Interest Rate Paths and Cash Flows39.3.2. Calculating the Present Value of a Bond Class for a Scenario Interest Rate Path39.3.3. Determining the Theoretical Value39.3.4. Option-Adjusted Spread39.3.5. Option Cost39.3.6. Simulated Average Life39.4. MEASURING INTEREST RISK39.4.1. Duration39.4.2. Convexity39.5. SUMMARY
REFERENCES
40. A Framework for Valuing Treasury Inflation-Protected Securities
40.1. REVIEW OF TIPS STRUCTURE40.2. ANALYSIS OF BREAKEVENS40.2.1. Extracting Inflation Expectations from Breakevens40.2.1.1. Convexity of TIPS and Nominal Rates40.2.1.2. Risk Premium40.2.1.3. Liquidity Premium40.2.1.4. Inflation Expectations40.3. SUMMARY
REFERENCES
41. Quantitative Models to Value Convertible Bonds
41.1. ANALYTICAL MODELS41.1.1. The Ingersoll Model41.2. NUMERICAL MODELS41.2.1. The Binomial Tree Model41.3. SUMMARY
REFERENCES
42. Introduction to the Pricing of Futures/Forwards and Options
42.1. PRICING OF FUTURES/FORWARD CONTRACTS42.1.1. Differences between Futures and Forward Contracts42.1.2. Basic Futures Pricing Model42.1.3. A Closer Look at the Theoretical Futures Price42.1.3.1. Interim Cash Flows42.1.3.2. Differences in Borrowing and Lending Rates42.1.3.3. Transaction Costs42.1.3.4. Short Selling42.1.3.5. Known Deliverable Asset and Settlement Date42.1.3.6. Deliverable Is a Basket of Securities42.1.3.7. Different Tax Treatment of Cash and Futures Transaction42.2. PRICING OF OPTIONS42.2.1. Basic Components of the Option Price42.2.1.1. Intrinsic Value42.2.1.2. Time Premium42.2.2. Put–Call Parity Relationship42.2.3. Factors that Influence the Option Price42.2.3.1. Market Price of the Underlying Asset42.2.3.2. Strike Price42.2.3.3. Time to Expiration of the Option42.2.3.4. Expected Volatility of the Underlying over the Life of the Option42.2.3.5. Short-Term, Risk-Free Interest Rate over the Life of the Option42.2.3.6. Anticipated Cash Payments on the Underlying over the Life of the Option42.2.4. Option Pricing Models42.3. SUMMARY
REFERENCES
43. Black-Scholes Option Pricing Model
43.1. MOTIVATION43.2. BLACK-SCHOLES FORMULA43.3. COMPUTING A CALL OPTION PRICE43.4. SENSITIVITY OF OPTION PRICE TO A CHANGE IN FACTORS: THE GREEKS43.4.1. Price of a Call Option Price and Price of the Underlying: Delta and Gamma43.4.2. The Call Option Price and Time to Expiration: Theta43.4.3. Option Price and Expected Volatility: Vega43.4.4. Call Option Price and Interest Rate: Rho43.4.5. The Greeks and Portfolio Applications43.5. COMPUTING A PUT OPTION PRICE43.6. ASSUMPTIONS UNDERLYING THE BLACK-SCHOLES MODEL AND BASIC EXTENSIONS43.6.1. Taxes and Transactions Costs43.6.2. Trading in Continuous Time, Short Selling, and Trading Arbitrary Fractions of Assets43.6.3. Variance of the Stock's Return43.6.4. Stochastic Process Generating Stock Prices43.6.5. Risk-Free Interest Rate43.7. BLACK-SCHOLES MODEL APPLIED TO THE PRICING OF OPTIONS ON BONDS: IMPORTANCE OF ASSUMPTIONS43.8. SUMMARY
REFERENCES
44. Valuing a Plain Vanilla Swap
