Jack Clark Francis, Dongcheol Kim

Modern Portfolio Theory (eBook, ePUB)

Foundations, Analysis, and New Developments

• Format: ePub

Produktbeschreibung

A through guide covering Modern Portfolio Theory as well as the recent developments surrounding it Modern 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 assets If you want to gain a complete understanding of modern portfolio theory this is the book you need to read.

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Produktdetails

• Verlag: Jossey-Bass
• Seitenzahl: 576
• Erscheinungstermin: 18. Januar 2013
• Englisch
• ISBN-13: 9781118417201
• Artikelnr.: 37757901

Autorenporträt

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.

Inhaltsangabe

Preface xvii CHAPTER 1 Introduction 1 1.1 The Portfolio Management Process 1 1.2 The Security Analyst's Job 1 1.3 Portfolio Analysis 2 1.3.1 Basic Assumptions 3 1.3.2 Reconsidering the Assumptions 3 1.4 Portfolio Selection 5 1.5 The Mathematics is Segregated 6 1.6 Topics to be Discussed 6 Appendix: Various Rates of Return 7 A1.1 Calculating the Holding Period Return 7 A1.2 After-Tax Returns 8 A1.3 Discrete and Continuously Compounded Returns 8 PART ONE Probability Foundations CHAPTER 2 Assessing Risk 13 2.1 Mathematical Expectation 13 2.2 What Is Risk? 15 2.3 Expected Return 16 2.4 Risk of a Security 17 2.5 Covariance of Returns 18 2.6 Correlation of Returns 19 2.7 Using Historical Returns 20 2.8 Data Input Requirements 22 2.9 Portfolio Weights 22 2.10 A Portfolio's Expected Return 23 2.11 Portfolio Risk 23 2.12 Summary of Notations and Formulas 27 CHAPTER 3 Risk and Diversi
cation 29 3.1 Reconsidering Risk 29 3.1.1 Symmetric Probability Distributions 31 3.1.2 Fundamental Security Analysis 32 3.2 Utility Theory 32 3.2.1 Numerical Example 33 3.2.2 Indifference Curves 35 3.3 Risk-Return Space 36 3.4 Diversi
cation 38 3.4.1 Diversi
cation Illustrated 38 3.4.2 Risky A + Risky B = Riskless Portfolio 39 3.4.3 Graphical Analysis 40 3.5 Conclusions 41 PART TWO Utility Foundations CHAPTER 4 Single-Period Utility Analysis 45 4.1 Basic Utility Axioms 46 4.2 The Utility of Wealth Function 47 4.3 Utility of Wealth and Returns 47 4.4 Expected Utility of Returns 48 4.5 Risk Attitudes 52 4.5.1 Risk Aversion 52 4.5.2 Risk-Loving Behavior 56 4.5.3 Risk-Neutral Behavior 57 4.6 Absolute Risk Aversion 59 4.7 Relative Risk Aversion 60 4.8 Measuring Risk Aversion 62 4.8.1 Assumptions 62 4.8.2 Power, Logarithmic, and Quadratic Utility 62 4.8.3 Isoelastic Utility Functions 64 4.8.4 Myopic, but Optimal 65 4.9 Portfolio Analysis 66 4.9.1 Quadratic Utility Functions 67 4.9.2 Using Quadratic Approximations to Delineate Max[E(Utility)] Portfolios 68 4.9.3 Normally Distributed Returns 69 4.10 Indifference Curves 69 4.10.1 Selecting Investments 71 4.10.2 Risk-Aversion Measures 73 4.11 Summary and Conclusions 74 Appendix: Risk Aversion and Indifference Curves 75 A4.1 Absolute Risk Aversion (ARA) 75 A4.2 Relative Risk Aversion (RRA) 76 A4.3 Expected Utility of Wealth 77 A4.4 Slopes of Indifference Curves 77 A4.5 Indifference Curves for Quadratic Utility 79 PART THREE Mean-Variance Portfolio Analysis CHAPTER 5 Graphical Portfolio Analysis 85 5.1 Delineating Ef
