Modern Portfolio Theory, + Website

JACK CLARK FRANCIS is Professor of Economics and Finance at Bernard M. Baruch College in New York City. His research focuses on investments, banking, and monetary economics, and he has had dozens of articles published in many refereed academic, business, and government journals. Dr. Francis was an assistant professor of finance at the University of Pennsylvania's Wharton School of Finance for five years and was a Federal Reserve economist for two years. He received his bachelor's and MBA from Indiana University and earned his PhD in finance from the University of Washington in Seattle. DONGCHEOL KIM is a Professor of Finance at Korea University in Seoul. He served as president of the Korea Securities Association and editor-in-chief of the Asia-Pacific Journal of Financial Studies. Previously, he was a finance professor at Rutgers University. Kim has published articles in Financial Management, the Accounting Review, Journal of Financial and Quantitative Analysis, Journal of Economic Research, Journal of Finance, and Journal of the Futures Market.

• Preface xviiCHAPTER 1 Introduction 11.1 The Portfolio Management Process 11.2 The Security Analyst’s Job 11.3 Portfolio Analysis 21.3.1 Basic Assumptions 31.3.2 Reconsidering the Assumptions 31.4 Portfolio Selection 51.5 The Mathematics is Segregated 61.6 Topics to be Discussed 6Appendix: Various Rates of Return 7A1.1 Calculating the Holding Period Return 7A1.2 After-Tax Returns 8A1.3 Discrete and Continuously Compounded Returns 8PART ONE Probability FoundationsCHAPTER 2 Assessing Risk 132.1 Mathematical Expectation 132.2 What Is Risk? 152.3 Expected Return 162.4 Risk of a Security 172.5 Covariance of Returns 182.6 Correlation of Returns 192.7 Using Historical Returns 202.8 Data Input Requirements 222.9 Portfolio Weights 222.10 A Portfolio’s Expected Return 232.11 Portfolio Risk 232.12 Summary of Notations and Formulas 27CHAPTER 3 Risk and Diversification 293.1 Reconsidering Risk 293.1.1 Symmetric Probability Distributions 313.1.2 Fundamental Security Analysis 323.2 Utility Theory 323.2.1 Numerical Example 333.2.2 Indifference Curves 353.3 Risk-Return Space 363.4 Diversification 383.4.1 Diversification Illustrated 383.4.2 Risky A + Risky B = Riskless Portfolio 393.4.3 Graphical Analysis 403.5 Conclusions 41PART TWO Utility FoundationsCHAPTER 4 Single-Period Utility Analysis 454.1 Basic Utility Axioms 464.2 The Utility of Wealth Function 474.3 Utility of Wealth and Returns 474.4 Expected Utility of Returns 484.5 Risk Attitudes 524.5.1 Risk Aversion 524.5.2 Risk-Loving Behavior 564.5.3 Risk-Neutral Behavior 574.6 Absolute Risk Aversion 594.7 Relative Risk Aversion 604.8 Measuring Risk Aversion 624.8.1 Assumptions 624.8.2 Power, Logarithmic, and Quadratic Utility 624.8.3 Isoelastic Utility Functions 644.8.4 Myopic, but Optimal 654.9 Portfolio Analysis 664.9.1 Quadratic Utility Functions 674.9.2 Using Quadratic Approximations to Delineate Max[E(Utility)] Portfolios 684.9.3 Normally Distributed Returns 694.10 Indifference Curves 694.10.1 Selecting Investments 