44.1. CALCULATING SWAP PAYMENTS44.1.1. Calculating the Floating Payments44.1.1.1. The Eurodollar Futures Contract44.1.1.2. Determining Future Floating Payments44.1.2. Calculating the Fixed Payments44.1.3. Dealing with Swaps with a Varying Notional Principal44.2. COMPUTING THE PRESENT VALUE OF SWAP PAYMENTS AND DETERMINING THE SWAP FIXED RATE44.2.1. Calculating the Present Value of the Floating Payments44.2.2. Determination of the Swap Fixed Rate44.3. VALUING THE CASH FLOWS44.3.1. Swap Floating Payments When Rates Change44.3.2. Period Forward Rates and Forward Discount Factors after Rates Change44.3.3. Valuing a Swap after Rates Change44.4. SUMMARY
REFERENCES
45. Valuing Swaptions
45.1. LATTICE APPROACH TO VALUATION45.1.1. Binomial Interest Rate Lattice45.1.2. Determining the Value at a Node45.1.3. Constructing the Binomial Interest Rate Lattice45.1.4. Obtaining the Cash Flow at Each Node of the Lattice45.2. TYPES OF SWAPTIONS45.3. ROLE OF THE CUMULATIVE SWAP VALUATION LATTICE45.4. EXPIRATION VALUES AND THE SWAPTION VALUATION LATTICE45.5. APPLYING THE BACKWARD INDUCTION METHODOLOGY TO OBTAIN A SWAPTION'S VALUE45.6. FACTORS THAT AFFECT THE VALUE OF A SWAPTION45.6.1. Expiration of the Swaption45.6.2. Strike Rate45.6.3. Assumed Interest Rate Volatility45.6.4. Changes in the Term Structure45.7. SUMMARY
REFERENCES
46. Pricing Options on Interest Rate Instruments
46.1. MODELING THE TERM STRUCTURE AND BOND PRICES46.1.1. Short-Rate Models of Term Interest Rate Structure46.2. MODELING IN PRACTICE46.3. HJM METHODOLOGY46.4. BOND OPTION PRICING46.4.1. European Options on the Money Fund46.4.2. Options on Discount Bonds46.4.2.1. Example: Valuing a Zero-Coupon Bond Call Option with the Vasicek Model46.4.2.2. Example: Valuing a Zero-Coupon Bond Call Option with the Hull-White Model46.4.2.3. Example: Valuing a Zero-Coupon Bond Call Option with the CIR Model46.4.3. Options on Coupon-Paying Bonds46.4.3.1. Example: Valuing a Coupon-Bond Call Option with the Vasicek Model46.4.3.2. Example: Valuing a Coupon-Bond Call Option with the CIR Model46.4.4. Pricing Swaptions46.5. PRACTICAL CONSIDERATIONS46.6. SUMMARY
REFERENCES
47. Credit Default Swaps Valuation
47.1. DEFAULT SWAPS47.1.1. Illustration47.1.2. The Mechanics of Settlement47.2. CREDIT EVENTS47.2.1. ISDA Credit Event Definitions47.2.2. Restructuring Controversy47.2.3. Credit Events and Implementation of Default Swap Pricing Models47.3. PRICING CREDIT DEFAULT SWAPS BY STATIC REPLICATION47.4. PRICING OF A SINGLE-NAME CREDIT DEFAULT SWAP47.4.1. Survival Probability47.4.2. Valuation of a Credit Default Swap47.4.3. CDS Risk and Sensitivities47.4.4. Calibrating the Recovery Rate Assumption47.4.5. The Practicalities of Unwinding a Credit Default Swap47.5. SUMMARY
REFERENCES
48. The Valuation of Fixed Income Total Return Swaps
48.1. AN INTUITIVE APPROACH48.2. USING THE DUFFIE-SINGLETON MODEL48.3. THE FORWARD MEASURE48.4. SUMMARY
REFERENCES
49. Valuing Inflation Derivatives
