Levy Stochastic Dominance

Investment Decision Making under Uncertainty
3rd Auflage 2016
ISBN: 978-3-319-21708-6
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 517 Seiten

This fully updated third edition is devoted to the analysis of various Stochastic Dominance (SD) decision rules. It discusses the pros and cons of each of the alternate SD rules, the application of these rules to various research areas like statistics, agriculture, medicine, measuring income inequality and the poverty level in various countries, and of course, to investment decision-making under uncertainty. The book features changes and additions to the various chapters, and also includes two completely new chapters. One deals with asymptotic SD and the relation between FSD and the maximum geometric mean (MGM) rule (or the maximum growth portfolio). The other new chapter discusses bivariate SD rules where the individual's utility is determined not only by his own wealth, but also by his standing relative to his peer group. Stochastic Dominance: Investment Decision Making under Uncertainty, 3rd Ed. covers the following basic issues: the SD approach, asymptotic SD rules, the mean-variance (MV) approach, as well as the non-expected utility approach. The non-expected utility approach focuses on Regret Theory (RT) and mainly on prospect theory (PT) and its modified version, cumulative prospect theory (CPT) which assumes S-shape preferences. In addition to these issues the book suggests a new stochastic dominance rule called the Markowitz stochastic dominance (MSD) rule corresponding to all reverse-S-shape preferences. It also discusses the concept of the multivariate expected utility and analyzed in more detail the bivariate expected utility case.From the reviews of the second edition:'This book is an economics book about stochastic dominance. ... is certainly a valuable reference for graduate students interested in decision making under uncertainty. It investigates and compares different approaches and presents many examples. Moreover, empirical studies and experimental results play an important role in this book, which makes it interesting to read.' (Nicole Bäuerle, Mathematical Reviews, Issue 2007 d)

Prof. Levy was born in Jerusalem in 1939. He received his PhD from the Hebrew University in 1969 and in 1976 was promoted to full professorship. He developed a new field of financial economics called Stochastic Dominance, and developed economic models for risk-management, especially risk-reduction in investment, by means of international diversification and mergers and acquisitions. He served as economic advisor to the Bank of Israel; the Israeli Ministry of Finance; Ministry of Industry, Trade and Labor; and Ministry of National Infrastructures, among other government offices. His many awards include the Hebrew University's Prize for Excellence in Research for 1996. The two 1990 Nobel Prize winners in Economics stated that to a large extent their work draws on Prof. Levy's pioneering writings.

Autoren/Hrsg.

Levy, Haim

Inhaltsverzeichnis

1;Preface;8
1.1;The Structure of the Book;11
1.2;The Main Changes in the Third Edition;13
1.3;Audience;14
1.4;Acknowledgements;15
2;Contents;16
