Stochastic dominance: investment decision making under uncertainty
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| Format: | Book |
| Language: | English |
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Cham
Springer
[2016]
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| Edition: | Third edition |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xxii, 505 Seiten Diagramme (73 schwarz-weiß, 9 farbig) 235 mm x 155 mm, 0 g |
| ISBN: | 3319217070 9783319217079 |
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| 245 | 1 | 0 | |a Stochastic dominance |b investment decision making under uncertainty |c Haim Levy |
| 250 | |a Third edition | ||
| 264 | 1 | |a Cham |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xxii, 505 Seiten |b Diagramme (73 schwarz-weiß, 9 farbig) |c 235 mm x 155 mm, 0 g | ||
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| 653 | |a Research ; Zielgruppe | ||
| 653 | |a KJT ; BIC Subject Heading | ||
| 653 | |a Stochastic Dominance | ||
| 653 | |a Cumulative Prospect Theory | ||
| 653 | |a Non-Expected Utility | ||
| 653 | |a Risk | ||
| 653 | |a Prospect Theory | ||
| 653 | |a Prospect Stochastic Dominance | ||
| 653 | |a Mean-Variance Approach | ||
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Contents
1 Risk: Is There a Unique Objective Measure?. 1
1.1 What Is Risk?. 1
1.2 Measures of Risk. 4
a) Domar and Musgrave Risk Indexes. 4
b) Roy’s Safety First Rule. 6
c) Dispersion as a Risk Index: Variance
and Standard Deviation. 8
d) Semi-Variance (SV) as an Index of Risk. 10
e) Beta as a Measure of Risk. 11
f) Baumol’s Risk Measure. 11
g) Value at Risk- VaR(a). 13
h) Shortfall VaR. 13
i) Loss as an Alternative Cost: The Minimax Regret. 14
j) Expected Utility and Risk. 16
k) Risk Perception Versus Actual Risk; Behavioral
Economic Approach. 16
l) The “Fear Index”. 17
1.3 Summary. 18
2 Expected Utility Theory . . 21
2.1 Introduction. 21
2.2 Investment Criteria. 22
a) The Maximum Return Criterion (MRC). 22
b) The Maximum Expected Return Criterion (MERC). 24
2.3 The Axioms and Proof of the Maximum Expected
Utility Criterion (MEUC). 26
a) The Payoff of the Investments. 27
b) The Axioms. 27
c) Proof That the Maximum Expected Utility
Criterion (MEUC) Is Optimal Decision Rule. 29
XV
XVI
Contents
2.4 The Properties of Utility Function. 31
a) Preference and Expected Utility. 31
b) Is U(x) a Probability Function or a Utility Function?. 33
2.5 The Meaning of the Utility Units. 35
2.6 MRC, MERC as Special Cases of MEUC. 38
2.7 Utility, Wealth and Change of Wealth. 39
2.8 Summary. 40
3 Stochastic Dominance Decision Rules. 41
3.1 Partial Ordering: Efficient and Inefficient Sets. 41
3.2 First Degree Stochastic Dominance (FSD). 44
a) Probability Function, Density Function
and Cumulative Probability Function. 44
b) The FSD Rule. 47
c) Graphical Exposition of the FSD Rule. 51
d) FSD: A Numerical Example of FSD. 52
e) The Intuitive Explanation of FSD. 54
3.3 Optimal Rule, Sufficient Rules and Necessary
Rules for FSD. 55
a) Sufficient Rules. 57
b) Necessary Rules. 59
3.4 FSD, Correlation and Arbitrage. 61
3.5 Type I and Type II Errors When Sufficient Rules
or Necessary Rules Are Employed. 63
3.6 Second Degree Stochastic Dominance (SSD). 65
a) Risk Aversion. 65
b) Idle SSD Investment Decision Rule. 67
c) Graphical Exposition of SSD. 70
d) An Intuitive Explanation of SSD. 75
3.7 Sufficient Rules and Necessary Rules for SSD. 78