cient Portfolios 85 5.2 Portfolio Analysis Inputs 86 5.3 Two-Asset Isomean Lines 87 5.4 Two-Asset Isovariance Ellipses 90 5.5 Three-Asset Portfolio Analysis 92 5.5.1 Solving for One Variable Implicitly 93 5.5.2 Isomean Lines 96 5.5.3 Isovariance Ellipses 97 5.5.4 The Critical Line 99 5.5.5 Inef
cient Portfolios 101 5.6 Legitimate Portfolios 102 5.7 ''Unusual'' Graphical Solutions Don't Exist 103 5.8 Representing Constraints Graphically 103 5.9 The Interior Decorator Fallacy 103 5.10 Summary 104 Appendix: Quadratic Equations 105 A5.1 Quadratic Equations 105 A5.2 Analysis of Quadratics in Two Unknowns 106 A5.3 Analysis of Quadratics in One Unknown 107 A5.4 Solving an Ellipse 108 A5.5 Solving for Lines Tangent to a Set of Ellipses 110 CHAPTER 6 Ef
cient Portfolios 113 6.1 Risk and Return for Two-Asset Portfolios 113 6.2 The Opportunity Set 114 6.2.1 The Two-Security Case 114 6.2.2 Minimizing Risk in the Two-Security Case 116 6.2.3 The Three-Security Case 117 6.2.4 The n-Security Case 119 6.3 Markowitz Diversi
cation 120 6.4 Ef
cient Frontier without the Risk-Free Asset 123 6.5 Introducing a Risk-Free Asset 126 6.6 Summary and Conclusions 131 Appendix: Equations for a Relationship between E(rp) and
p 131 CHAPTER 7 Advanced Mathematical Portfolio Analysis 135 7.1 Ef
cient Portfolios without a Risk-Free Asset 135 7.1.1 A General Formulation 135 7.1.2 Formulating with Concise Matrix Notation 140 7.1.3 The Two-Fund Separation Theorem 145 7.1.4 Caveat about Negative Weights 146 7.2 Ef
cient Portfolios with a Risk-Free Asset 146 7.3 Identifying the Tangency Portfolio 150 7.4 Summary and Conclusions 152 Appendix: Mathematical Derivation of the Ef
cient Frontier 152 A7.1 No Risk-Free Asset 152 A7.2 With a Risk-Free Asset 156 CHAPTER 8 Index Models and Return-Generating Process 165 8.1 Single-Index Models 165 8.1.1 Return-Generating Functions 165 8.1.2 Estimating the Parameters 168 8.1.3 The Single-Index Model Using Excess Returns 171 8.1.4 The Riskless Rate Can Fluctuate 173 8.1.5 Diversi
cation 176 8.1.6 About the Single-Index Model 177 8.2 Ef
cient Frontier and the Single-Index Model 178 8.3 Two-Index Models 186 8.3.1 Generating Inputs 187 8.3.2 Diversi
cation 188 8.4 Multi-Index Models 189 8.5 Conclusions 190 Appendix: Index Models 191 A8.1 Solving for Ef
cient Portfolios with the Single-Index Model 191 A8.2 Variance Decomposition 196 A8.3 Orthogonalizing Multiple Indexes 196 PART FOUR Non-Mean-Variance Portfolios CHAPTER 9 Non-Normal Distributions of Returns 201 9.1 Stable Paretian Distributions 201 9.2 The Student's t-Distribution 204 9.3 Mixtures of Normal Distributions 204 9.3.1 Discrete Mixtures of Normal Distributions 204 9.3.2 Sequential Mixtures of Normal Distributions 205 9.4 Poisson Jump-Diffusion Process 206 9.5 Lognormal Distributions 206 9.5.1 Speci
cations of Lognormal Distributions 207 9.5.2 Portfolio Analysis under Lognormality 208 9.6 Conclusions 213 CHAPTER 10 Non-Mean-Variance Investment Decisions 215 10.1 Geometric Mean Return Criterion 215 10.1.1 Maximizing the Terminal Wealth 216 10.1.2 Log Utility and the GMR Criterion 216 10.1.3 Diversi