49.1. INFLATION INDICES AND REAL RETURNS49.2. VALUING ZERO-COUPON INFLATION SWAPS49.3. CONSTRUCTING AN INFLATION CURVE49.3.1. Incorporating Seasonality Effects49.4. MARKING TO MARKET INFLATION SWAPS49.5. MANAGING INFLATION AND INTEREST RATE RISK49.5.1. Inflation PV0149.5.2. Nominal PV0149.6. MANAGING SEASONALITY RISK49.7. THE JARROW-YILDIRIM MODEL49.8. VALUATION OF PERIOD-ON-PERIOD INFLATION SWAPS49.9. VALUATION OF INFLATION INDEX OPTIONS49.10. VALUATION OF INFLATION OPTIONS49.11. VALUATION OF REAL RATE INFLATION SWAPTIONS49.12. VALUATION OF INFLATION-EQUITY HYBRID49.13. SUMMARY
REFERENCES
50. The Pricing and Economics of Commodity Futures
50.1. THE RELATIONSHIP BETWEEN FUTURES PRICES AND SPOT PRICES50.1.1. Financial Futures50.1.2. Currencies50.1.3. Commodity Futures50.2. ECONOMICS OF THE COMMODITY MARKETS: NORMAL BACKWARDATION VERSUS CONTANGO50.3. COMMODITY PRICES COMPARED TO FINANCIAL ASSET PRICES50.4. SUMMARY
REFERENCES
51. Introduction to Currency Option Pricing Models
51.1. BASIC PROPERTIES51.2. THEORETICAL VALUATION51.3. BLACK-SCHOLES MODEL51.4. EXAMPLES OF OTHER MODELS51.5. PRICING WITHOUT A COMPUTER MODEL51.5.1. Educated Guess51.6. THE PRICE OF AN OPTION51.6.1. Option Premium Profile51.6.1.1. Time Value and Intrinsic Value51.6.1.2. Time to Expiry51.6.1.3. Volatility51.6.1.4. Strike Price and Forward Rates51.6.1.5. Interest Rates51.6.1.6. American versus European51.7. THE GREEKS51.7.1. Delta51.7.2. Gamma51.7.3. Theta51.7.4. Vega51.7.5. Rho51.7.6. Beta and Omega51.8. SUMMARY
REFERENCES
52. Pricing Commercial Real Estate Derivatives
52.1. PRICING THE FORWARD CONTRACT52.2. PRICING A REAL ESTATE INDEX RETURN SWAP: EQUILIBRIUM ANALYSIS52.2.1. Numerical Example52.3. SUMMARY
REFERENCES
5. Mathematical Tools and Techniques for Financial Modeling and Analysis
53. Cash-Flow Analysis
53.1. DIFFICULTIES WITH MEASURING CASH FLOW53.2. CASH FLOWS AND THE STATEMENT OF CASH FLOWS53.3. FREE CASH FLOW53.4. CALCULATING FREE CASH FLOW53.5. NET FREE CASH FLOW53.6. USEFULNESS OF CASH FLOWS IN FINANCIAL ANALYSIS53.6.1. Ratio Analysis53.6.2. Using Cash-Flow Information53.7. SUMMARY
REFERENCES
54. Financial Ratio Analysis
54.1. RATIOS AND THEIR CLASSIFICATION54.2. RETURN-ON-INVESTMENT RATIOS54.2.1. Recap: Return-on-Investment Ratios54.2.2. DuPont System54.3. LIQUIDITY54.3.1. Operating Cycle54.3.2. Measures of Liquidity54.3.3. Recap: Liquidity Ratios54.4. PROFITABILITY RATIOS54.4.1. Recap: Profitability Ratios54.5. ACTIVITY RATIOS54.5.1. Inventory Management54.5.2. Accounts Receivable Management54.5.3. Overall Asset Management54.5.4. Recap: Activity Ratios54.6. FINANCIAL LEVERAGE RATIOS54.6.1. Component Percentage Ratios54.6.1.1. Book Value versus Market Value54.6.2. Coverage Ratios54.6.3. Recap: Financial Leverage Ratios54.7. COMMON-SIZE ANALYSIS54.8. USING FINANCIAL RATIO ANALYSIS54.9. SUMMARY
REFERENCES
55. Mathematics of Finance
