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


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.


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


  1. Abhyankar, A., Copeland, L., & Wong, W. (1997). Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100. Journal of Business & Economic Statistics, 15(1), 1–14.Google Scholar
  2. Advisor Perspectives. (2008, May). Equal weighted indexing – A critique of S&P’s study.
  3. Ahn, C., Byoun, S., & Park, H. Y. (2003). Put-call parity: The case of KOSPI200 options in Korea (Working paper).
  4. Ajmi, A., Aye, G., et al. (2005). Causality between US economic policy and equity market uncertainties: Evidence from linear and nonlinear tests. Journal of Applied Economics, 18(2), 225–246.Google Scholar
  5. Akem, A. (2018). Measuring substitution bias and the CPI – Theory and practice. Australian Bureau of Statistics.
  6. Aksu, M. H., & Onder, T. (2003). The size and book-to-market effects and their role as risk proxies in the Istanbul Stock Exchange (Working paper).
  7. Alexander, C., & Barbosa, A. (2007). Effectiveness of minimum-variance hedging: The impact of electronic trading and exchange-traded funds. Journal of Portfolio Management, 1–7.Google Scholar
  8. Alfares, H., & Duffaa, S. (2008). Determining aggregate criteria weights from criteria rankings, by a group of decision makers. International Journal of Information Technology & Decision Making, 7(4), 769–781.Google Scholar
  9. Alighanbari, M., & Chia, C. (2016). Multifactor indexes made simple: A review of static and dynamic approaches. The Journal of Index Investing, 7(2), 87–99.Google Scholar
  10. Alighanbari, M., & Doole, S. (2018). The capacity of factor index strategies: Assessment and control. The Journal of Index Investing, 9(2), 34–52.Google Scholar
  11. Amenc, N., & Goltz, F. (2016). Who cares about purity of factor indexes? A comment on “evaluating the efficiency of ‘smart beta’ indexes”. The Journal of Index Investing, 7(1), 10–13.Google Scholar
  12. Amenc, N., Goltz, F., & Le Sourd, V. (2006, September). Assessing the quality of stock market indices: Requirements for asset allocation and performance measurement (Working paper). EDHEC. EDHEC Publication.
  13. Amenc, N., Goltz, F., & Martellini, L. (2011a). A survey of alternative equity index strategies: A comment. Letters to the editor. Financial Analysts Journal, 67(6), 14–16.Google Scholar
  14. Amenc, N., Goltz, F., Martellini, L., & Retkowsky, P. (2011b). Efficient indexation: An alternative to cap-weighted indices. Journal of Investment Management, 9(4), 1–23.Google Scholar
  15. Amenc, N., Goltz, F., & Tang, L. (2011c, October). EDHEC-Risk European index survey 2011 (Working paper). EDHEC-Risk Institute Publication.Google Scholar
  16. Amenc, N., Goltz, F., Tang, L., & Vaidyanathan, V. (2012, April). EDHEC-Risk North American index survey 2011 (Working paper). EDHEC.Google Scholar
  17. Ang, A., Hodrick, R., Xing, Y., & Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance, LXI(1), 259–299.Google Scholar
  18. Antonakakis, N., Chatziantoniou, I., & Filis, G. (2013). Dynamic co-movements between stock market returns and policy uncertainty. Economics Letters, 120(1), 87–92.Google Scholar
  19. Arnott, R., Hsu, J., & Moore, P. (2005). Fundamental indexation. Financial Analysts Journal, 61(2), 83–99.Google Scholar
  20. Arnott, R. D., Little, B., & Shepherd, S. (2008, September). Using fundamental index strategies to increase return, reduce risk, and improve portfolio efficiency (Working paper).