cation and the GMR 217 10.2 The Safety-First Criterion 218 10.2.1 Roy's Safety-First Criterion 218 10.2.2 Kataoka's Safety-First Criterion 222 10.2.3 Telser's Safety-First Criterion 225 10.3 Semivariance Analysis 228 10.3.1 De
nition of Semivariance 228 10.3.2 Utility Theory 230 10.3.3 Portfolio Analysis with the Semivariance 231 10.3.4 Capital Market Theory with the Semivariance 234 10.3.5 Summary about Semivariance 236 10.4 Stochastic Dominance Criterion 236 10.4.1 First-Order Stochastic Dominance 236 10.4.2 Second-Order Stochastic Dominance 241 10.4.3 Third-Order Stochastic Dominance 244 10.4.4 Summary of Stochastic Dominance Criterion 245 10.5 Mean-Variance-Skewness Analysis 246 10.5.1 Only Two Moments Can Be Inadequate 246 10.5.2 Portfolio Analysis in Three Moments 247 10.5.3 Ef
cient Frontier in Three-Dimensional Space 249 10.5.4 Undiversi
able Risk and Undiversi
able Skewness 252 10.6 Summary and Conclusions 254 Appendix A: Stochastic Dominance 254 A10.1 Proof for First-Order Stochastic Dominance 254 A10.2 Proof That FA(r)
FB(r) Is Equivalent to EA(r)
EB(r) for Positive r 255 Appendix B: Expected Utility as a Function of Three Moments 257 CHAPTER 11 Risk Management: Value at Risk 261 11.1 VaR of a Single Asset 261 11.2 Portfolio VaR 263 11.3 Decomposition of a Portfolio's VaR 265 11.3.1 Marginal VaR 265 11.3.2 Incremental VaR 266 11.3.3 Component VaR 267 11.4 Other VaRs 269 11.4.1 Modi
ed VaR (MVaR) 269 11.4.2 Conditional VaR (CVaR) 270 11.5 Methods of Measuring VaR 270 11.5.1 Variance-Covariance (Delta-Normal) Method 270 11.5.2 Historical Simulation Method 274 11.5.3 Monte Carlo Simulation Method 276 11.6 Estimation of Volatilities 277 11.6.1 Unconditional Variance 277 11.6.2 Simple Moving Average 277 11.6.3 Exponentially Weighted Moving Average 278 11.6.4 GARCH-Based Volatility 278 11.6.5 Volatility Measures Using Price Range 279 11.6.6 Implied Volatility 281 11.7 The Accuracy of VaR Models 282 11.7.1 Back-Testing 283 11.7.2 Stress Testing 284 11.8 Summary and Conclusions 285 Appendix: The Delta-Gamma Method 285 PART FIVE Asset Pricing Models CHAPTER 12 The Capital Asset Pricing Model 291 12.1 Underlying Assumptions 291 12.2 The Capital Market Line 292 12.2.1 The Market Portfolio 292 12.2.2 The Separation Theorem 293 12.2.3 Ef
cient Frontier Equation 294 12.2.4 Portfolio Selection 294 12.3 The Capital Asset Pricing Model 295 12.3.1 Background 295 12.3.2 Derivation of the CAPM 296 12.4 Over- and Under-priced Securities 299 12.5 The Market Model and the CAPM 300 12.6 Summary and Conclusions 301 Appendix: Derivations of the CAPM 301 A12.1 Other Approaches 301 A12.2 Tangency Portfolio Research 305 CHAPTER 13 Extensions of the Standard CAPM 311 13.1 Risk-Free Borrowing or Lending 311 13.1.1 The Zero-Beta Portfolio 311 13.1.2 No Risk-Free Borrowing 314 13.1.3 Lending and Borrowing Rates Can Differ 314 13.2 Homogeneous Expectations 316 13.2.1 Investment Horizons 316 13.2.2 Multivariate