a) Sufficient Rules. 78
b) Necessary Rules. 79
3.8 Third Degree Stochastic Dominance (TSD) . . 80
a) A Preference for Positive Skewness as
a Motivation for TSD . 80
b) The Definition of Skewness. 81
c) Lottery, Insurance and Preference
for Positive Skewness . *. 83
d) Empirical Studies and Positive Skewness
Preference (or U/7/ 0). 84
e) Decreasing Absolute Risk Aversion (DARA),
and Positive Skewness Preferences (or U/7/ 0). 87
f) The Third Degree Stochastic Dominance (TSD)
Investment Rule. 87
g) Graphical Exposition of TSD. 93
h) The Intuitive Explanation of TSD. 100
Contents XV ii
3.9 Sufficient Rules and Necessary Rules for UëU3. 104
a) Sufficient Rules. 104
b) Necessary Rules. 104
3.10 Decreasing Absolute Risk Aversion (DARA)
Stochastic Dominance (DSD). 105
a) DARA Utility Functions. 105
b) DSD with Equal Mean Distributions. 107
3.11 Risk-Seeking Stochastic Dominance (RSSD):
The SSD Rule. 110
a) The Risk-Seeking Stochastic Dominance (RSSD) Rule. 110
b) Graphical Exposition of SSD. 112
c) The Relationship Between SSD and SSD. 113
d) The Relationship Between FSD, SSD and SSD. 114
3.12 Nth Order Stochastic Dominance. 115
3.13 Stochastic Dominance Rules: Extension
to Discrete Distributions. 116
3.14 The Role of the Mean and Variance in Stochastic
Dominance Rules. 121
3.15 Summary. 123
4 Stochastic Dominance: The Quantile Approach. 125
4.1 The Quantile Function. 125
4.2 Stochastic Dominance Rules: The Quantile Approach. 129
a) The FSD Rule with Quantiles. 130
b) The SSD Rule with Quantiles. 133
4.3 Stochastic Dominance Rules with a Riskless Asset:
A Perfect Capital Market. 137
a) FSD with a Riskless Asset: The FSDR Rule. 137
b) Graphical Illustration of the FSDR Rule. 141
c) SSD with a Riskless Asset: The SSDR Rule. 143
d) The SD and SDR Efficient Sets. 149
4.4 Stochastic Dominance Rules with a Riskless Asset:
An Imperfect Capital Market. 149
4.5 Summary. 152
5 Algorithms for Stochastic Dominance. 155
5.1 Using the Necessary Conditions and Transitivity
to Reduce the Number of Comparisons. 156
5.2 The FSD Algorithm. 159
5.3 The SSD Algorithm. 160
5.4 The TSD Algorithm. 164
5.5 A Numerical Example Showing the Flaw
in Existing TSD Algorithm. 169
5.6 The Empirical Results. 130
xvni Contents
5.7 The SDR Algorithm. 172
a) FSDR Algorithm. 172
b) SSDR Algorithm. 173
5.8 Summary. 174
6 Stochastic Dominance with Specific Distributions. 177
6.1 Normal Distributions. 178
a) Properties of the Normal Distribution. 178
b) Dominance Without a Riskless Asset. 180
c) Dominance with a Riskless Asset. 183
6.2 Lognormal Distributions. 185
a) Properties of the Lognormal Distribution. 185
Ե) Dominance Without a Riskless Asset. 187
c) Dominance with a Riskless Asset. 189
6.3 Truncated Normal Distributions. 191
a) Symmetrical Truncation. 191
b) Non-symmetrical Truncation. 195
6.4 Distributions That Intercept Once. 197
6.5 Summary. 199
7 Almost Stochastic Dominance (ASD). 201
7.1 The Possible Paradoxes. 202
7.2 FSD* Criterion Corresponding to UJ(e). 206
7.3 The SSD* Criterion Corresponding to Սշ(ր). 210
7.4 The Effectiveness of the Almost SD Rules. 218
7.5 Application of FSD* to Investment Choices: Stocks
Versus Bonds. 219
a) The Decrease in the Violation Area as the
Horizon Increases. 219
Ե) Moshe Levy’s Study: The Preference Set
May Decrease Rather Than Increase with the
Increase in the Horizon. 221
7.6 ASD: Experimental Results . ,. 222
7.7 Summary. 225