714.10.2 Risk-Aversion Measures 734.11 Summary and Conclusions 74Appendix: Risk Aversion and Indifference Curves 75A4.1 Absolute Risk Aversion (ARA) 75A4.2 Relative Risk Aversion (RRA) 76A4.3 Expected Utility of Wealth 77A4.4 Slopes of Indifference Curves 77A4.5 Indifference Curves for Quadratic Utility 79PART THREE Mean-Variance Portfolio AnalysisCHAPTER 5 Graphical Portfolio Analysis 855.1 Delineating Efficient Portfolios 855.2 Portfolio Analysis Inputs 865.3 Two-Asset Isomean Lines 875.4 Two-Asset Isovariance Ellipses 905.5 Three-Asset Portfolio Analysis 925.5.1 Solving for One Variable Implicitly 935.5.2 Isomean Lines 965.5.3 Isovariance Ellipses 975.5.4 The Critical Line 995.5.5 Inefficient Portfolios 1015.6 Legitimate Portfolios 1025.7 ‘‘Unusual’’ Graphical Solutions Don’t Exist 1035.8 Representing Constraints Graphically 1035.9 The Interior Decorator Fallacy 1035.10 Summary 104Appendix: Quadratic Equations 105A5.1 Quadratic Equations 105A5.2 Analysis of Quadratics in Two Unknowns 106A5.3 Analysis of Quadratics in One Unknown 107A5.4 Solving an Ellipse 108A5.5 Solving for Lines Tangent to a Set of Ellipses 110CHAPTER 6 Efficient Portfolios 1136.1 Risk and Return for Two-Asset Portfolios 1136.2 The Opportunity Set 1146.2.1 The Two-Security Case 1146.2.2 Minimizing Risk in the Two-Security Case 1166.2.3 The Three-Security Case 1176.2.4 The n-Security Case 1196.3 Markowitz Diversification 1206.4 Efficient Frontier without the Risk-Free Asset 1236.5 Introducing a Risk-Free Asset 1266.6 Summary and Conclusions 131Appendix: Equations for a Relationship between E(rp) and σp 131CHAPTER 7 Advanced Mathematical Portfolio Analysis 1357.1 Efficient Portfolios without a Risk-Free Asset 1357.1.1 A General Formulation 1357.1.2 Formulating with Concise Matrix Notation 1407.1.3 The Two-Fund Separation Theorem 1457.1.4 Caveat about Negative Weights 1467.2 Efficient Portfolios with a Risk-Free Asset 1467.3 Identifying the Tangency Portfolio 1507.4 Summary and Conclusions 152Appendix: Mathematical Derivation of the Efficient Frontier 152A7.1 No Risk-Free Asset 152A7.2 With a Risk-Free Asset 156CHAPTER 8 Index Models and Return-Generating Process 1658.1 Single-Index Models 1658.1.1 Return-Generating Functions 1658.1.2 Estimating the Parameters 1688.1.3 The Single-Index Model Using Excess Returns 1718.1.4 The Riskless Rate Can Fluctuate 1738.1.5 Diversification 1768.1.6 About the Single-Index Model 1778.2 Efficient Frontier and the Single-Index Model 1788.3 Two-Index Models 1868.3.1 Generating Inputs 1878.3.2 Diversification 1888.4 Multi-Index Models 1898.5 Conclusions 190Appendix: Index Models 191A8.1 Solving for Efficient Portfolios with the Single-Index Model 191A8.2 Variance Decomposition 196A8.3 Orthogonalizing Multiple Indexes 196PART FOUR Non-Mean-Variance PortfoliosCHAPTER 9 Non-Normal Distributions of Returns 2019.1 Stable Paretian Distributions 2019.2 The Student’s t-Distribution 2049.3 Mixtures of Normal Distributions 2049.3.1 Discrete Mixtures of Normal Distributions 2049.3.2 Sequential Mixtures of Normal Distributions 2059.4 Poisson