Stochastic dominance: investment decision making under uncertainty
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| Format: | Electronic eBook |
|---|---|
| Language: | English |
| Published: |
New York
Springer
2006
|
| Edition: | 2. ed. |
| Series: | Studies in risk and uncertainty
12 |
| Subjects: | |
| Online Access: | BTU01 FHM01 FHR01 UBG01 UBR01 UBT01 UBY01 UEI03 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 0387293027 9780387293028 9780387293110 |
| DOI: | 10.1007/0-387-29311-6 |
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| adam_text | TABLE OF CONTENTS
Preface
1
On the Measurement of Risk 7
1.1 What is Risk?
1.2 Measures of Risk
a) Domar and Musgrave Risk Indexes
b) Roy s Safety First Rule
c) Dispersion as a Risk Index: Variance and Standard Deviation
d) Semi variance (SV) as an index of risk
e) Baumol s Risk Measure
f) Value at risk VaR( a)
g) Shortfall VaR
1.3 Summary
2
Expected Utility Theory 25
2.1 Introduction
2.2 Investment Criteria
a) The Maximum Return Criterion (MRC)
b) The Maximum Expected Return Criterion (MERC)
2.3 The Axioms and Proof of the Maximum Expected Utility
Criterion (MEUC)
a) The Payoff of the Investments
b) The Axioms
c) Proof that the Maximum Expected Utility Criterion (MEUC)
is Optimal Decision Rule
2.4 The Properties of Utility Function
a) Preference and Expected Utility
b) Is U(x) a Probability Function or a Utility Function?
2.5 The Meaning of the Utility Units
2.6 MRC, MERC as Special Cases of MEUC
2.7 Utility, Wealth and Change of Wealth
2.8 Summary
viii STOCHASTIC DOMINANCE
3
Stochastic Dominance Decision Rules 49
3.1 Partial Ordering: Efficient and Inefficient Sets
a) The Objective Decision
b) The Subjective Decision
3.2 First Degree Stochastic Dominance (FSD)
a) Probability Function, Density Function and Cumulating
Probability Function
b) The FSD Rule
c) The Graphical Exposition of the FSD Rule
d) FSD: A Numerical Example of FSD
e) The Intuitive Explanation of FSD
3.3 Optimal Rule, Sufficient Rules and Necessary Rules for FSD
a) Sufficient Rules
b) Necessary Rules
3.4 Type I and Type II Errors When Sufficient Rules or Necessary
Rules are not Optimal for Investment Screening
3.5 Second Degree Stochastic Dominance (SSD)
a) Risk Aversion
b) The SSD Investment Decision Rule
c) Graphical Exposition of SSD
d) An Intuitive Explanation of SSD
3.6 Sufficient Rules and Necessary Rules for SSD
a) Sufficient Rules
b) Necessary Rules for SSD
3.7 Third Degree Stochastic Dominance (TSD)
a) A Preference for Positive Skewness as a Motivation for TSD
b) The Definition of Skewness
c) Lottery, Insurance and Preference for Positive Skewness
d) Empirical Studies and Positive Skewness Preference (or U 0)
e) Decreasing Absolute Risk Aversion (DARA), and Positive
Skewness Preferences (or U 0)
0 The Optimal Investment Rule for U 6 U3: TSD
g) Graphical Exposition of TSD
h) The Intuitive Explanation of TSD
3.8 Sufficient Rules and Necessary Rules for U e U3
a) Sufficient Rules
b) Necessary Rules for TSD
3.9 Decreasing Absolute Risk Aversion (DARA) Stochastic
Dominance (DSD)
a) DARA Utility Functions
b) DSD with Equal Mean Distributions
TABLE OF CONTENTS ix
3.10 Risk seeking Stochastic Dominance (RSSD)
a) Risk seeking Stochastic Dominance (RSSD)
b) Graphical Exposition of SSD
c) The Relationship Between SSD and SSD
d) The Relationship Between FSD, SSD and SSD
3.11 nth Order Stochastic Dominance
3.12 Stochastic Dominance Rules: Extension to Discrete Distributions
3.13 The Role of the Mean and Variance in Stochastic Dominance Rules
3.14 Summary
4
Stochastic Dominance: The Quantile 143
4.1 The Distribution Quantile
4.2 Stochastic Dominance Rules Stated in Terms of Distribution
Quantiles
a) The FSD Rule with Quantiles
b) The SSD Rule with Quantiles
4.3 Stochastic Dominance Rules with a Riskless Asset: A Perfect
Capital Market
a) FSD with a Riskless Asset: The FSDR Rule
b) Graphical Illustration of the FSDR Rule
c) SSD with a Riskless Asset: The SSDR Rule
d) The SD and SDR Efficient Sets
4.4 Stochastic Dominance Rules with a Riskless Asset: An Imperfect
Capital Market
4.5 Summary
5
Algorithms for Stochastic Dominance 173
5.1 Using the Necessary Conditions and Transitivity to Reduce the
Number of Comparisons
5.2 The FSD Algorithm
5.3 The SSD Algorithm
5.4 The TSD Algorithm
5.5 A Numerical Example Showing the Flaw In Existing TSD Algorithm
5.6 The Empirical Results
5.7 The SDR Algorithms
a) FSDR Algorithm
b) SSDR Algorithm
5.8 Summary
x STOCHASTIC DOMINANCE
6
Stochastic Dominance with Specific Distributions 197
6.1 Normal Distributions
a) Properties of the Normal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.2 Lognormal Distributions
a) Properties of the Lognormal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.3 Truncated Normal Distributions
a) Symmetrical Truncation
b) Non symmetrical Truncation
6.4 Distributions that Intercept Once at Most
6.5 Summary
7
The Empirical Studies 223
7.1 The Effectiveness of the Various Decision Rules: A Perfect
Market
7.2 The Effectiveness of the Various Decision Rules: An Imperfect
Market
7.3 The Performance of Mutual Funds with Transaction Costs
7.4 Further Reduction in the Efficient Sets: Convex Stochastic Dominance
(CSD)