8 Stochastic Dominance and Risk Measures. 227
8.1 When Is One Investment Riskier Than
Another Investment?. 228
8.2 Mean Preserving Spread (MPS). 229
8.3 Unequal Means and “Riskier Than” with the
Riskless Asset. 232
8.4 “Riskier Than” and DARA Utility Function:
Mean Preserving Antispread. 235
a) Spread and Antispread. 236
b) Increasing Risk and DARA. 237
8.5 Summary. 238
Contents
XIX
9 Stochastic Dominance and Diversification. 239
9.1 Arrow’s Conditions for Diversification and SD Rules. 240
a) Diversification with One Risky and the
Riskless Asset. 240
b) The Effect of Shifts in Parameters
or Diversification. 246
9.2 Extension of the SD Analyses to the Case
of Two Risky Assets. 247
9.3 Diversification and Expected Utility: Some
Common Utility Functions. 251
a) Shift in r. 252
b) Shift in X. 253
c) MPS Shifts. 254
d) MPA Shifts. 255
e) MPS A Shifts. 256
9.4 Improving Diversification: The Marginal Conditional
Stochastic Dominance (MCSD) Approach. 256
9.5 Linear Programing Approach and Efficient
SSD Diversification. 260
9.6 The Mean Gini Diversification Model. 261
9.7 Summary. 262
10 The CAPM and Stochastic Dominance. 265
10.1 The CAPM with Heterogeneous Investment Horizons. 266
a) Quadratic Utility Function. 267
b) Single-Period Normal Distributions. 268
c) Multi-period Normal Distributions. 270
d) Log-Normal Distributions. 271
10.2 Summary. 279
11 The Empirical Studies: Dominance and Significance Tests. 281
11.1 The Effectiveness of the Various Decision Rules:
A Perfect Market. 283
11.2 The Effectiveness of the Various Decision Rules:
An Imperfect Market. 288
11.3 The Performance of Mutual Funds with
Transaction Costs. 290
11.4 Further Reduction in the Efficient Sets:
Convex Stochastic Dominance (CSD). 293
a) FSD, CSD with. Three Assets in the
Efficient Set (N=3). 294
b) Extension to N Assets in the FSD Efficient Set. 295
11.5 Sampling Errors: Test for Significance of SD. 298
a) Kolmogorov-Smimov: One Sample Test. 298
b) Kolmogorov—Smirnov: Two-Sample Test. 299
XX
Contents
c) The First Phase of Statistical Studies: Pairwise
Comparisons Without Diversification. 301
d) The Second Phase of Studies: Income Inequality
and Diversification. 304
11.6 Summary. 307
12 Applications of Stochastic Dominance Rules. 309
12.1 Capital Structure and the Value of the Firm. 309
12.2 Production, Saving and Diversification. 312
12.3 Estimating the Probability of Bankruptcy. 314
12.4 Option Evaluation, Insurance Premium
and Portfolio Insurance. 316
12.5 Application of SD Rules in Agricultural Economics. 319
12.6 Application of SD Rules in Medicine. 320
a) Stochastic Dominance Rules and Medical Decision. 320
b) Employing SD Rules in the Small Abdominal
Aortic Aneurysms Case: Actual Data. 326
12.7 Measuring, Welfare, Poverty and Income Inequality. 329
12.8 Summary. 332
13 Mean-Variance, Stochastic Dominance and
the Investment Horizon. 333
13.1 Tobin’s MV Multi-period Analysis. 334
13.2 Sharpe’s Reward-to-Variability Ratio
and the Investment Horizon. 336
13.3 The Effect of the Investment Horizon on Correlations. 339
13.4 The Effect of the Investment Horizon on the
Composition of MV Portfolios. 342
13.5 The Effect of the Investment Horizon on Beta. 345
13.6 Stochastic Dominance and the Investment Horizon. 348
13.7 Contrasting the Size of the MV and SD Efficient Set. 351
13.8 Summary ։ 353
14 Stocks Versus Bonds: A Stochastic Dominance Approach. 355
14.1 The Geometric Mean Investment Rule