  21. Arnott, R., Kalesnik, V., Moghtader, P., & Scholl, P. (2010). Beyond cap weight: The empirical evidence for a diversified beta. Journal of Indexes, 16, 16–26.Google Scholar
  22. Arouri, M., Estay, C., et al. (2016). Economic policy uncertainty and stock markets: Long-run evidence from the US. Finance Research Letters, 18, 136–141.Google Scholar
  23. Ascioglu, A., & Mcdermott, J. (2014). U.S. small-cap indexes: An empirical analysis of factor exposure and return. The Journal of Index Investing, 5(3), 21–32.Google Scholar
  24. Aydin, S., & Ozer, G. (2005). National customer satisfaction indices: An implementation in the Turkish mobile telephone market. Marketing Intelligence & Planning, 23(5), 486–504.Google Scholar
  25. Backus, D., Routledge, B., & Zin, S. (2005, December). Recursive preferences (NYU working paper no. EC-05-19). Available at SSRN:
  26. Badlyans, D., Soe, A., & Xie, H. (2018). A look inside green bonds: Combining sustainability with core fixed income. S&P Dow Jones Indices.Google Scholar
  27. Balatti, M., Brooks, C., & Kappou, K. (2017). Fundamental indexation revisited: New evidence on alpha. International Review of Financial Analysis, 51, 1–15.Google Scholar
  28. Berger, A., & McCarthy, C. (2016). The last smart beta paper you’ll ever (have to) read: Nuggets of hope beneath the hype. The Journal of Index Investing, 7(1), 116–123.Google Scholar
  29. Berger, D., & Pukthuanthong, K. (2012). Market fragility and international market crashes. Journal of Financial Economics, 105(3), 565–580.Google Scholar
  30. Berk, J. B. (1995). A critique of size-related anomalies. Review of Financial Studies, 8, 275–286.Google Scholar
  31. Bernhard, R. (1971). A comprehensive comparison and critique of discounting indices proposed for capital investment evaluation. The Engineering Economist, 16(3), 157–186.Google Scholar
  32. Bharadwaj, A., & Wiggins, J. (2001). Box spread and put-call parity tests for the S&P 500 index LEAPS market. The Journal of Derivatives, 8(4), 62–71.Google Scholar
  33. Bi, G., Ding, J., Luo, Y., & Liang, L. (2011). A new malmquist productivity index based on semi-discretionary variables with an application to commercial banks of China. International Journal of Information Technology & Decision Making, 10, 713–717.Google Scholar
  34. Blitz, D., & Van Vliet, P. (2007). The volatility effect lower risk without lower returns. Journal of Portfolio Management, 34(1), 102–113.Google Scholar
  35. Blitzer, D. (Standard & Poors). (2004). Free float adjustment for the S&P. New York: Standard & Poors.Google Scholar
  36. Bloomberg. (2018a). Index methodology: Bloomberg commodity index family.
  37. Bloomberg Index Services Limited (BISL). (2017, March). Bloomberg Barclays index methodology.
  38. Blume, M. E., & Edelen, R. M. (2004). S&P 500 indexers, tracking error and liquidity. Journal of Portfolio Management, 30, 37–46.Google Scholar
  39. Blume, M. E., & Stambaugh, R. F. (1983). Biases in computed returns: An application to the size effect. Journal of Financial Economics, 12, 387–404.Google Scholar
  40. Bonilla, C., Romera-Meza, R., & Hinich, M. (2006). Episodic nonlinearity in Latin American stock market indices. Applied Economics Letters, 13, 195–199.Google Scholar
  41. Bonanno, G., Caldarelli, G., et al. (2004). Networks of equities in financial markets. The European Physical Journal B-Condensed Matter & Complex Systems, 38(2), 363–371.Google Scholar
  42. Brunetti, M., & Torricelli, C. (2005). Put–call parity and cross-markets efficiency in the index options markets: Evidence from the Italian market. International Review of Financial Analysis, 14(5), 508–532.Google Scholar
  43. Bryan, J., & DePledge, W. (2015). Practical investing: Evaluating actively managed mutual funds in relation to their respective indexes. The Journal of Index Investing, 6(3), 33–39.Google Scholar
  44. Carhart, M. M., Carpenter, J. N., Lynch, A. W., & Musto, D. K. (2002). Mutual fund survivorship. Review of Financial Studies, 15, 1439–1463.Google Scholar