55.1. THE IMPORTANCE OF THE TIME VALUE OF MONEY55.2. DETERMINING THE FUTURE VALUE55.2.1. Compounding More than One Time per Year55.2.2. Continuous Compounding55.2.3. Multiple Rates55.3. DETERMINING THE PRESENT VALUE55.4. DETERMINING THE UNKNOWN INTEREST RATE55.5. DETERMINING THE NUMBER OF COMPOUNDING PERIODS55.6. THE TIME VALUE OF A SERIES OF CASH FLOWS55.6.1. Shortcuts: Annuities55.7. VALUING CASH FLOWS WITH DIFFERENT TIME PATTERNS55.7.1. Valuing a Perpetual Stream of Cash Flows55.7.2. Valuing an Annuity Due55.7.3. Valuing a Deterred Annuity55.8. LOAN AMORTIZATION55.9. THE CALCULATION OF INTEREST RATES AND YIELDS55.9.1. Annual Percentage Rate versus Effective Annual Rate55.9.2. Yields on Investments55.10. SUMMARY
REFERENCES
56. Calculating Investment Returns
56.1. SINGLE-PERIOD RATE OF RETURN56.1.1. Components of Single-Period Returns56.1.2. Return on Investment56.2. TIME VALUE OF MONEY56.2.1. Returns That Take Time into Account56.3. PERFORMANCE OF THE INVESTOR: MONEY-WEIGHTED RETURNS56.3.1. Timing of Investor Decisions56.3.2. Timing of Investment Manager Decisions56.3.3. Segregating Investor and Manager Timing Decisions56.3.4. Internal Rate of Return56.3.5. Problems with the IRR56.3.6. Modified Dietz Return56.4. PERFORMANCE OF THE INVESTMENT MANAGER: TIME-WEIGHTED RETURNS56.4.1. Time-Weighted Return56.4.1.1. Divide the Period into Subperiods56.4.1.2. Calculate Subperiod Returns56.4.1.3. Calculate Multiple-Period Returns56.4.2. Estimating the Time-Weighted Return56.5. MULTIPLE-PERIOD RETURN CALCULATION56.5.1. Cumulative Returns56.5.2. Averaging Returns56.5.3. Geometric Mean Return56.5.4. Annualizing Returns56.6. SUMMARY
REFERENCES
57. Basic Data Description for Financial Modeling and Analysis
57.1. DATA TYPES57.1.1. Information Contained in the Data57.1.2. Data Levels and Scale57.1.3. Cross-Sectional Data and Time Series57.2. FREQUENCY DISTRIBUTIONS57.2.1. Sorting and Counting Data57.2.2. Formal Presentation of Frequency57.3. EMPIRICAL CUMULATIVE FREQUENCY DISTRIBUTION57.3.1. Accumulating Frequencies57.3.2. Formal Presentation of Cumulative Frequency Distributions57.4. DATA CLASSES57.4.1. Reasons for Classifying57.4.2. Formal Procedure of Classifying57.4.3. Example of Classing Procedures57.5. CUMULATIVE FREQUENCY DISTRIBUTIONS57.6. SUMMARY
REFERENCES
58. Elementary Statistics
58.1. POPULATION VERSUS SAMPLE58.1.1. Summary of the Statistical Method58.2. RANDOM VARIABLES58.2.1. Mean58.2.2. Variance and Standard Deviation58.2.3. Covariance and Correlation58.2.4. Semivariance and Semistandard Deviation58.2.5. Semicovariance and Semicorrelation58.2.6. Skewness58.2.7. Kurtosis58.3. PROPERTIES OF EXPECTATION OPERATORS58.4. ESTIMATION58.4.1. Estimator of Mean58.4.2. Estimator of Variance58.4.3. Estimator of Covariance and Correlation58.4.4. Estimator of Lower Semivariance58.4.5. Estimators of Semicovariance and Semicorrelation58.4.6. Estimator of Skewness58.4.7. Estimator of Kurtosis58.4.8. Illustration: Estimate of Mean, Variance, Standard Deviation, Skewness, and Excess Kurtosis of Monthly Stock Returns for IBM58.5. PROBABILITY DISTRIBUTIONS58.5.1. Normal Distribution58.5.1.1. Empirical Distribution58.5.1.2. Normal Distribution58.5.2. Chi-Square Distribution58.5.2.1. Tests for Normality58.5.3. t-Distribution58.5.3.1. Test for Zero Mean58.5.3.2. Test for Equivalence of Means58.5.3.3. Test for Equivalence of Means in a Paired Sample58.5.4. Type I and Type II Errors and the Power of a Test58.5.5. F-Distribution58.5.5.1. Test for Equivalence of Variances58.5.6. Test for Autocorrelation58.5.7. Central Limit Theorem58.6. SUMMARY
