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# Modern Portfolio Theory 2017-04-17

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CHAPTER 1 (Introduction)
1.1 The Portfolio Management Process 1
1.2 The Security Analyst’s Job 1
1.3 Portfolio Analysis 2
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

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 Diversification) 29
3.1 Reconsidering Risk 29
3.2 Utility Theory 32
3.3 Risk-Return Space 36
3.4 Diversification 38
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
4.6 Absolute Risk Aversion 59
4.7 Relative Risk Aversion 60
4.8 Measuring Risk Aversion 62
4.9 Portfolio Analysis 66
4.10 Indifference Curves 69
4.11 Summary and Conclusions 74
Appendix: Risk Aversion and Indifference Curves 75

PART THREE: Mean-Variance Portfolio Analysis
CHAPTER 5 (Graphical Portfolio Analysis) 85
5.1 Delineating Efficient 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
5.6 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

CHAPTER 6 (Efficient Portfolios) 113
6.1 Risk and Return for Two-Asset Portfolios 113
6.2 The Opportunity Set 114
6.3 Markowitz Diversification 120
6.4 Efficient 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 Erp) and σp

CHAPTER 7 (Advanced Mathematical Portfolio Analysis) 135
7.1 Efficient Portfolios without a Risk-Free Asset 135
7.2 Efficient 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 Efficient Frontier 152

CHAPTER 8 Index Models and Return-Generating Process 165
8.1 Single-Index Models 165
8.2 Efficient Frontier and the Single-Index Model 178
8.3 Two-Index Models 186
8.4 Multi-Index Models 189
8.5 Conclusions 190
Appendix: Index Models 191

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
9.4 Poisson Jump-Diffusion Process 206
9.5 Lognormal Distributions 206
9.6 Conclusions 213

CHAPTER 10 (Non-Mean-Variance Investment Decisions) 215
10.1 Geometric Mean Return Criterion 215
10.2 The Safety-First Criterion 218
10.3 Semivariance Analysis 228
10.4 Stochastic Dominance Criterion 236
10.5 Mean-Variance-Skewness Analysis 246
10.6 Summary and Conclusions 254
Appendix A: Stochastic Dominance 254
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
11.4 Other VaRs 269
11.5 Methods of Measuring VaR 270
11.6 Estimation of Volatilities 277
11.7 The Accuracy of VaR Models 282
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
12.3 The Capital Asset Pricing Model 295
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

CHAPTER 13 (Extensions of the Standard CAPM) 311
13.1 Risk-Free Borrowing or Lending 311
13.2 Homogeneous Expectations 316
13.3 Perfect Markets 318
13.4 Unmarketable Assets 322
13.5 Summary and Conclusions 323
Appendix: Derivations of a Non-Standard CAPM 324

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
14.3 Empirical Misspecifications in Cross-Sectional Regression Tests 345
14.4 Multivariate Tests 353
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
15.3 Conclusions 366
Appendix: Lognormality and the Consumption-Based CAPM 367

CHAPTER 16 (Arbitrage Pricing Theory) 371
16.1 Arbitrage Concepts 371
16.2 Index Arbitrage 375
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 Efficient Markets 395
17.2 Using Portfolio Theories to Construct and Select Portfolios 398
17.3 Security Analysis 400
17.4 Market Timing 401
17.5 Diversification 407
17.6 Constructing an Active Portfolio 415
17.7 Portfolio Revision 424
17.8 Summary and Conclusions 430
Appendix: Proofs for Some Ratios from Active Portfolios 431

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
18.5 Market Timing 449
18.6 Comparing Single-Parameter Portfolio Performance Measures 452
18.7 The Index of Total Portfolio Risk (ITPR) and the Portfolio Beta 454
18.8 Measurement Problems 457
18.9 Do Winners or Losers Repeat? 461
18.10 Summary about Investment Performance Evaluation 465
Appendix: Sharpe Ratio of an Active Portfolio 467

19.1 Factor Model Analysis 474
19.2 Return-Based Style Analysis 475
19.3 Return Decomposition-Based Analysis 479
19.4 Conclusions 485
Appendix: Regression Coefficients Estimation with Constraints 486

CHAPTER 20 (Stock Market Developments) 489
20.1 Recent NYSE Consolidations 489
20.2 International Securities Exchange (ISE) 492
20.3 Nasdaq 492
20.4 Downward Pressures on Transactions Costs 494
20.5 The Venerable Limit Order 497
20.6 Market Microstructure 498
20.8 Alternative Trading Systems (ATSs) 500
20.10 Symbiotic Stock Market Developments 505
20.11 Detrimental Stock Market Developments 505
20.12 Summary and Conclusions 506
Author
David Harper CFA FRM