for the Very Long Horizon. 356
14.2 The MGM Portfolio and Expected Utility. 362
a) The Contradiction Between MGM Rule and
the Myopic Utility Functions. 362
b) A Suggested Resolution of the MGM Rule
and Expected Utility Contradictory Results. 364
14.3 Long But Finite Horizon: FSD and Almost FSD
with Log-Normal Distributions. 366
Contents
XXI
14.4 The Empirical Evidence. 373
a) Investment for the Long Run: Ibbotson’s Data. 373
b) The AFSD in the Long Run: The Study of Bali et al. 375
14.5 The MV and the Log-Normal Efficient Frontiers. 379
14.6 Summary. 385
15 Non-expected Utility and Stochastic Dominance. 389
15.1 The Expected Utility: Some Paradoxes. 391
a) The Allars Paradox. 391
b) The Ellsberg Paradox: Ambiguity Aversion. 393
15.2 Non֊expected Utility Theory. 394
a) Probability Weighting. 395
b) PT’s Decision Weights. 397
c) CPT’s Decision Weights: No FSD Violation. 398
d) Rank Dependent Expected Utility (RDEU) and FSD. 399
e) Configural Decision Weights. 401
f) Regret Theory. 401
15.3 FSD Violations: Decision Weights or Bounded Rationality? . . . 403
15.4 Temporary and Permanent Attitude Toward Risk. 409
15.5 Summary. 413
16 Stochastic Dominance and Prospect Theory. 415
16.1 CPT, Expected Utility and FSD Rule. 417
16.2 Prospect Stochastic Dominance (PSD). 418
16.3 Markowitz's Stochastic Dominance. 425
16.4 CPT, MV and the CAPM. 430
16.5 Experimental Testing the Competing Theories:
SD Approach. 433
a) The Certainty Equivalent Approach. 433
b) The Stochastic Dominance Approach. 435
c) Are People Risk Averse? (SSD Tests). 435
d) Is CPT Valid Theory? (PSD Tests). 436
16.6 SSD, PSD, MSD Rules and the Efficiency
of the Market Portfolio . 437
16.7 Summary. 440
17 Bivariate FSD (BFSD). . 441
17.1 The Suggested Bivariate Preferences. 443
a) The Suggested Bivariate Preference by Abel. 443
b) The Ultimatum Game Experiments and the
Suggested Bivariate Preferences. 444
17.2 Bivariate First Degree Stochastic Dominance. 447
17.3 The Cross Derivative and Attitude Toward Correlation. 457
17.4 Summary. 464
xxii Contents
18 Future Research. 467
18.1 Portfolio Construction and Stochastic Dominance
Equilibrium . 467
18.2 Risk Attitude and Equilibrium. 471
18.3 The Stochastic Dominance Rules and the Length
of the Investment Horizon. 473
18.4 Uncertain Investment Horizon. 476
18.5 Risk Index. 476
18.6 Stochastic Dominance and Increasing Interest Rate. 477
18.7 Truncated Distributions and Stochastic Dominance. 477
18.8 Employing Stochastic Dominance Criteria in Other
Research Areas. . . 478
18.9 Refining the Stochastic Dominance Criteria. . 479
18.10 Stochastic Dominance and Option Valuation. . 480
18.11 Experimental Stochastic Dominance Criteria. 480
18.12 Multivariate Stochastic Dominance. 481
18.13 Conditional Dominance (Monotonicity). 481
Bibliography. 483
Index. 501 |
| any_adam_object | 1 |
| author | Levy, Haim 1939- |
| author_GND | (DE-588)170156605 |
| author_facet | Levy, Haim 1939- |
| author_role | aut |
| author_sort | Levy, Haim 1939- |
| author_variant | h l hl |
| building | Verbundindex |
| bvnumber | BV043176003 |
| classification_rvk | QK 800 QP 720 |
| classification_tum | MAT 624f WIR 160f |
| ctrlnum | (OCoLC)935825702 (DE-599)DNB1072310090 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Third edition |
| format | Book |
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| id | DE-604.BV043176003 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T02:48:04Z |
