Anomalies in Net Present Value, Returns and Polynomials, and Regret Theory in Decision-Making

Anomalies in Net Present Value, Returns and Polynomials, and Regret Theory in Decision-Making

Michael C.I. Nwogugu Anomalies in Net Present Value, Returns and Polynomials, and Regret Theory in Decision-Making

Michael C.I. Nwogugu Nigeria ISBN 978-1-137-44697-8 DOI 10.1057/978-1-137-44698-5 ISBN 978-1-137-44698-5 (ebook) Library of Congress Control Number: 2016962451 The Editor(s) (if applicable) and The Author(s) 2016 The author(s) has/have asserted their right(s) to be identified as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988. This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover design by Samantha Johnson Printed on acid-free paper This Palgrave Macmillan imprint is published by Springer Nature The registered company is Macmillan Publishers Ltd. The registered company address is: The Campus, 4 Crinan Street, London, N1 9XW, United Kingdom

Contents 1 Introduction 1 1.1 The NPV-IRR Model and Related Approaches (Such As AIRR, MIRR, NFV, APV; GIRR; SIRR; AROI; etc.) are Wrong 4 1.2 The NPV-IRR Model, Discounting and Macroeconomics 8 1.3 NPV-IRR Model (And Related Approaches) in Academia 9 1.4 The Un-Reliability of Empirical Methods/Models in Operations Research, Computer Science and Psychology 11 1.5 The Chapters 12 1.6 Anomalies in Real Options Analysis (Used in Valuation or Capital Budgeting) 14 1.7 Financial Options Valuation in Capital Budgeting 15 Bibliography 16 2 Spatio-Temporal Framing Anomalies in the NPV-MIRR-IRR Model and Related Approaches; and Regret Theory 23 2.1 Existing Literature 23 2.2 Framing Effects in the Mean-Variance Framework 28 v

vi Contents 2.3 Spatio-Temporal Cognition, Framing Effects, and Game Theory 29 2.3.1 A Critique of Iturbe-Ormaetxe, Ponti, Tomás and Ubeda (2010) 30 2.3.2 Rights of First Refusal (ROFRs) and a Critique of Grosskopf and Roth (2009) 32 2.3.3 Framing Effects in the NPV-IRR Model (And Related Approaches) 35 2.3.4 Quasi-Frames and Some Framing-Related Inconsistencies in the NPV-IRR Model 45 2.4 Regret-Based Decision Models as an Alternative to the NPV-IRR Model (And Related Approaches) 49 2.5 Conclusion 54 Bibliography 54 3 Regret Theory and Asset Pricing Anomalies in Incomplete Markets with Dynamic Unaggregated Preferences 69 3.1 Existing Literature 70 3.2 Inaccurate Assumptions on Which ICAPM/IAPT and CML Are Based; And Why The Conditions Are Wrong and Not Feasible 76 3.3 The Consumption-Savings-Investment-Production Dichotomy Is Inaccurate 90 3.3.1 Savings 93 3.3.2 Aggregate Investment and Investment 95 3.3.3 Intangibles: The Production and Consumption of Intangibles Differs from General Consumption and Traditional Production and Investment 95 3.3.4 Leisure Differs from General Consumption, Investment and Production 97 3.3.5 The Consumption of Housing Differs from General Consumption and Traditional Savings 98 3.3.6 Regret Theory and Behavior Based Asset Pricing Models 101

Contents vii 3.4 The Unified Intertemporal Wealth- Allocation Decision (UIWD) 102 3.5 The Elasticity of Intertemporal Substitution Is Inaccurate 106 3.6 Relationships Among the Factors: The Marginal Rate of Intertemporal Joint Substitution 112 3.7 Other Recent Research on Asset Pricing 117 3.8 Conclusion 117 Bibliography 118 4 The Descartes Sign Rule, Sturm s Theorem, Vincent s Theorem and the Fourier-Budan Theorem Are Wrong 133 4.1 Existing Literature 133 4.2 The Descartes Sign Rule and Fourier- Boudan Theorem Are Wrong 134 4.3 Sturm s Theorem and Vincent s Theorem Are Wrong 140 4.4 Conclusion 170 Bibliography 170 5 MN-2 Invariants and Homomorphisms for Solving Polynomials; And Anomalies in the Binomial Theorem and the Fundamental Theorem Of Algebra 173 5.1 Existing Literature 174 5.2 Factoring of Some Higher Order Polynomials Using a New Approach (Invariants and Homomorphisms) 174 5.2.1 Solving a Six-Degree Polynomial 175 5.2.2 Solving a Nine-Degree Polynomial Using Invariants and Homomorphisms 178 5.3 The Binomial Theorem Is Wrong 183 5.4 The Fundamental Theorem Of Algebra Is Wrong 185 5.5 Traditional Root Calculation Can Lead to Inaccurate Results 190 5.6 Conclusion 193 Bibliography 205

