Skip to main content
main-content

## Über dieses Buch

Indices, index funds and ETFs are grossly inaccurate and inefficient and affect more than €120 trillion worth of securities, debts and commodities worldwide. This book analyzes the mathematical/statistical biases, misrepresentations, recursiveness, nonlinear risk and homomorphisms inherent in equity, debt, risk-adjusted, options-based, CDS and commodity indices – and by extension, associated index funds and ETFs. The book characterizes the “Popular-Index Ecosystems,” a phenomenon that provides artificial price-support for financial instruments, and can cause systemic risk, financial instability, earnings management and inflation. The book explains why indices and strategic alliances invalidate Third-Generation Prospect Theory (PT3), related approaches and most theories of Intertemporal Asset Pricing. This book introduces three new decision models, and some new types of indices that are more efficient than existing stock/bond indices. The book explains why the Mean-Variance framework, the Put-Call Parity theorem, ICAPM/CAPM, the Sharpe Ratio, Treynor Ratio, Jensen’s Alpha, the Information Ratio, and DEA-Based Performance Measures are wrong. Leveraged/inverse ETFs and synthetic ETFs are misleading and inaccurate and non-legislative methods that reduce index arbitrage and ETF arbitrage are introduced.

## Inhaltsverzeichnis

Abstract
Indices, index funds and exchange-traded funds (ETFs) have become major asset classes in debt, equity, real estate, currency and commodity markets worldwide—and their management, maintenance and use often occurs within the context of human–computer interactions (HCI). As of 2018, there were more indices in the world than the number of exchange-traded companies. The relatively sudden and significant growth of indices, passive/active ETFs and index funds during 1995–2018 (combined with the Internet, increasing volume of cross-border transactions, and improved global settlement/clearing systems) have increased the potential for systemic risk, financial instability and the failure of regulations. The major problem is that more than US$3.5 trillion is invested in indices through ETFs, index funds and equity swaps apparently without regard to the quality and valuation of the underlying companies and commodities. The net effects are that: (i) the companies and commodities in these indices are overvalued and enjoy artificial price support (from these ETFs and index funds); (ii) there is substantial over-investment and “Gambling” in the underlying companies and under-investment in non-listed, micro-cap, small-cap and emerging markets companies, which affects economic growth, development and capital mobility; and (iii) these indices, index funds and ETF and their component companies pose increasing systemic risk and financial instability threats. Michael I. C. Nwogugu ### Chapter 2. Number Theory, “Structural Biases” and Homomorphisms in Traditional Stock/Bond/Commodity Index Calculation Methods in Incomplete Markets with Partially Observable Un-aggregated Preferences, MN-Transferable-Utilities and Regret–Minimization Regimes Abstract While stock/bond indices, index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems inherent in index calculation methodologies and the legal/economic structure of ETFs and Index Funds. These problems raise actionable issues of “suitability” and “fraud” under US securities laws, because many indices, Index Funds and ETFs are misleading and have substantial tracking errors. This chapter contributes to the existing literature by (i) introducing new critiques of, and Spatio-Temporal Cognitive Biases in the calculation methods for traditional (non-option) stock/bond indices and showing that these indices don’t evolve in tandem with, and thus don’t represent the markets that they are supposed to, partly due to the equivalents of Reproduction (e.g. the announcement of quarterly operating results of companies in the index); Natural Selection (e.g. index-rebalancing, and demand/supply of shares that constitute the index); Recombination (e.g. the effects of arbitrage and use of spread trading); and Mutation (e.g. changes in the inherent risk and or relative risk of underlying companies in the index); (ii) explaining how such biases affect representations and analysis of pattern formation and adaptive systems; and (iii) showing how these biases/effects can form the basis for harmful arbitrage activities. Michael I. C. Nwogugu ### Chapter 3. A Critique of Credit Default Swaps (CDS) Indices Abstract While CDS Indices have grown in popularity during then last ten years, there are many structural problems inherent in the associated index calculation methodologies, which create substantial tracking errors. As of 2018, the global CDS market covered notional amounts that exceeded US$50 trillion.
CDS indices are widely used in valuation and risk management around the world; for example, during the Global Financial Crisis (2007–2010) the ABX family of CDS indices and the Markit CDX CDS indices (http://​www.​markit.​com/​en/​products/​data/​indices/​credit-and-loan-indices/​cdx/​cdx.​page) were used to value a wide range of assets such as MBS and corporate bonds. This chapter explains why CDS Indices are inaccurate and, thus, can cause and/or amplify financial instability and systemic risk.
Michael I. C. Nwogugu