3;Chapter 1: Risk: Is There a Unique Objective Measure?;24
3.1;1.1 What Is Risk?;24
3.2;1.2 Measures of Risk;27
3.2.1;a)?Domar and Musgrave Risk Indexes;27
3.2.2;b)?Roy´s Safety First Rule;29
3.2.3;c)?Dispersion as a Risk Index: Variance and Standard Deviation;31
3.2.4;d)?Semi-Variance (SV) as an Index of Risk;33
3.2.5;e)?Beta as a Measure of Risk;34
3.2.6;f)?Baumol´s Risk Measure;34
3.2.7;g)?Value at Risk-VaR(?);36
3.2.8;h)?Shortfall VaR;36
3.2.9;i)?Loss as an Alternative Cost: The Minimax Regret;37
3.2.10;j)?Expected Utility and Risk;39
3.2.11;k)?Risk Perception Versus Actual Risk; Behavioral Economic Approach;39
3.2.12;l)?The ``Fear Index´´;40
3.3;1.3 Summary;41
4;Chapter 2: Expected Utility Theory;43
4.1;2.1 Introduction;43
4.2;2.2 Investment Criteria;44
4.2.1;a) The Maximum Return Criterion (MRC);44
4.2.2;b) The Maximum Expected Return Criterion (MERC);46
4.3;2.3 The Axioms and Proof of the Maximum Expected Utility Criterion (MEUC);48
4.3.1;a) The Payoff of the Investments;49
4.3.2;b) The Axioms;49
4.3.3;c) Proof That the Maximum Expected Utility Criterion (MEUC) Is Optimal Decision Rule;51
4.4;2.4 The Properties of Utility Function;53
4.4.1;a) Preference and Expected Utility;53
4.4.2;b) Is U(x) a Probability Function or a Utility Function?;55
4.5;2.5 The Meaning of the Utility Units;57
4.6;2.6 MRC, MERC as Special Cases of MEUC;60
4.7;2.7 Utility, Wealth and Change of Wealth;61
4.8;2.8 Summary;62
5;Chapter 3: Stochastic Dominance Decision Rules;63
5.1;3.1 Partial Ordering: Efficient and Inefficient Sets;63
5.2;3.2 First Degree Stochastic Dominance (FSD);66
5.2.1;a) Probability Function, Density Function and Cumulative Probability Function;66
5.2.2;b) The FSD Rule;69
5.2.3;c) Graphical Exposition of the FSD Rule;73
5.2.4;d) FSD: A Numerical Example of FSD;74
5.2.5;e) The Intuitive Explanation of FSD;76
5.3;3.3 Optimal Rule, Sufficient Rules and Necessary Rules for FSD;77
5.3.1;a) Sufficient Rules;79
5.3.2;b) Necessary Rules;81
5.4;3.4 FSD, Correlation and Arbitrage;83
5.5;3.5 Type I and Type II Errors When Sufficient Rules or Necessary Rules Are Employed;85
5.6;3.6 Second Degree Stochastic Dominance (SSD);87
5.6.1;a) Risk Aversion;87
5.6.2;b) The SSD Investment Decision Rule;89
5.6.3;c) Graphical Exposition of SSD;92
5.6.4;d) An Intuitive Explanation of SSD;97
5.7;3.7 Sufficient Rules and Necessary Rules for SSD;100
5.7.1;a) Sufficient Rules;100
5.7.2;b) Necessary Rules;101
5.8;3.8 Third Degree Stochastic Dominance (TSD);102
5.8.1;a) A Preference for Positive Skewness as a Motivation for TSD;102
5.8.2;b) The Definition of Skewness;103
5.8.3;c) Lottery, Insurance and Preference for Positive Skewness;105
5.8.4;d) Empirical Studies and Positive Skewness Preference (or U0);106
5.8.5;e) Decreasing Absolute Risk Aversion (DARA), and Positive Skewness Preferences (or U0);109
5.8.6;f) The Third Degree Stochastic Dominance (TSD) Investment Rule;109
5.8.7;g) Graphical Exposition of TSD;115
5.8.8;h) The Intuitive Explanation of TSD;121
5.9;3.9 Sufficient Rules and Necessary Rules for UU3;126
5.9.1;a) Sufficient Rules;126
5.9.2;b) Necessary Rules;126
5.10;3.10 Decreasing Absolute Risk Aversion (DARA) Stochastic Dominance (DSD);127
5.10.1;a) DARA Utility Functions;127
5.10.2;b) DSD with Equal Mean Distributions;129