Distribution of Returns 317 13.3 Perfect Markets 318 13.3.1 Taxes 318 13.3.2 Transaction Costs 320 13.3.3 Indivisibilities 321 13.3.4 Price Competition 321 13.4 Unmarketable Assets 322 13.5 Summary and Conclusions 323 Appendix: Derivations of a Non-Standard CAPM 324 A13.1 The Characteristics of the Zero-Beta Portfolio 324 A13.2 Derivation of Brennan's After-Tax CAPM 325 A13.3 Derivation of Mayers's CAPM for Nonmarketable Assets 328 CHAPTER 14 Empirical Tests of the CAPM 333 14.1 Time-Series Tests of the CAPM 333 14.2 Cross-Sectional Tests of the CAPM 335 14.2.1 Black, Jensen, and Scholes's (1972) Tests 336 14.2.2 Fama and MacBeth's (1973) Tests 340 14.2.3 Fama and French's (1992) Tests 344 14.3 Empirical Misspeci
cations in Cross-Sectional Regression Tests 345 14.3.1 The Errors-in-Variables Problem 346 14.3.2 Sensitivity of Beta to the Return Measurement Intervals 351 14.4 Multivariate Tests 353 14.4.1 Gibbons's (1982) Test 353 14.4.2 Stambaugh's (1982) Test 355 14.4.3 Jobson and Korkie's (1982) Test 355 14.4.4 Shanken's (1985) Test 356 14.4.5 Generalized Method of Moment (GMM) Tests 356 14.5 Is the CAPM Testable? 356 14.6 Summary and Conclusions 357 CHAPTER 15 Continuous-Time Asset Pricing Models 361 15.1 Intertemporal CAPM (ICAPM) 361 15.2 The Consumption-Based CAPM (CCAPM) 363 15.2.1 Derivation 363 15.2.2 The Consumption-Based CAPM with a Power Utility Function 365 15.3 Conclusions 366 Appendix: Lognormality and the Consumption-Based CAPM 367 A15.1 Lognormality 367 A15.2 The Consumption-Based CAPM with Lognormality 367 CHAPTER 16 Arbitrage Pricing Theory 371 16.1 Arbitrage Concepts 371 16.2 Index Arbitrage 375 16.2.1 Basic Ideas of Index Arbitrage 376 16.2.2 Index Arbitrage and Program Trading 377 16.2.3 Use of ETFs for Index Arbitrage 377 16.3 The Asset Pricing Equation 378 16.3.1 One Single Factor with No Residual Risk 379 16.3.2 Two Factors with No Residual Risk 380 16.3.3 K Factors with No Residual Risk 381 16.3.4 K Factors with Residual Risk 382 16.4 Asset Pricing on a Security Market Plane 383 16.5 Contrasting APT with CAPM 385 16.6 Empirical Evidence 386 16.7 Comparing the APT and CAPM Empirically 388 16.8 Conclusions 389 PART SIX Implementing the Theory CHAPTER 17 Portfolio Construction and Selection 395 17.1 Ef
cient Markets 395 17.1.1 Fama's Classi
cations 395 17.1.2 Formal Models 396 17.2 Using Portfolio Theories to Construct and Select Portfolios 398 17.3 Security Analysis 400 17.4 Market Timing 401 17.4.1 Forecasting Beta 401 17.4.2 Nonstationarity of Beta 404 17.4.3 Determinants of Beta 406 17.5 Diversi
cation 407 17.5.1 Simple Diversi
cation 408 17.5.2 Timing and Diversi
cation 409 17.5.3 International Diversi
cation 411 17.6 Constructing an Active Portfolio 415 17.7 Portfolio Revision 424 17.7.1 Portfolio Revision Costs 424 17.7.2 Controlled Transition 426 17.7.3 The Attainable Ef
cient Frontier 428 17.7.4 A Turnover-Constrained Approach 428 17.8 Summary and Conclusions 430 Appendix: Proofs for Some Ratios from Active Portfolios 431 A17.1 Proof for
A/
2
A=
Ki=1(
i/
2
i) 431 A17.2 Proof for (
AßA/
2
A) =