viii Contents 6 The Historical and Current Concepts of Plain Interest Rates, Forward Rates and Discount Rates Are or Can Be Misleading 207 6.1 Existing Literature 207 6.2 Concepts of Plain Interest Rates, Forward Rates and Discount Rates Can Be Misleading 212 6.2.1 The Weak Money-Rate Relationship 214 6.2.2 Excessive Dependence On Interest Rate Policy Is Detrimental 217 6.2.3 The Relationship Between Interest Rates and Stock Markets 220 6.2.4 Interest Rate Parity Does Not Exist In Many Circumstances 221 6.2.5 The Marginal Utility Of Wealth and The Marginal Utility Of Consumption are Almost Irrelevant In The Formation Of Equilibrium Interest Rates 223 6.2.6 On Discount Rates 225 6.3 The NPV-MIRR-IRR Model (And Related Approaches) Differs from Actual Human Decision Processes 233 6.4 The NPV-IRR Model (And Related Approaches Such as NFV, APV, AIRR; etc.) Does Not Account for Wllingness-To-Accept-Losses (WTAL) 236 6.5 The Use of WACC Further Distorts the NPV-MIRR-IRR (and Similar) Models and Can Create Additional Frames 242 6.6 Conditions for Negative Discount Rates 244 6.7 Conclusion 247 Bibliography 247 7 On Algebraic Anomalies in Polynomials and Net Present Value Decisions 263 7.1 Existing Literature 263 7.2 Biases in the NPV-IRR-MIRR Model and Related Approaches 269

Contents ix 7.3 Conclusion 291 Bibliography 291 8 Some Biases and Evolutionary Homomorphisms Implicit in the Calculation of Returns 297 8.1 Existing Literature 298 8.2 Biases in Compounded Returns 302 8.3 Volatility has Minimal Effects on the Downward Returns Bias 309 8.4 Conclusion 312 Bibliography 320 9 Conclusion 325 Bibliography 327

Abbreviations AIRR APT APV AROI CAPM CML CPT CSIP DC DCA DIM EIS ETF EVA FTA IAPT ICAPM IRR LPVR MIRR MRIS MRIJS Average Internal Rate of Return Arbitrage Pricing Theory Adjusted Present Value Aggregate Return on Investment Capital Asset Pricing Model Capital Market Line Cumulative Prospect Theory Consumption, Savings, Investment, and Production Defined Contribution Decision Curve Analysis Differential Importance Measure Elasticity of Intertemporal Substitution Exchange Traded Fund Economic Value Added Fundamental Theory of Algebra Intertemporal Arbitrage Pricing Theory Intertemporal Capital Asset Pricing Model Internal Rate of Return Least Present Value of the Revenues Modified Internal Rate of Return Marginal Rate of Intertemporal Substitution Marginal Rate of Intertemporal Joint Substitution xi

xii NDRB NFV NPV NPVv PIH PT PT 3 RRA ROFR ROI SEG SEHK SEU SML SVA TCM TVM UIWD WACC WTAL Abbreviations Non-Zero Discount Rate Bias Net Future Value Net Present Value NPV of the variance Permanent Income Hypothesis Prospect Theory Third-Generation Prospect Theory Relative Risk Aversion Rights of First Refusal Return on Investment Socio-Emotional Goods Hong Kong Stock Exchange Social Expected Utility Model Security Market Line Systemic Value Added Transaction Costs and Monitoring Costs Time Value of Money Unified Intertemporal Wealth-Allocation Decision Weighted Average Cost of Capital Willingness To Accept Losses

List of Tables Chart 4A 142 Chart 4B 160 Chart 4C 168 Chart 5A 194 Chart 7A 289 Chart 7B 290 Chart 8A 312 Chart 8B The downward bias effect 313 Chart 8C 314 Chart 8D 317 xiii