Jump-Diffusion Process 2069.5 Lognormal Distributions 2069.5.1 Specifications of Lognormal Distributions 2079.5.2 Portfolio Analysis under Lognormality 2089.6 Conclusions 213CHAPTER 10 Non-Mean-Variance Investment Decisions 21510.1 Geometric Mean Return Criterion 21510.1.1 Maximizing the Terminal Wealth 21610.1.2 Log Utility and the GMR Criterion 21610.1.3 Diversification and the GMR 21710.2 The Safety-First Criterion 21810.2.1 Roy’s Safety-First Criterion 21810.2.2 Kataoka’s Safety-First Criterion 22210.2.3 Telser’s Safety-First Criterion 22510.3 Semivariance Analysis 22810.3.1 Definition of Semivariance 22810.3.2 Utility Theory 23010.3.3 Portfolio Analysis with the Semivariance 23110.3.4 Capital Market Theory with the Semivariance 23410.3.5 Summary about Semivariance 23610.4 Stochastic Dominance Criterion 23610.4.1 First-Order Stochastic Dominance 23610.4.2 Second-Order Stochastic Dominance 24110.4.3 Third-Order Stochastic Dominance 24410.4.4 Summary of Stochastic Dominance Criterion 24510.5 Mean-Variance-Skewness Analysis 24610.5.1 Only Two Moments Can Be Inadequate 24610.5.2 Portfolio Analysis in Three Moments 24710.5.3 Efficient Frontier in Three-Dimensional Space 24910.5.4 Undiversifiable Risk and Undiversifiable Skewness 25210.6 Summary and Conclusions 254Appendix A: Stochastic Dominance 254A10.1 Proof for First-Order Stochastic Dominance 254A10.2 Proof That FA(r) ≤ FB(r) Is Equivalent to EA(r) ≥ EB(r) for Positive r 255Appendix B: Expected Utility as a Function of Three Moments 257CHAPTER 11 Risk Management: Value at Risk 26111.1 VaR of a Single Asset 26111.2 Portfolio VaR 26311.3 Decomposition of a Portfolio’s VaR 26511.3.1 Marginal VaR 26511.3.2 Incremental VaR 26611.3.3 Component VaR 26711.4 Other VaRs 26911.4.1 Modified VaR (MVaR) 26911.4.2 Conditional VaR (CVaR) 27011.5 Methods of Measuring VaR 27011.5.1 Variance-Covariance (Delta-Normal) Method 27011.5.2 Historical Simulation Method 27411.5.3 Monte Carlo Simulation Method 27611.6 Estimation of Volatilities 27711.6.1 Unconditional Variance 27711.6.2 Simple Moving Average 27711.6.3 Exponentially Weighted Moving Average 27811.6.4 GARCH-Based Volatility 27811.6.5 Volatility Measures Using Price Range 27911.6.6 Implied Volatility 28111.7 The Accuracy of VaR Models 28211.7.1 Back-Testing 28311.7.2 Stress Testing 28411.8 Summary and Conclusions 285Appendix: The Delta-Gamma Method 285PART FIVE Asset Pricing ModelsCHAPTER 12 The Capital Asset Pricing Model 29112.1 Underlying Assumptions 29112.2 The Capital Market Line 29212.2.1 The Market Portfolio 29212.2.2 The Separation Theorem 29312.2.3 Efficient Frontier Equation 29412.2.4 Portfolio Selection 29412.3 The Capital Asset Pricing Model 29512.3.1 Background 29512.3.2 Derivation of the CAPM 29612.4 Over- and Under-priced Securities 29912.5 The Market Model and the CAPM 30012.6 Summary and Conclusions 301Appendix: Derivations of the CAPM 301A12.1 Other Approaches 301A12.2 Tangency Portfolio Research 305CHAPTER 13 Extensions of the Standard CAPM 31113.1 Risk-Free Borrowing or Lending 31113.1.1 The Zero-Beta Portfolio 31113.1.2 No