5.11;3.11 Risk-Seeking Stochastic Dominance (RSSD): The Rule;132
5.11.1;a) The Risk-Seeking Stochastic Dominance (RSSD) Rule;132
5.11.2;b) Graphical Exposition of;134
5.11.3;c) The Relationship Between SSD and;135
5.11.4;d) The Relationship Between FSD, SSD and;136
5.12;3.12 Nth Order Stochastic Dominance;137
5.13;3.13 Stochastic Dominance Rules: Extension to Discrete Distributions;138
5.14;3.14 The Role of the Mean and Variance in Stochastic Dominance Rules;143
5.15;3.15 Summary;145
6;Chapter 4: Stochastic Dominance: The Quantile Approach;147
6.1;4.1?The Quantile Function;147
6.2;4.2?Stochastic Dominance Rules: The Quantile Approach;151
6.2.1;a)?The FSD Rule with Quantiles;152
6.2.2;b)?The SSD Rule with Quantiles;155
6.3;4.3?Stochastic Dominance Rules with a Riskless Asset: A Perfect Capital Market;159
6.3.1;a)?FSD with a Riskless Asset: The FSDR Rule;159
6.3.2;b)?Graphical Illustration of the FSDR Rule;163
6.3.3;c)?SSD with a Riskless Asset: The SSDR Rule;165
6.3.4;d)?The SD and SDR Efficient Sets;171
6.4;4.4?Stochastic Dominance Rules with a Riskless Asset: An Imperfect Capital Market;171
6.5;4.5?Summary;174
7;Chapter 5: Algorithms for Stochastic Dominance;176
7.1;5.1?Using the Necessary Conditions and Transitivity to Reduce the Number of Comparisons;177
7.2;5.2?The FSD Algorithm;180
7.3;5.3?The SSD Algorithm;181
7.4;5.4?The TSD Algorithm;185
7.5;5.5?A Numerical Example Showing the Flaw in Existing TSD Algorithm;190
7.6;5.6?The Empirical Results;191
7.7;5.7?The SDR Algorithm;193
7.7.1;a)?FSDR Algorithm;193
7.7.2;b)?SSDR Algorithm;194
7.8;5.8?Summary;195
8;Chapter 6: Stochastic Dominance with Specific Distributions;197
8.1;6.1?Normal Distributions;198
8.1.1;a)?Properties of the Normal Distribution;198
8.1.2;b)?Dominance Without a Riskless Asset;200
8.1.3;c)?Dominance with a Riskless Asset;203
8.2;6.2?Lognormal Distributions;205
8.2.1;a)?Properties of the Lognormal Distribution;205
8.2.2;b)?Dominance Without a Riskless Asset;207
8.2.3;c)?Dominance with a Riskless Asset;209
8.3;6.3?Truncated Normal Distributions;211
8.3.1;a)?Symmetrical Truncation;211
8.3.2;b)?Non-symmetrical Truncation;215
8.4;6.4?Distributions That Intercept Once;217
8.5;6.5 Summary;219
9;Chapter 7: Almost Stochastic Dominance (ASD);220
9.1;7.1?The Possible Paradoxes;221
9.2;7.2?FSD* Criterion Corresponding to U1*(epsi);225
9.3;7.3?The SSD* Criterion Corresponding to U2*(epsi);229
9.4;7.4?The Effectiveness of the Almost SD Rules;237
9.5;7.5?Application of FSD* to Investment Choices: Stocks Versus Bonds;238
9.5.1;a)?The Decrease in the Violation Area as the Horizon Increases;238
9.5.2;b)?Moshe Levy´s Study: The Preference Set May Decrease Rather Than Increase with the Increase in the Horizon;240
9.6;7.6?ASD: Experimental Results;241
9.7;7.7?Summary;244
10;Chapter 8: Stochastic Dominance and Risk Measures;245
10.1;8.1?When Is One Investment Riskier Than Another Investment?;246
10.2;8.2?Mean Preserving Spread (MPS);247
10.3;8.3?Unequal Means and ``Riskier Than´´ with the Riskless Asset;250
10.4;8.4?``Riskier Than´´ and DARA Utility Function: Mean Preserving Antispread;253
10.4.1;a)?Spread and Antispread;254
10.4.2;b)?Increasing Risk and DARA;255
10.5;8.5?Summary;256
