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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

  • Michael I. C. Nwogugu
Chapter

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.

Keywords

Nonlinear risk Optimization Homomorphisms Stocks, bonds and commodities index calculation methods MN-Transferable Utility Arbitrage Regret minimization regimes Misrepresentation 

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Authors and Affiliations

  • Michael I. C. Nwogugu
    • 1
  1. 1.EnuguNigeria

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