Risk-Free Borrowing 31413.1.3 Lending and Borrowing Rates Can Differ 31413.2 Homogeneous Expectations 31613.2.1 Investment Horizons 31613.2.2 Multivariate Distribution of Returns 31713.3 Perfect Markets 31813.3.1 Taxes 31813.3.2 Transaction Costs 32013.3.3 Indivisibilities 32113.3.4 Price Competition 32113.4 Unmarketable Assets 32213.5 Summary and Conclusions 323Appendix: Derivations of a Non-Standard CAPM 324A13.1 The Characteristics of the Zero-Beta Portfolio 324A13.2 Derivation of Brennan’s After-Tax CAPM 325A13.3 Derivation of Mayers’s CAPM for Nonmarketable Assets 328CHAPTER 14 Empirical Tests of the CAPM 33314.1 Time-Series Tests of the CAPM 33314.2 Cross-Sectional Tests of the CAPM 33514.2.1 Black, Jensen, and Scholes’s (1972) Tests 33614.2.2 Fama and MacBeth’s (1973) Tests 34014.2.3 Fama and French’s (1992) Tests 34414.3 Empirical Misspecifications in Cross-Sectional Regression Tests 34514.3.1 The Errors-in-Variables Problem 34614.3.2 Sensitivity of Beta to the Return Measurement Intervals 35114.4 Multivariate Tests 35314.4.1 Gibbons’s (1982) Test 35314.4.2 Stambaugh’s (1982) Test 35514.4.3 Jobson and Korkie’s (1982) Test 35514.4.4 Shanken’s (1985) Test 35614.4.5 Generalized Method of Moment (GMM) Tests 35614.5 Is the CAPM Testable? 35614.6 Summary and Conclusions 357CHAPTER 15 Continuous-Time Asset Pricing Models 36115.1 Intertemporal CAPM (ICAPM) 36115.2 The Consumption-Based CAPM (CCAPM) 36315.2.1 Derivation 36315.2.2 The Consumption-Based CAPM with a Power Utility Function 36515.3 Conclusions 366Appendix: Lognormality and the Consumption-Based CAPM 367A15.1 Lognormality 367A15.2 The Consumption-Based CAPM with Lognormality 367CHAPTER 16 Arbitrage Pricing Theory 37116.1 Arbitrage Concepts 37116.2 Index Arbitrage 37516.2.1 Basic Ideas of Index Arbitrage 37616.2.2 Index Arbitrage and Program Trading 37716.2.3 Use of ETFs for Index Arbitrage 37716.3 The Asset Pricing Equation 37816.3.1 One Single Factor with No Residual Risk 37916.3.2 Two Factors with No Residual Risk 38016.3.3 K Factors with No Residual Risk 38116.3.4 K Factors with Residual Risk 38216.4 Asset Pricing on a Security Market Plane 38316.5 Contrasting APT with CAPM 38516.6 Empirical Evidence 38616.7 Comparing the APT and CAPM Empirically 38816.8 Conclusions 389PART SIX Implementing the TheoryCHAPTER 17 Portfolio Construction and Selection 39517.1 Efficient Markets 39517.1.1 Fama’s Classifications 39517.1.2 Formal Models 39617.2 Using Portfolio Theories to Construct and Select Portfolios 39817.3 Security Analysis 40017.4 Market Timing 40117.4.1 Forecasting Beta 40117.4.2 Nonstationarity of Beta 40417.4.3 Determinants of Beta 40617.5 Diversification 40717.5.1 Simple Diversification 40817.5.2 Timing and Diversification 40917.5.3 International Diversification 41117.6 Constructing an Active Portfolio 41517.7 Portfolio Revision 42417.7.1 Portfolio Revision Costs 42417.7.2 Controlled Transition 42617.7.3 The Attainable Efficient Frontier 42817.7.4 A Turnover-Constrained Approach 42817.8 Summary and Conclusions 430Appendix: Proofs for Some Ratios from Active Portfolios 431A17.1 