7.5 Sampling Errors: Statistical Limitations of the Empirical Studies
7.6 Summary
8
Applications of Stochastic Dominance Rules 241
8.1 Capital Structure and the Value of the Firm
8.2 Production, Saving and Diversification
8.3 Estimating the Probability of Bankruptcy
8.4 Option Evaluation, Insurance Premium and Portfolio Insurance
8.5 Application of SD Rules in Agricultural Economics
8.6 Application of SD Rules in Medicine
8.7 Measuring Income Inequity
8.8 Application of SD Rules in the Selection of Parameter
Estimators
8.9 Summary
TABLE OF CONTENTS xi
9
Stochastic Dominance and Risk Measures 257
9.1 When is One Investment Riskier Than Another Investment?
9.2 Mean Preserving Spread (MPS)
9.3 Unequal Means and Riskier Than with the Riskless Asset
9.4 Riskier Than and DARA Utility Function: Mean Preserving
Antispread
9.5 Summary
10
Stochastic Dominance and Diversification 271
10.1 Arrow s Condition for Diversification
a) Diversification Between a Risky and a Riskless Asset
b) The Effect of Shifts in Parameters on Diversification
10.2 Extension of the SD Analyses to the Case of Two Risky Assets
10.3 Diversification and Expected Utility: Some Common Utility
Functions
a) Shift in r
b) Shift in x
c) MPS Shifts
d) MPA Shifts
e) MPSA Shifts
10.4 Summary
11
Decision Making and the Investment Horizon 293
11.1 Tobin s M V Multi Period Analysis
11.2 Sharpe s Reward to Variability Ratio and the Investment
Horizon
11.3 The Effect of the Investment Horizon on Correlations
11.4 The Effect of the Investment Horizon on the Composition
of M V Portfolios
11.5 The Effect of the Investment Horizon on Beta
11.6 Stochastic Dominance and the Investment Horizon
11.7 Contrasting The Size of the M V and SD Efficient Set
11.8 Summary
xii STOCHASTIC DOMINANCE
12
The CAPM and Stochastic Dominance 313
12.1 The CAPM with Heterogeneous Investment Horizon
a) Quadratic Utility Function
b) Single Period Normal Distributions
c) Multiperiod Normal Distributions
d) Lognormal Distributions
12.2 Summary
13
Almost Stochastic Dominance (ASD) 331
13.1 The Possible Paradoxes
13.2 FSD* Criterion Corresponding to U j .
13.3 SSD* Criterion Corresponding to U .
13.4 Application of FSD* To Investment Choices: Stocks Versus Bonds
13.5 ASD: Experimental Results
13.6 Summary
14
Non Expected Utility and Stochastic Dominance 353
14.1 The Allais Paradox
14.2 Non Expected Utility Theory
14.3 Decision Weights and FSD Violation
14.4 Temporary and Permanent Attitude Toward Risk
14.5 Summary
15
Stochastic Dominance and Prospect Theory 373
15.1 CPT and FSD Rule
15.2 Prospect Stochastic Dominance (PSD)
15.3 Markowitz s Stochastic Dominance
15.4 CPT, M V And The CAPM
15.5 Testing the Competing Theories: SD Approach
a) Testing the Competing Theories: SD Approach
b) The Stochastic Dominance Approach
c) Are People Risk Averse? (SSD)
d) Is CPT Valid Theory? (PSD)
15.6 SSD, PSD, MSD and the Efficiency of the Market Portfolio
15.7 Summary
TABLE OF CONTENTS xiii
16
Future Research 395
Bibliography 407
Index 431
|
| adam_txt |
TABLE OF CONTENTS
Preface \
1
On the Measurement of Risk 7
1.1 What is Risk?
1.2 Measures of Risk
a) Domar and Musgrave Risk Indexes
b) Roy's Safety First Rule
c) Dispersion as a Risk Index: Variance and Standard Deviation
d) Semi variance (SV) as an index of risk
e) Baumol's Risk Measure
f) Value at risk VaR( a)
g) Shortfall VaR
1.3 Summary
2
Expected Utility Theory 25
2.1 Introduction
2.2 Investment Criteria
a) The Maximum Return Criterion (MRC)
b) The Maximum Expected Return Criterion (MERC)
2.3 The Axioms and Proof of the Maximum Expected Utility
Criterion (MEUC)
a) The Payoff of the Investments
b) The Axioms
c) Proof that the Maximum Expected Utility Criterion (MEUC)
is Optimal Decision Rule
2.4 The Properties of Utility Function
a) Preference and Expected Utility
b) Is U(x) a Probability Function or a Utility Function?