REFERENCES
A. DATA FOR ILLUSTRATION
B. Statistical Tables
59. Regression Analysis
59.1. THE CONCEPT OF DEPENDENCE59.2. REGRESSIONS AND LINEAR MODELS59.2.1. Case Where All Regressors Are Random Variables59.2.2. Linear Models and Linear Regressions59.2.3. Case Where Regressors Are Deterministic Variables59.3. ESTIMATION OF LINEAR REGRESSIONS59.3.1. Maximum Likelihood Estimates59.3.1.1. Generalization to Multiple Independent Variables59.3.2. Ordinary Least Squares Method59.4. SAMPLING DISTRIBUTIONS OF REGRESSIONS59.5. DETERMINING THE EXPLANATORY POWER OF A REGRESSION59.5.1. Coefficient of Determination59.5.2. Adjusted R259.5.3. Relation of R2 to Correlation Coefficient59.6. USING REGRESSION ANALYSIS IN FINANCE59.6.1. Characteristic Line for Common Stocks59.6.2. Characteristic Line for Mutual Funds59.6.3. Empirical Duration of Common Stock59.7. STEPWISE REGRESSION59.8. NONNORMALITY AND AUTOCORRELATION OF THE RESIDUALS59.8.1. Detecting Autocorrelation59.9. PITFALLS OF REGRESSIONS59.9.1. Spurious Regressions59.9.2. Collinearity59.9.3. Increasing the Number of Regressors59.10. SUMMARY59.11. ACKNOWLEDGMENTS
REFERENCES
60. ARCH/GARCH Models in Applied Financial Econometrics
60.1. REVIEW OF LINEAR REGRESSION AND AUTOREGRESSIVE MODELS60.2. ARCH/GARCH MODELS60.2.1. Application to Value at Risk60.3. WHY ARCH/GARCH?60.4. GENERALIZATIONS OF THE ARCH/GARCH MODELS60.4.1. Integration of First, Second, and Higher Moments60.4.2. Generalizations to High-Frequency Data60.4.3. Multivariate Extensions60.5. SUMMARAY
REFERENCES
61. Cointegration and Its Application in Finance
61.1. STATIONARY AND NONSTATIONARY VARIABLES AND COINTEGRATION61.2. TESTING FOR COINTEGRATION61.2.1. Engle-Granger Cointegration Tests61.3. EMPIRICAL ILLUSTRATION USING THE DIVIDEND GROWTH MODEL61.3.1. Johansen-Juselius Cointegration Tests61.4. TESTING OF THE DYNAMIC RELATIONSHIPS AMONG COUNTRY STOCK MARKETS61.5. SUMMARY
REFERENCES
62. Moving Average Models for Volatility and Correlation, and Covariance Matrices
62.1. BASIC PROPERTIES OF COVARIANCE AND CORRELATION MATRICES62.2. EQUALLY WEIGHTED AVERAGES62.2.1. Statistical Methodology62.2.2. Confidence Intervals for Variance and Volatility62.2.3. Standard Errors for Equally Weighted Average Estimators62.2.4. Equally Weighted Moving Average Covariance Matrices62.2.5. Case Study: Measuring the Volatility and Correlation of U.S Treasuries62.2.5.1. Decision 1: How Long a Historical Data Period Should Be Used?62.2.5.2. Decision 2: Which Frequency of Observations Should Be Used?62.2.5.3. Decision 3: Absolute versus Relative Measures62.2.6. Pitfalls of the Equally Weighted Moving Average Method62.2.7. Using Equally Weighted Moving Averages62.3. EXPONENTIALLY WEIGHTED MOVING AVERAGES62.3.1. Statistical Methodology62.3.2. Interpretation of λ62.3.3. Properties of the Estimates62.3.4. The EWMA Forecasting Model62.3.5. Standard Errors for EWMA Forecasts62.3.6. The RiskMetricsTM Methodology62.4. SUMMARY