Ki=1 (
ißi/
2
i) 431 A17.3 Proof for (
2A/
2
A) =
Ki=1 (
2 i/
2
i) 432 CHAPTER 18 Portfolio Performance Evaluation 435 18.1 Mutual Fund Returns 435 18.2 Portfolio Performance Analysis in the Good Old Days 436 18.3 Capital Market Theory Assumptions 438 18.4 Single-Parameter Portfolio Performance Measures 438 18.4.1 Sharpe's Reward-to-Variability Ratio 439 18.4.2 Treynor's Reward-to-Risk Ratio 441 18.4.3 Jensen's Measure 444 18.4.4 Information Ratio (or Appraisal Ratio) 447 18.4.5 M2 Measure 448 18.5 Market Timing 449 18.5.1 Interpreting the Market Timing Coefficient 450 18.5.2 Henriksson and Merton's Model 451 18.5.3 Descriptive Comments 452 18.6 Comparing Single-Parameter Portfolio Performance Measures 452 18.6.1 Ranking Undiversi
ed Investments 452 18.6.2 Contrasting the Three Models 453 18.6.3 Survivorship Bias 454 18.7 The Index of Total Portfolio Risk (ITPR) and the Portfolio Beta 454 18.8 Measurement Problems 457 18.8.1 Measurement of the Market Portfolio's Returns 458 18.8.2 Nonstationarity of Portfolio Return Distributions 460 18.9 Do Winners or Losers Repeat? 461 18.10 Summary about Investment Performance Evaluation 465 Appendix: Sharpe Ratio of an Active Portfolio 467 A18.1 Proof that S2q= S2m+ [
A/
(
A)]2 467 CHAPTER 19 Performance Attribution 473 19.1 Factor Model Analysis 474 19.2 Return-Based Style Analysis 475 19.3 Return Decomposition-Based Analysis 479 19.4 Conclusions 485 19.4.1 Detrimental Uses of Portfolio Performance Attribution 486 19.4.2 Symbiotic Possibilities 486 Appendix: Regression Coef
cients Estimation with Constraints 486 A19.1 With No Constraints 487 A19.2 With the Constraint of
Kk=1 ßik 475 CHAPTER 20 Stock Market Developments 489 20.1 Recent NYSE Consolidations 489 20.1.1 Archipelago 490 20.1.2 Paci
c Stock Exchange (PSE) 490 20.1.3 ArcaEx 490 20.1.4 New York Stock Exchange (NYSE) 490 20.1.5 NYSE Group 491 20.1.6 NYSE Diversi
es Internationally 491 20.1.7 NYSE Alliances 491 20.2 International Securities Exchange (ISE) 492 20.3 Nasdaq 492 20.3.1 London Stock Exchange (LSE) 493 20.3.2 OMX Group 493 20.3.3 Bourse Dubai 493 20.3.4 Boston Stock Exchange (BSE) 494 20.3.5 Philadelphia Stock Exchange (PHLX) 494 20.4 Downward Pressures on Transactions Costs 494 20.4.1 A National Market System (NMS) 495 20.4.2 The SEC's Reg ATS 496 20.4.3 Reg FD 496 20.4.4 Decimalization of Stock Prices 496 20.4.5 Technological Advances 496 20.5 The Venerable Limit Order 497 20.5.1 What Are Limit Orders? 497 20.5.2 Creating Market Liquidity 498 20.6 Market Microstructure 498 20.6.1 Inventory Management 498 20.6.2 Brokers 499 20.7 High-Frequency Trading 499 20.8 Alternative Trading Systems (ATSs) 500 20.8.1 Crossing Networks 500 20.8.2 Dark Pools 500 20.9 Algorithmic Trading 501 20.9.1 Some Algorithmic Trading Applications 501 20.9.2 Trading Curbs 503 20.9.3 Conclusions about Algorithmic Trading 504 20.10 Symbiotic Stock Market Developments 505 20.11 Detrimental Stock Market Developments 505 20.12 Summary and Conclusions 506 Mathematical Appendixes 509 Bibliography 519 About the Authors 539 Author Index 541 Subject Index 547