2.5 The Meaning of the Utility Units
2.6 MRC, MERC as Special Cases of MEUC
2.7 Utility, Wealth and Change of Wealth
2.8 Summary
viii STOCHASTIC DOMINANCE
3
Stochastic Dominance Decision Rules 49
3.1 Partial Ordering: Efficient and Inefficient Sets
a) The Objective Decision
b) The Subjective Decision
3.2 First Degree Stochastic Dominance (FSD)
a) Probability Function, Density Function and Cumulating
Probability Function
b) The FSD Rule
c) The Graphical Exposition of the FSD Rule
d) FSD: A Numerical Example of FSD
e) The Intuitive Explanation of FSD
3.3 Optimal Rule, Sufficient Rules and Necessary Rules for FSD
a) Sufficient Rules
b) Necessary Rules
3.4 Type I and Type II Errors When Sufficient Rules or Necessary
Rules are not Optimal for Investment Screening
3.5 Second Degree Stochastic Dominance (SSD)
a) Risk Aversion
b) The SSD Investment Decision Rule
c) Graphical Exposition of SSD
d) An Intuitive Explanation of SSD
3.6 Sufficient Rules and Necessary Rules for SSD
a) Sufficient Rules
b) Necessary Rules for SSD
3.7 Third Degree Stochastic Dominance (TSD)
a) A Preference for Positive Skewness as a Motivation for TSD
b) The Definition of Skewness
c) Lottery, Insurance and Preference for Positive Skewness
d) Empirical Studies and Positive Skewness Preference (or U'" 0)
e) Decreasing Absolute Risk Aversion (DARA), and Positive
Skewness Preferences (or U'" 0)
0 The Optimal Investment Rule for U 6 U3: TSD
g) Graphical Exposition of TSD
h) The Intuitive Explanation of TSD
3.8 Sufficient Rules and Necessary Rules for U e U3
a) Sufficient Rules
b) Necessary Rules for TSD
3.9 Decreasing Absolute Risk Aversion (DARA) Stochastic
Dominance (DSD)
a) DARA Utility Functions
b) DSD with Equal Mean Distributions
TABLE OF CONTENTS ix
3.10 Risk seeking Stochastic Dominance (RSSD)
a) Risk seeking Stochastic Dominance (RSSD)
b) Graphical Exposition of SSD
c) The Relationship Between SSD and SSD
d) The Relationship Between FSD, SSD and SSD
3.11 nth Order Stochastic Dominance
3.12 Stochastic Dominance Rules: Extension to Discrete Distributions
3.13 The Role of the Mean and Variance in Stochastic Dominance Rules
3.14 Summary
4
Stochastic Dominance: The Quantile 143
4.1 The Distribution Quantile
4.2 Stochastic Dominance Rules Stated in Terms of Distribution
Quantiles
a) The FSD Rule with Quantiles
b) The SSD Rule with Quantiles
4.3 Stochastic Dominance Rules with a Riskless Asset: A Perfect
Capital Market
a) FSD with a Riskless Asset: The FSDR Rule
b) Graphical Illustration of the FSDR Rule
c) SSD with a Riskless Asset: The SSDR Rule
d) The SD and SDR Efficient Sets
4.4 Stochastic Dominance Rules with a Riskless Asset: An Imperfect
Capital Market
4.5 Summary
5
Algorithms for Stochastic Dominance 173
5.1 Using the Necessary Conditions and Transitivity to Reduce the
Number of Comparisons
5.2 The FSD Algorithm
5.3 The SSD Algorithm
5.4 The TSD Algorithm
5.5 A Numerical Example Showing the Flaw In Existing TSD Algorithm
5.6 The Empirical Results
5.7 The SDR Algorithms
a) FSDR Algorithm
b) SSDR Algorithm
5.8 Summary
x STOCHASTIC DOMINANCE
6
Stochastic Dominance with Specific Distributions 197
6.1 Normal Distributions
a) Properties of the Normal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.2 Lognormal Distributions
a) Properties of the Lognormal Distribution
b) Dominance Without a Riskless Asset
c) Dominance With a Riskless Asset
6.3 Truncated Normal Distributions
a) Symmetrical Truncation
b) Non symmetrical Truncation
6.4 Distributions that Intercept Once at Most
6.5 Summary
7
The Empirical Studies 223
7.1 The Effectiveness of the Various Decision Rules: A Perfect
Market
7.2 The Effectiveness of the Various Decision Rules: An Imperfect
Market
7.3 The Performance of Mutual Funds with Transaction Costs
7.4 Further Reduction in the Efficient Sets: Convex Stochastic Dominance
(CSD)