### Chapter 4. Invariants and Homomorphisms Implicit in, and the Invalidity of the Mean-Variance Framework and Other Causality Approaches: Some Structural Effects

Abstract
Many aspects of modern statistical analysis, Data Science and optimization are based almost entirely on the Mean–Variance (M-V) Framework and its elements—Variance, Semivariance, Correlation and Covariance. This chapter explains why these measures are very inaccurate and don’t reflect reality and also introduces Invariants for analysis of rates-of-change and Pattern Formation. That is, some of the illustrated limitations of the M-V Framework are Invariants that present new opportunities in computing and computational methods in various fields including Optimization, Pattern Formation, Chaos and Evolutionary Computation, given the discussions in Sandfeld and Zaiser (Modelling and Simulation in Materials Science and Engineering, 23(6), 065005, 2015), Kriener et al. (Frontiers of Computational Neuroscience, 7, 187–191, 2014), Fenn et al. (Physics Review E, 84, 61–65, 2011), Preis et al. (Scientific Reports, 2, Article number: 752, 2012), Kenett et al. (International Journal of Bifurcation & Chaos, 22, 1250181, 2012), Pearson (Philosophical Transactions of the Royal Society of London Series A, 186, 343–414, 1895), Fuwape and Ogunjo (CBN Journal of Applied Statistics, 4(2), 129–134, 2013), Menna et al. (International Journal of Modern Physics C, 13(1), 31–39, 2002), Egozcue (Cogent Mathematics, 2(1), 991082, 2015), and Andrade et al. (Physica D: Nonlinear Phenomena, 223(2), 139–145, 2006), all of which omitted the limitations. One of the biggest problems inherent in the M-V Framework is that its main components (Variance, Covariance, Correlation and Semivariance) measure the results but not the causes of variation and covariation.
Michael I. C. Nwogugu

### Chapter 5. Decision-Making, Sub-additive Recursive “Matching” Noise and Biases in Risk-Weighted Stock/Bond Commodity Index Calculation Methods in Incomplete Markets with Partially Observable Multi-attribute Preferences

Abstract
Risk-adjusted indices, index tracking funds and ETFs have grown in popularity but have many structural and tracking-error problems that raise actionable issues of “suitability” and “fraud” under securities laws. This chapter contributes to the existing literature by (a) introducing and characterizing the errors and biases inherent in “risk-adjusted” index weighting methods and the associated adverse effects; and (b) showing how these biases/effects inherent in index calculation methods can reduce social welfare, amplify financial instability, systemic risk and harmful arbitrage activities.
Michael I. C. Nwogugu

### Chapter 6. Informationless Trading and Biases in Performance Measurement: Inefficiency of the Sharpe Ratio, Treynor Ratio, Jensen’s Alpha, the Information Ratio and DEA-Based Performance Measures and Related Measures

Abstract
The Sharpe Ratio, Conditional Sharpe Ratio, Conditional Treynor Ratio, Treynor Ratio, Jensen’s Alpha, Appraisal Ratio, Sortino and Van der Meer Ratio (1991), Sortino, Van der Meer and Plantinga (1999) Ratio, Information Ratio, DEA-based Methods and the Henriksson-Merton market timing measure are all based on the Mean–Variance (“M-V”) Framework and are hereafter referred to as the “M-V Performance Measures.” This chapter explains why the M-V Performance Measures are grossly inaccurate and inefficient. The M-V Performance Measures have been theoretically and empirically shown to be inaccurate and unrealistic, primarily because returns cannot be accurately characterized by any mixture of distributions over time, and because Standard Deviations (SD) and returns are not sufficient to accurately define investors’ preferences. Value at Risk (VaR) and Expected Shortfall were addressed in Nwogugu (2005) and Nwogugu (Applied Mathematics and Computation, 185(1), 178–196).
Michael I. C. Nwogugu