REFERENCES
63. Introduction to Stochastic Processes
63.1. STOCHASTIC PROCESSES IN DISCRETE TIME63.1.1. Autoregressive Moving Average Models63.1.1.1. White Noise63.1.1.2. Autoregressive Processes63.1.1.3. Moving Average Processes63.1.1.4. Autoregressive Moving Average Processes with Exogenous Variables63.1.2. Summary of Properties of Linear Time Series Models63.2. ARCH and GARCH Models63.3. STOCHASTIC PROCESSES IN CONTINUOUS TIME63.3.1. The Poisson Process63.3.1.1. Transforms of the Poisson Process63.3.2. Brownian Motion63.3.2.1. Transforms of Brownian Motion63.3.2.2. Fractional Brownian Motion63.3.3. Stochastic Differential Equations63.3.4. Lévy Processes63.3.4.1. α-Stable Lévy Motion63.4. SUMMARY
REFERENCES
64. Bayesian Probability for Investors
64.1. CONCEPT AND CONTEXT64.1.1. Fundamental Bayesian Concepts64.1.1.1. The Laws of Probability64.1.1.2. Probability Distributions64.1.1.3. A Second Level of Abstraction64.1.2. Predictions64.1.3. Origins, Diffusion, and Elaboration64.1.3.1. Bayesian Approaches Become Respectable64.1.3.2. Modern Bayesians64.1.3.3. Notable Investment Examples64.2. BAYES ON A SPREADSHEET64.2.1. Summarizing Simple Evidence condition64.2.1.1. Quantifying the Qualitative64.2.1.2. Estimating a Probability from Sequences of Binomial Data64.2.1.3. Back to our Canadian Farmland Questions64.2.1.4. Longer Sequences of Evidence64.2.2. Intuition for Blending Priors and Likelihoods64.2.3. When Quantifying Scale Is Critical64.2.4. The Normal, Scaled Inverse Chi-Squared Joint Distribution64.2.5. Back to our Value-Oriented Active Management Question64.3. SOME PROGRAMMING REQUIRED64.3.1. Taking Advantage of Group Relations64.3.1.1. Creating Exchangeable Individuals64.3.1.2. Procedure64.3.1.3. Getting to τ64.3.1.4. Inferring the Distribution for µ64.3.1.5. Inferring the Distributions for Each Individual Mean64.3.1.6. The Result for Our Mutual Fund Study64.3.1.7. With More Advanced Techniques64.3.1.8. Thinking about Other Applications of Hierarchical Models64.3.2. Improving Markowitz Mean-Variance Optimization64.3.3. Harnessing Advanced Techniques64.4. ADDITIONAL RELATED WORK64.5. SUMMARY
REFERENCES
65. Monte Carlo Simulation in Finance
65.1. MAIN IDEAS AND IMPORTANT CONCEPTS65.1.1. How Many Scenarios?65.1.2. Estimator Bias65.1.3. Estimator Efficiency65.2. FINANCIAL APPLICATIONS OF SIMULATION65.2.1. Financial Derivative Pricing65.2.2. Estimating Sensitivities65.2.3. Protfolio Risk Management65.2.4. Valuing Mortgage-Backed Securities65.2.5. Valuing Credit-Risky Securities65.3. RANDOM NUMBER GENERATION65.3.1. From a Uniform Random Variable to a Variable from an Arbitrary Distribution65.3.2. What Defines a "Good" Random Number Generator?65.3.3. Pseudo-Random Numbers Generators65.4. VARIANCE REDUCTION TECHNIQUES65.4.1. Antithetic Variables65.4.2. Stratified Sampling65.4.3. Importance Sampling65.4.4. Quasi-Random (Low-Discrepancy) Sequences65.5. SIMULATION SOFTWARE65.6. SUMMARY