11;Chapter 9: Stochastic Dominance and Diversification;257
11.1;9.1?Arrow´s Conditions for Diversification and SD Rules;258
11.1.1;a)?Diversification with One Risky and the Riskless Asset;258
11.1.2;b)?The Effect of Shifts in Parameters or Diversification;264
11.2;9.2?Extension of the SD Analyses to the Case of Two Risky Assets;265
11.3;9.3?Diversification and Expected Utility: Some Common Utility Functions;269
11.3.1;a)?Shift in r;270
11.3.2;b)?Shift in X;271
11.3.3;c)?MPS Shifts;272
11.3.4;d)?MPA Shifts;273
11.3.5;e)?MPSA Shifts;274
11.4;9.4?Improving Diversification: The Marginal Conditional Stochastic Dominance (MCSD) Approach;274
11.5;9.5?Linear Programing Approach and Efficient SSD Diversification;278
11.6;9.6?The Mean Gini Diversification Model;279
11.7;9.7?Summary;280
12;Chapter 10: The CAPM and Stochastic Dominance;282
12.1;10.1?The CAPM with Heterogeneous Investment Horizons;283
12.1.1;a)?Quadratic Utility Function;284
12.1.2;b)?Single-Period Normal Distributions;285
12.1.3;c)?Multi-period Normal Distributions;287
12.1.4;d)?Log-Normal Distributions;288
12.1.4.1;(1) ?Stationary Distributions;288
12.1.4.2;(2)?Non-stationary Distributions of Returns;295
12.2;10.2?Summary;296
13;Chapter 11: The Empirical Studies: Dominance and Significance Tests;298
13.1;11.1?The Effectiveness of the Various Decision Rules: A Perfect Market;300
13.2;11.2?The Effectiveness of the Various Decision Rules: An Imperfect Market;305
13.3;11.3?The Performance of Mutual Funds with Transaction Costs;307
13.4;11.4?Further Reduction in the Efficient Sets: Convex Stochastic Dominance (CSD);310
13.4.1;a)?FSD, CSD with Three Assets in the Efficient Set (N=3);311
13.4.2;b)?Extension to N Assets in the FSD Efficient Set;312
13.5;11.5?Sampling Errors: Test for Significance of SD;315
13.5.1;a)?Kolmogorov-Smirnov: One Sample Test;315
13.5.2;b)?Kolmogorov-Smirnov: Two-Sample Test;316
13.5.3;c)?The First Phase of Statistical Studies: Pairwise Comparisons Without Diversification;318
13.5.4;d)?The Second Phase of Studies: Income Inequality and Diversification;321
13.6;11.6?Summary;324
14;Chapter 12: Applications of Stochastic Dominance Rules;325
14.1;12.1?Capital Structure and the Value of the Firm;325
14.2;12.2?Production, Saving and Diversification;328
14.3;12.3?Estimating the Probability of Bankruptcy;330
14.4;12.4?Option Evaluation, Insurance Premium and Portfolio Insurance;332
14.5;12.5?Application of SD Rules in Agricultural Economics;335
14.6;12.6?Application of SD Rules in Medicine;336
14.6.1;a)?Stochastic Dominance Rules and Medical Decision;336
14.6.2;b)?Employing SD Rules in the Small Abdominal Aortic Aneurysms Case: Actual Data;342
14.7;12.7?Measuring, Welfare, Poverty and Income Inequality;345
14.8;12.8?Summary;348
15;Chapter 13: Mean-Variance, Stochastic Dominance and the Investment Horizon;349
15.1;13.1?Tobin´s MV Multi-period Analysis;350
15.2;13.2?Sharpe´s Reward-to-Variability Ratio and the Investment Horizon;352
15.3;13.3?The Effect of the Investment Horizon on Correlations;355
15.4;13.4?The Effect of the Investment Horizon on the Composition of MV Portfolios;358
15.5;13.5?The Effect of the Investment Horizon on Beta;361
15.6;13.6?Stochastic Dominance and the Investment Horizon;364