| institution | BVB |
| institution_GND | (DE-588)1064344704 |
| isbn | 3319217070 9783319217079 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028600085 |
| oclc_num | 935825702 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | xxii, 505 Seiten Diagramme (73 schwarz-weiß, 9 farbig) 235 mm x 155 mm, 0 g |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| spelling | Levy, Haim 1939- Verfasser (DE-588)170156605 aut Stochastic dominance investment decision making under uncertainty Haim Levy Third edition Cham Springer [2016] © 2016 xxii, 505 Seiten Diagramme (73 schwarz-weiß, 9 farbig) 235 mm x 155 mm, 0 g txt rdacontent n rdamedia nc rdacarrier Finanzanalyse (DE-588)4133000-6 gnd rswk-swf Investitionsentscheidung (DE-588)4162244-3 gnd rswk-swf Stochastische Dominanz (DE-588)4219516-0 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Research ; Zielgruppe KJT ; BIC Subject Heading Stochastic Dominance Cumulative Prospect Theory Non-Expected Utility Risk Prospect Theory Prospect Stochastic Dominance Mean-Variance Approach Finanzanalyse (DE-588)4133000-6 s Stochastischer Prozess (DE-588)4057630-9 s Investitionsentscheidung (DE-588)4162244-3 s Entscheidungstheorie (DE-588)4138606-1 s 1\p DE-604 Entscheidung bei Unsicherheit (DE-588)4070864-0 s Stochastische Dominanz (DE-588)4219516-0 s 2\p DE-604 Springer International Publishing (DE-588)1064344704 pbl Erscheint auch als Online-Ausgabe 978-3-319-21708-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5291631&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028600085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Levy, Haim 1939- Stochastic dominance investment decision making under uncertainty Finanzanalyse (DE-588)4133000-6 gnd Investitionsentscheidung (DE-588)4162244-3 gnd Stochastische Dominanz (DE-588)4219516-0 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4133000-6 (DE-588)4162244-3 (DE-588)4219516-0 (DE-588)4070864-0 (DE-588)4138606-1 (DE-588)4057630-9 |
| title | Stochastic dominance investment decision making under uncertainty |
| title_auth | Stochastic dominance investment decision making under uncertainty |
| title_exact_search | Stochastic dominance investment decision making under uncertainty |
| title_full | Stochastic dominance investment decision making under uncertainty Haim Levy |
| title_fullStr | Stochastic dominance investment decision making under uncertainty Haim Levy |
| title_full_unstemmed | Stochastic dominance investment decision making under uncertainty Haim Levy |
| title_short | Stochastic dominance |
| title_sort | stochastic dominance investment decision making under uncertainty |
| title_sub | investment decision making under uncertainty |
| topic | Finanzanalyse (DE-588)4133000-6 gnd Investitionsentscheidung (DE-588)4162244-3 gnd Stochastische Dominanz (DE-588)4219516-0 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Finanzanalyse Investitionsentscheidung Stochastische Dominanz Entscheidung bei Unsicherheit Entscheidungstheorie Stochastischer Prozess |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=5291631&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028600085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT levyhaim stochasticdominanceinvestmentdecisionmakingunderuncertainty AT springerinternationalpublishing stochasticdominanceinvestmentdecisionmakingunderuncertainty |