REFERENCES
66. Principles of Optimization for Portfolio Selection
66.1. UNCONSTRAINED OPTIMIZATION66.1.1. Minima and Maxima of a Differentiable Function66.1.2. Convex Functions66.1.3. Quasi-Convex Functions66.2. CONSTRAINED OPTIMIZATION66.2.1. Lagrange Multipliers66.2.2. Convex Programming66.2.3. Linear Programming66.2.4. Quadratic Programming66.3. SUMMARY
REFERENCES
67. Introduction to Stochastic Programming and Its Applications to Finance
67.1. WHAT IS STOCHASTIC PROGRAMMING?67.1.1. Stochastic Programming in Finance67.2. STOCHASTIC PROGRAMMING VERSUS OTHER METHODS IN FINANCE67.2.1. Static versus Dynamic Models in Financial Planning67.2.2. Continuous-Time Models versus Stochastic Programming67.3. A GENERAL MULTISTAGE STOCHASTIC PROGRAMMING MODEL FOR FINANCIAL PLANNING67.3.1. Model Formulation67.3.1.1. Parameters67.3.1.2. Decision Variables67.3.2. Modeling Future Uncertainties (Scenario Generation)67.4. SUMMARY
REFERENCES
68. Robust Portfolio Optimization
68.1. THE ROBUST OPTIMIZATION APPROACH68.1.1. Selecting Uncertainty Sets from Statistical Procedures68.1.2. Clarifying a Misconception about Robust Optimization68.2. THE RELATIONSHIP TO BAYESIAN METHODS AND ECONOMIC THEORY68.3. USING ROBUST PORTFOLIO OPTIMIZATION IN PRACTICE68.3.1. Effect of Robust Portfolio Optimization Formulations on Performance68.4. PRACTICAL CONSIDERATIONS FOR ROBUST PORTFOLIO ALLOCATION68.5. FUTURE DIRECTIONS68.6. SUMMARY
REFERENCES

Content preview from Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 37. Yield Curves and Valuation Lattices

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

ANDREW KALOTAY, PhD

President, Andrew Kalotay Associates

MICHAEL DORIGAN, PhD

Senior Quantitative Analyst, PNC Capital Advisors

Abstract: The complication in valuing bonds with embedded options and option-type derivatives is that cash flows depend on interest rates in the future. Academicians and practitioners have attempted to capture this interest rate uncertainty through various models, often designed as one- or two-factor processes. These models attempt to capture the stochastic behavior of rates. In practice, these elegant mathematical models must be implemented numerically in order to be useful. One such model is a single factor model that assumes a stationary variance, or volatility.

Keywords: interest rate lattice, yield curve, one-factor model, binomial interest rate tree, recursive valuation

An often used framework for the valuation of interest rate instruments with embedded options and interest rate option–type derivatives is the lattice framework. Effectively, the lattice specifies the distribution of short-term interest rates over time. The lattice holds all the information required to perform the valuation of certain option-like interest rate products. First, the lattice is used to generate the cash flows across the life of the security. Next, the interest rates on the lattice are used to compute the present value of those cash flows. ...

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