15.7;13.7?Contrasting the Size of the MV and SD Efficient Set;367
15.8;13.8?Summary;369
16;Chapter 14: Stocks Versus Bonds: A Stochastic Dominance Approach;370
16.1;14.1?The Geometric Mean Investment Rule for the Very Long Horizon;371
16.2;14.2?The MGM Portfolio and Expected Utility;377
16.2.1;a)?The Contradiction Between MGM Rule and the Myopic Utility Functions;377
16.2.2;b)?A Suggested Resolution of the MGM Rule and Expected Utility Contradictory Results;379
16.3;14.3?Long But Finite Horizon: FSD and Almost FSD with Log-Normal Distributions;381
16.4;14.4?The Empirical Evidence;388
16.4.1;a)?Investment for the Long Run: Ibbotson´s Data;388
16.4.2;b)?The AFSD in the Long Run: The Study of Bali et al.;390
16.5;14.5?The MV and the Log-Normal Efficient Frontiers;394
16.6;14.6?Summary;400
17;Chapter 15: Non-expected Utility and Stochastic Dominance;404
17.1;15.1?The Expected Utility: Some Paradoxes;406
17.1.1;a)?The Allais Paradox;406
17.1.2;b)?The Ellsberg Paradox: Ambiguity Aversion;408
17.2;15.2?Non-expected Utility Theory;409
17.2.1;a)?Probability Weighting;410
17.2.2;b)?PT´s Decision Weights;412
17.2.3;c)?CPT´s Decision Weights: No FSD Violation;413
17.2.4;d)?Rank Dependent Expected Utility (RDEU) and FSD;414
17.2.5;e)?Configural Decision Weights;416
17.2.6;f)?Regret Theory;416
17.3;15.3?FSD Violations: Decision Weights or Bounded Rationality?;418
17.4;15.4?Temporary and Permanent Attitude Toward Risk;424
17.5;15.5?Summary;428
18;Chapter 16: Stochastic Dominance and Prospect Theory;430
18.1;16.1?CPT, Expected Utility and FSD Rule;432
18.2;16.2?Prospect Stochastic Dominance (PSD);433
18.3;16.3?Markowitz´s Stochastic Dominance;440
18.4;16.4?CPT, MV and the CAPM;445
18.5;16.5?Experimental Testing the Competing Theories: SD Approach;448
18.5.1;a) The Certainty Equivalent Approach;448
18.5.2;b) The Stochastic Dominance Approach;450
18.5.3;c) Are People Risk Averse? (SSD Tests);450
18.5.4;d) Is CPT Valid Theory? (PSD Tests);451
18.6;16.6?SSD, PSD, MSD Rules and the Efficiency of the Market Portfolio;452
18.7;16.7?Summary;455
19;Chapter 17: Bivariate FSD (BFSD);456
19.1;17.1?The Suggested Bivariate Preferences;458
19.1.1;a)?The Suggested Bivariate Preference by Abel;458
19.1.2;b)?The Ultimatum Game Experiments and the Suggested Bivariate Preferences;459
19.2;17.2?Bivariate First Degree Stochastic Dominance;462
19.3;17.3?The Cross Derivative and Attitude Toward Correlation;472
19.4;17.4?Summary;479
20;Chapter 18: Future Research;481
20.1;18.1?Portfolio Construction and Stochastic Dominance Equilibrium;481
20.2;18.2?Risk Attitude and Equilibrium;485
20.3;18.3?The Stochastic Dominance Rules and the Length of the Investment Horizon;487
20.4;18.4?Uncertain Investment Horizon;490
20.5;18.5?Risk Index;490
20.6;18.6?Stochastic Dominance and Increasing Interest Rate;491
20.7;18.7?Truncated Distributions and Stochastic Dominance;491
20.8;18.8?Employing Stochastic Dominance Criteria in Other Research Areas;492
20.9;18.9?Refining the Stochastic Dominance Criteria;493
20.10;18.10?Stochastic Dominance and Option Valuation;494
20.11;18.11?Experimental Stochastic Dominance Criteria;494
20.12;18.12?Multivariate Stochastic Dominance;495
20.13;18.13?Conditional Dominance (Monotonicity);495
21;Bibliography;496
22;Index;513