A through guide covering Modern Portfolio Theory as well as the recent developments surrounding itModern portfolio theory (MPT), which originated with Harry Markowitz's seminal paper "Portfolio Selection" in 1952, has stood the test of time and continues to be the intellectual foundation for real-world portfolio management. This book presents a comprehensive picture of MPT in a manner that can be effectively used by financial practitioners and understood by students.Modern Portfolio Theory provides a summary of the important findings from all of the financial research done since MPT was created and presents all the MPT formulas and models using one consistent set of mathematical symbols. Opening with an informative introduction to the concepts of probability and utility theory, it quickly moves on to discuss Markowitz's seminal work on the topic with a thorough explanation of the underlying mathematics.* Analyzes portfolios of all sizes and types, shows how the advanced findings and formulas are derived, and offers a concise and comprehensive review of MPT literature* Addresses logical extensions to Markowitz's work, including the Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio ranking models, and performance attribution* Considers stock market developments like decimalization, high frequency trading, and algorithmic trading, and reveals how they align with MPT* Companion Website contains Excel spreadsheets that allow you to compute and graph Markowitz efficient frontiers with riskless and risky assetsIf you want to gain a complete understanding of modern portfolio theory this is the book you need to read.

ContentsPreface xviiCHAPTER 1 Introduction 11.1 The Portfolio Management Process 11.2 The Security Analyst's Job 11.3 Portfolio Analysis 21.4 Portfolio Selection 51.5 The Mathematics is Segregated 61.6 Topics to be Discussed 6Appendix: Various Rates of Return 7PART 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 293.2 Utility Theory 323.3 Risk-Return Space 363.4 Diversification 383.5 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 524.6 Absolute Risk Aversion 594.7 Relative Risk Aversion 604.8 Measuring Risk Aversion 624.9 Portfolio Analysis 664.10 Indifference Curves 694.11 Summary and Conclusions 74Appendix: Risk Aversion and Indifference Curves 75PART 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 925.6 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 105CHAPTER 6 Efficient Portfolios 1136.1 Risk and Return for Two-Asset Portfolios 1136.2 The Opportunity Set 1146.3 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 Erp) and sigmapCHAPTER 7 Advanced Mathematical Portfolio Analysis 1357.1 Efficient Portfolios without a Risk-Free Asset 1357.2 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 152CHAPTER 8 Index Models and Return-Generating Process 1658.1 Single-Index Models 1658.2 Efficient Frontier and the Single-Index Model 1788.3 Two-Index Models 1868.4 Multi-Index Models 1898.5 Conclusions 190Appendix: Index Models 191PART 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 2049.4 Poisson Jump-Diffusion Process 2069.5 Lognormal Distributions 2069.6 Conclusions 213CHAPTER 10 Non-Mean-Variance Investment Decisions 21510.1 Geometric Mean Return Criterion 21510.2 The Safety-First Criterion 21810.3 Semivariance Analysis 22810.4 Stochastic Dominance Criterion 23610.5 Mean-Variance-Skewness Analysis 24610.6 Summary and Conclusions 254Appendix A: Stochastic Dominance 254Appendix 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 26511.4 Other VaRs 26911.5 Methods of Measuring VaR 27011.6 Estimation of Volatilities 27711.7 The Accuracy of VaR Models 28211.8 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 29212.3 The Capital Asset Pricing Model 29512.4 Over- and Under-priced Securities 29912.5 The Market Model and the CAPM 30012.6 Summary and Conclusions 301Appendix: Derivations of the CAPM 301CHAPTER 13 Extensions of the Standard CAPM 31113.1 Risk-Free Borrowing or Lending 31113.2 Homogeneous Expectations 31613.3 Perfect Markets 31813.4 Unmarketable Assets 32213.5 Summary and Conclusions 323Appendix: Derivations of a Non-Standard CAPM 324CHAPTER 14 Empirical Tests of the CAPM 33314.1 Time-Series Tests of the CAPM 33314.2 Cross-Sectional Tests of the CAPM 33514.3 Empirical Misspecifications in Cross-Sectional Regression Tests 34514.4 Multivariate Tests 35314.5 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) 36315.3 Conclusions 366Appendix: Lognormality and the Consumption-Based CAPM 367CHAPTER 16 Arbitrage Pricing Theory 37116.1 Arbitrage Concepts 37116.2 Index Arbitrage 37516.4 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 39517.2 Using Portfolio Theories to Construct and Select Portfolios 39817.3 Security Analysis 40017.4 Market Timing 40117.5 Diversification 40717.6 Constructing an Active Portfolio 41517.7 Portfolio Revision 42417.8 Summary and Conclusions 430Appendix: Proofs for Some Ratios from Active Portfolios 431CHAPTER 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 43818.5 Market Timing 44918.6 Comparing Single-Parameter Portfolio Performance Measures 45218.7 The Index of Total Portfolio Risk (ITPR) and the Portfolio Beta 45418.8 Measurement Problems 45718.9 Do Winners or Losers Repeat? 46118.10 Summary about Investment Performance Evaluation 465Appendix: Sharpe Ratio of an Active Portfolio 467CHAPTER 19 Performance Attribution 47319.1 Factor Model Analysis 47419.2 Return-Based Style Analysis 47519.3 Return Decomposition-Based Analysis 47919.4 Conclusions 485Appendix: Regression Coefficients Estimation with Constraints 486CHAPTER 20 Stock Market Developments 48920.1 Recent NYSE Consolidations 48920.2 International Securities Exchange (ISE) 49220.3 Nasdaq 49220.4 Downward Pressures on Transactions Costs 49420.5 The Venerable Limit Order 49720.6 Market Microstructure 49820.7 High-Frequency Trading 49920.8 Alternative Trading Systems (ATSs) 50020.9 Algorithmic Trading 50120.10 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