Proof for αA/σ2 εA= ∑Ki=1(αi/σ2 εi) 431A17.2 Proof for (αAβA/ σ2 εA) = ∑Ki=1 (αiβi/σ2 εi) 431A17.3 Proof for (α2A/ σ2 εA) = ∑Ki=1 (σ2 i/σ2 εi) 432CHAPTER 18 Portfolio Performance Evaluation 43518.1 Mutual Fund Returns 43518.2 Portfolio Performance Analysis in the Good Old Days 43618.3 Capital Market Theory Assumptions 43818.4 Single-Parameter Portfolio Performance Measures 43818.4.1 Sharpe’s Reward-to-Variability Ratio 43918.4.2 Treynor’s Reward-to-Risk Ratio 44118.4.3 Jensen’s Measure 44418.4.4 Information Ratio (or Appraisal Ratio) 44718.4.5 M2 Measure 44818.5 Market Timing 44918.5.1 Interpreting the Market Timing Coefficient 45018.5.2 Henriksson and Merton’s Model 45118.5.3 Descriptive Comments 45218.6 Comparing Single-Parameter Portfolio Performance Measures 45218.6.1 Ranking Undiversified Investments 45218.6.2 Contrasting the Three Models 45318.6.3 Survivorship Bias 45418.7 The Index of Total Portfolio Risk (ITPR) and the Portfolio Beta 45418.8 Measurement Problems 45718.8.1 Measurement of the Market Portfolio’s Returns 45818.8.2 Nonstationarity of Portfolio Return Distributions 46018.9 Do Winners or Losers Repeat? 46118.10 Summary about Investment Performance Evaluation 465Appendix: Sharpe Ratio of an Active Portfolio 467A18.1 Proof that S2q= S2m+ [αA/σ (εA)]2 467CHAPTER 19 Performance Attribution 47319.1 Factor Model Analysis 47419.2 Return-Based Style Analysis 47519.3 Return Decomposition-Based Analysis 47919.4 Conclusions 48519.4.1 Detrimental Uses of Portfolio Performance Attribution 48619.4.2 Symbiotic Possibilities 486Appendix: Regression Coefficients Estimation with Constraints 486A19.1 With No Constraints 487A19.2 With the Constraint of ∑Kk=1 βik 475CHAPTER 20 Stock Market Developments 48920.1 Recent NYSE Consolidations 48920.1.1 Archipelago 49020.1.2 Pacific Stock Exchange (PSE) 49020.1.3 ArcaEx 49020.1.4 New York Stock Exchange (NYSE) 49020.1.5 NYSE Group 49120.1.6 NYSE Diversifies Internationally 49120.1.7 NYSE Alliances 49120.2 International Securities Exchange (ISE) 49220.3 Nasdaq 49220.3.1 London Stock Exchange (LSE) 49320.3.2 OMX Group 49320.3.3 Bourse Dubai 49320.3.4 Boston Stock Exchange (BSE) 49420.3.5 Philadelphia Stock Exchange (PHLX) 49420.4 Downward Pressures on Transactions Costs 49420.4.1 A National Market System (NMS) 49520.4.2 The SEC’s Reg ATS 49620.4.3 Reg FD 49620.4.4 Decimalization of Stock Prices 49620.4.5 Technological Advances 49620.5 The Venerable Limit Order 49720.5.1 What Are Limit Orders? 49720.5.2 Creating Market Liquidity 49820.6 Market Microstructure 49820.6.1 Inventory Management 49820.6.2 Brokers 49920.7 High-Frequency Trading 49920.8 Alternative Trading Systems (ATSs) 50020.8.1 Crossing Networks 50020.8.2 Dark Pools 50020.9 Algorithmic Trading 50120.9.1 Some Algorithmic Trading Applications 50120.9.2 Trading Curbs 50320.9.3 Conclusions about Algorithmic Trading 50420.10 Symbiotic Stock Market Developments 50520.11 Detrimental Stock Market Developments 50520.12 Summary and Conclusions 506Mathematical Appendixes 509Bibliography 519About the Authors 539Author Index 541Subject Index 547