### Chapter 7. Anomalies in Taylor Series, and Tracking Errors and Homomorphisms in the Returns of Leveraged/Inverse ETFs and Synthetic ETFs/Funds

Abstract
This chapter illustrates and explains the biases, anomalies and problems inherent in Leveraged/Inverse EFTs and Synthetic ETFs/Funds which often have tracking errors and misleading advertising, but are considered to be an improvement over leveraged mutual funds. A group of asset management companies, including Direxion and ProShares, have launched Leveraged/Inverse ETFs that focus on specific markets around the world. As of 2018, more than the equivalent of USD\$500 billion had been invested in Leveraged/Inverse ETFs and Synthetic ETFs/Funds worldwide. However, the advertised terms of most Leveraged/Inverse ETFs (such as the ProShares leveraged/Inverse ETFs) and Synthetic ETFs/Funds are inaccurate and grossly misleading.
Michael I. C. Nwogugu

### Chapter 8. Human Computer Interaction, Misrepresentation and Evolutionary Homomorphisms in the VIX and Options-Based Indices in Incomplete Markets with Unaggregated Preferences and NT-Utilities Under a Regret Minimization Regime

Abstract
While options-based indices have grown in popularity, there are many structural problems inherent in the associated index calculation methodologies, which create substantial tracking errors. Many Synthetic ETFs/Funds are constructed with swaps and or futures contracts, and have evolved into quasi-indices. This chapter contributes to the existing literature by: (i) critiquing the calculation methods for options-based indices (Futures Indices, VIX Index and related indices, Buy-Write Indices); (ii) introducing the inherent biases in such indices which may raise issues of “suitability” and misinformation; (iii) showing that these options-based indices don’t evolve in tandem with, and thus don’t represent, the markets that they are supposed to represent, partly due to the equivalents of reproduction (e.g. the timing, rates of, and amount of creation of options contracts); natural selection (e.g. changes in the demand for, and supply of options contracts that constitute the index); recombination (e.g. the effects of the creation and use of options spreads — which are combinations of options contracts); and mutation (e.g. changes in the inherent risk and or relative risk of a group of options contracts on one asset); and (iv) introducing new critiques and Spatio-Temporal Cognitive Biases in the calculation methods for Indices.
Michael I. C. Nwogugu

### Chapter 9. Human–Computer Interaction, Incentive-Conflicts and Methods for Eliminating Index Arbitrage, Index-Related Mutual Fund Arbitrage and ETF Arbitrage

Abstract
Around the world, Index Arbitrage and ETF Arbitrage remains a major problem (this chapter does not cover the arbitrage of Mutual Funds). The US Congress and many governments have attempted to tackle these problems and have enacted various laws which have not been effective. Index Arbitrage and ETF Arbitrage don’t facilitate price discovery, they amplify volatility and financial instability and distort indices and the perceptions of the true values and risks of companies. This chapter contributes to the existing literature by: (i) introducing new adverse effects of Index Arbitrage and ETF Arbitrage, (ii) introducing new methods for eliminating Index Arbitrage and ETF Arbitrage, (iii) introducing new theories-of-liability and causes-of-action against perpetrators of Index Arbitrage and ETF Arbitrage.
Michael I. C. Nwogugu

### Chapter 10. Some New Index-Calculation Methods and Their Mathematical Properties

Abstract
While indices, index tracking funds and ETFs have grown in popularity during then last 10 years, there are many structural problems inherent in the daily trading of indices and ETFs, primarily in the form of Index Arbitrage and ETF Arbitrage (this chapter does not cover the arbitrage of Mutual Funds). The US Congress and many governments have attempted to tackle these problems and have enacted various laws, which have not been effective. Index Arbitrage does not facilitate price discovery, creates excessive and unnecessary volatility and distorts indices and the perceptions of the true values and risks of companies. This chapter contributes to the existing literature by introducing new index calculation methods (for fixed income, equity and commodity indices) that substantially reduce or eliminate Index Arbitrage and ETF Arbitrage.
Michael I. C. Nwogugu