7.5 Sampling Errors: Statistical Limitations of the Empirical Studies
7.6 Summary
8
Applications of Stochastic Dominance Rules 241
8.1 Capital Structure and the Value of the Firm
8.2 Production, Saving and Diversification
8.3 Estimating the Probability of Bankruptcy
8.4 Option Evaluation, Insurance Premium and Portfolio Insurance
8.5 Application of SD Rules in Agricultural Economics
8.6 Application of SD Rules in Medicine
8.7 Measuring Income Inequity
8.8 Application of SD Rules in the Selection of Parameter
Estimators
8.9 Summary
TABLE OF CONTENTS xi
9
Stochastic Dominance and Risk Measures 257
9.1 When is One Investment Riskier Than Another Investment?
9.2 Mean Preserving Spread (MPS)
9.3 Unequal Means and "Riskier Than" with the Riskless Asset
9.4 "Riskier Than" and DARA Utility Function: Mean Preserving
Antispread
9.5 Summary
10
Stochastic Dominance and Diversification 271
10.1 Arrow's Condition for Diversification
a) Diversification Between a Risky and a Riskless Asset
b) The Effect of Shifts in Parameters on Diversification
10.2 Extension of the SD Analyses to the Case of Two Risky Assets
10.3 Diversification and Expected Utility: Some Common Utility
Functions
a) Shift in r
b) Shift in x
c) MPS Shifts
d) MPA Shifts
e) MPSA Shifts
10.4 Summary
11
Decision Making and the Investment Horizon 293
11.1 Tobin's M V Multi Period Analysis
11.2 Sharpe's Reward to Variability Ratio and the Investment
Horizon
11.3 The Effect of the Investment Horizon on Correlations
11.4 The Effect of the Investment Horizon on the Composition
of M V Portfolios
11.5 The Effect of the Investment Horizon on Beta
11.6 Stochastic Dominance and the Investment Horizon
11.7 Contrasting The Size of the M V and SD Efficient Set
11.8 Summary
xii STOCHASTIC DOMINANCE
12
The CAPM and Stochastic Dominance 313
12.1 The CAPM with Heterogeneous Investment Horizon
a) Quadratic Utility Function
b) Single Period Normal Distributions
c) Multiperiod Normal Distributions
d) Lognormal Distributions
12.2 Summary
13
Almost Stochastic Dominance (ASD) 331
13.1 The Possible Paradoxes
13.2 FSD* Criterion Corresponding to U j .
13.3 SSD* Criterion Corresponding to U \.
13.4 Application of FSD* To Investment Choices: Stocks Versus Bonds
13.5 ASD: Experimental Results
13.6 Summary
14
Non Expected Utility and Stochastic Dominance 353
14.1 The Allais Paradox
14.2 Non Expected Utility Theory
14.3 Decision Weights and FSD Violation
14.4 Temporary and Permanent Attitude Toward Risk
14.5 Summary
15
Stochastic Dominance and Prospect Theory 373
15.1 CPT and FSD Rule
15.2 Prospect Stochastic Dominance (PSD)
15.3 Markowitz's Stochastic Dominance
15.4 CPT, M V And The CAPM
15.5 Testing the Competing Theories: SD Approach
a) Testing the Competing Theories: SD Approach
b) The Stochastic Dominance Approach
c) Are People Risk Averse? (SSD)
d) Is CPT Valid Theory? (PSD)
15.6 SSD, PSD, MSD and the Efficiency of the Market Portfolio
15.7 Summary
TABLE OF CONTENTS xiii
16
Future Research 395
Bibliography 407
Index 431 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1007/0-387-29311-6 |
| edition | 2. ed. |
| format | Electronic eBook |
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| id | DE-604.BV022372577 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:07:48Z |
| indexdate | 2024-07-09T20:56:12Z |