### Chapter 11. Financial Indices, Joint Ventures and Strategic Alliances Invalidate Cumulative Prospect Theory, Third-Generation Prospect Theory, Related Approaches and Intertemporal Asset Pricing Theory: HCI and Three New Decision Models

Abstract
The Global Financial Crisis and stock market crashes that occurred in various countries during 2000–2015 have exposed significant weaknesses in economies, Stock Indices and “Regulatory Strategic Alliances” and Intertemporal Asset Pricing Theories.
Several researchers have also noted that PT/CPT/PT3 and related methods are invalid. Rieger and Bui (2011) developed alternative specifications for Prospect Theory (PT), and noted that in financial markets where the majority of participants are PT-maximizers, the classic PT value function (v) results in non-existence of equilibria, and the problem can be solved by using exponential value functions. Neilson and Stowe (2002) and Nwogugu (Appl Math Comput 179: 451–465, 2006a) critiqued CPT and found that CPT is an extension of Expected Utility Theory; and their results—and Nwogugu (2005), which is cited in Nwogugu (Appl Math Comput 179: 451–465, 2006a)—contradict findings in Bleichrodt et al. (2013) and Wakker (2010, Cambridge University Press). Schmidt (2003) critiqued CPT, and redefined reference-dependence in CPT. Woolford (Why South African boards construe elements of their regulatory obligations differently in respect of Enterprise Risk Management (ERM). Thesis for Doctor of Business Administration, Edinburgh Business School at Heriott Watt University, Scotland. http://​www.​ros.​hw.​ac.​uk/​bitstream/​10399/​2621/​1/​WoolfordG_​1013_​ebs.​pdf, 2013) noted that corporate governance statutes (such as SOX in the US) require BODs to manage enterprise risk and BODs’ behavior towards risk is linked to their degree of regulatory compliance with such statutes.
Michael I. C. Nwogugu

### Chapter 12. Economic Policy, Complex Adaptive Systems, Human-Computer-Interaction and Managerial Psychology: Popular-Index Ecosystems

Abstract
During 1990–2017 there was substantial debate about the nature and extent of earnings management by companies included in popular stock indices (such as S&P-500, Nikkei-225, MSCI-1500 and DAX-100 companies). These popular indices have created “Popular-Index Ecosystems,” which are a critical economic policy issue because they increase systemic risk and financial instability, and they affect managerial psychology and group decisions in large and medium-sized companies. This article contributes to the literature by (i) providing evidence of, and surveys in, endemic earnings management, asset quality management and tax evasion by “Popular-Index companies”; (ii) characterizing “Popular-Index Ecosystems” and the effects of such systems on the business climate in general; (iii) introducing new theories of corporate governance, managerial psychology, networks and risk.
Michael I. C. Nwogugu

### Chapter 13. Implications for Decision Theory, Enforcement, Financial Stability and Systemic Risk

Abstract
Some of the problems inherent in the structure of Financial Indices, ETFs and Index Funds were discussed in earlier chapters in this book—and the large size of the Global Index Products Market amplifies these problems. Another dimension is that the Social Welfare problems of Indexing can have wide-ranging negative “Multiplier Effects” (on households, companies and government agencies) and which have not been addressed by index sponsors, fund sponsors or regulators. This chapter: (i) discusses the implications of ETFs, Indices and Index Funds for enforcement, Sustainability, Inequality and financial stability; (ii) discusses “path-dependence” and “Lock-ins” and proposes new models of government intervention; and (iii) proposes new sustainability measures that are designed to reduce the wide-ranging adverse effects of Indices, Index Funds and ETFs (such as Destructive Urbanization, Inequality, Pollution and Climate Change, harmful Arbitrage, and Costly Technological Change).
Michael I. C. Nwogugu
Weitere Informationen

## Premium Partner

Bildnachweise