| institution | BVB |
| isbn | 0387293027 9780387293028 9780387293110 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015581715 |
| oclc_num | 315796583 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-945 DE-739 DE-706 DE-898 DE-BY-UBR DE-M347 DE-355 DE-BY-UBR DE-634 DE-703 |
| owner_facet | DE-473 DE-BY-UBG DE-945 DE-739 DE-706 DE-898 DE-BY-UBR DE-M347 DE-355 DE-BY-UBR DE-634 DE-703 |
| physical | 1 Online-Ressource |
| psigel | ZDB-2-SBE |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Studies in risk and uncertainty |
| series2 | Studies in risk and uncertainty |
| spelling | Stochastic dominance investment decision making under uncertainty by Haim Levy 2. ed. New York Springer 2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Studies in risk and uncertainty 12 Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Investitionsentscheidung (DE-588)4162244-3 gnd rswk-swf Finanzanalyse (DE-588)4133000-6 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Dominanz (DE-588)4219516-0 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf 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 DE-604 Entscheidung bei Unsicherheit (DE-588)4070864-0 s Stochastische Dominanz (DE-588)4219516-0 s 1\p DE-604 Levy, Haim 1939- Sonstige (DE-588)170156605 oth Studies in risk and uncertainty 12 (DE-604)BV004567594 12 https://doi.org/10.1007/0-387-29311-6 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015581715&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 |
| spellingShingle | Stochastic dominance investment decision making under uncertainty Studies in risk and uncertainty Entscheidungstheorie (DE-588)4138606-1 gnd Investitionsentscheidung (DE-588)4162244-3 gnd Finanzanalyse (DE-588)4133000-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Dominanz (DE-588)4219516-0 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd |
| subject_GND | (DE-588)4138606-1 (DE-588)4162244-3 (DE-588)4133000-6 (DE-588)4057630-9 (DE-588)4219516-0 (DE-588)4070864-0 |
| 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_exact_search_txtP | Stochastic dominance investment decision making under uncertainty |
| title_full | Stochastic dominance investment decision making under uncertainty by Haim Levy |
| title_fullStr | Stochastic dominance investment decision making under uncertainty by Haim Levy |
| title_full_unstemmed | Stochastic dominance investment decision making under uncertainty by Haim Levy |
| title_short | Stochastic dominance |
| title_sort | stochastic dominance investment decision making under uncertainty |
| title_sub | investment decision making under uncertainty |
| topic | Entscheidungstheorie (DE-588)4138606-1 gnd Investitionsentscheidung (DE-588)4162244-3 gnd Finanzanalyse (DE-588)4133000-6 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Dominanz (DE-588)4219516-0 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd |
| topic_facet | Entscheidungstheorie Investitionsentscheidung Finanzanalyse Stochastischer Prozess Stochastische Dominanz Entscheidung bei Unsicherheit |
| url | https://doi.org/10.1007/0-387-29311-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015581715&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004567594 |
| work_keys_str_mv | AT levyhaim stochasticdominanceinvestmentdecisionmakingunderuncertainty |