  45. Carlson, J., Pelz, E., & Sahinoz, E. (2004). Mutual funds, fee transparency, and competition. Federal Reserve Bank of Cleveland – Economic Commentary. Federal Reserve Bank of Cleveland.Google Scholar
  46. Caves, D., Christensen, L., & Diewert, R. (1982). The economic theory of index numbers and the measurement of input, output and productivity. Econometrica, 50(6), 1393–1414.Google Scholar
  47. Chan, H. W. H., & Howard, P. F. (2002). Additions to, and deletions from an open-ended market index: Evidence from the Australian all ordinaries. Australian Journal of Management, 27, 45–74.Google Scholar
  48. Chan, L. K. C., Karceski, J., & Lakonishok, J. (1999). On portfolio optimization: Forecasting covariances and choosing the risk model. Review of Financial Studies, 12(5), 937–974.Google Scholar
  49. Chen, T. (2012). Non linear assignment-based methods for interval-valued intuitionistic fuzzy multi-criteria decision analysis with incomplete preference information. International Journal of Information Technology & Decision Making, 11, 821–827.Google Scholar
  50. Chen, H., et al. (2006). Index changes and losses to index fund investors. Financial Analysts Journal, 62, 31–34.Google Scholar
  51. Choueifaty, Y. (2010). Diversification and the inefficiency of the market cap portfolio. VBA Journal, 1, 26–30.Google Scholar
  52. Choueifaty, Y., & Coignard, Y. (2008). Toward maximum diversification. Journal of Portfolio Management, 35(1), 40–51.Google Scholar
  53. Chow, T., Hsu, J., Kalesnik, V., & Little, B. (2011). A survey of alternative equity index strategies. Financial Analyst Journal, 67(5), 37–57.Google Scholar
  54. Chowdhury, O. H. (1991). Human development index: A critique. Bangladesh Development Studies, 19(3), 125–127.Google Scholar
  55. Christou, C., Cunado, J., Gupt, R., & Hassapis, C. (2017). Economic policy uncertainty and stock market returns in Pacific rim countries: Evidence based on a Bayesian panel VAR model. Journal of Multinational Financial Management, 40, 92–102.Google Scholar
  56. Chuliá, H., Gupta, R., et al. (2017). Impact of us uncertainties on emerging and mature markets: Evidence from a quantile-vector autoregressive approach. Journal of International Financial Markets, Institutions and Money, 48, 178–191.Google Scholar
  57. Clarke, R., de Silva, H., & Thorley S. (2006). Minimum-variance portfolios in the U.S. Equity Market. Journal of Portfolio Management (fall), 1–14.Google Scholar
  58. Clarke, R., de Silva, H., & Thorley, S. (2018). When does capitalization weighting outperform? Factor-based explanations. The Journal of Index Investing, 9(2), 6–17.Google Scholar
  59. Conrad, J., & Kaul, G. (1993). Long-term market overreaction or biases in computed returns. Journal of Finance, 48(1), 39–63.Google Scholar
  60. Copeland, L., & Zhu, Y. (2006). Hedging effectiveness in the index futures market (Working paper E2006/10). Cardiff University, Cardiff Business School, Economics Section.Google Scholar
  61. Daniel, K., & Titman, S. (1997). Evidence on the characteristics of cross sectional variation in stock returns. Journal of Finance, 52, 1–33.Google Scholar
  62. Danielsson, J., Jorgensen, B., Sarma, M., & Vries, C. (2006). Comparing downside risk measures for heavy tailed distributions. Economic Letters, 92(2), 202–208.Google Scholar
  63. Dash, S., & Loggie, K. (Standard & Poors). (2008, April). Equal weight indexing – Five years later. Standard & Poors.
  64. Deas, I., Robson, B., Wong, C., & Bradford, M. (2003). Measuring neighbourhood deprivation: A critique of the index of multiple deprivation. Environment and Planning C: Government and Policy, 21(6), 883–903.Google Scholar
  65. DeMiguel, V., Garlappi, L., & Uppal, R. (2007). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915–1953.Google Scholar
  66. Denis, D., McConnell, J., Ovtchinnikov, A., & Yu, Y. (2003). S&P 500 index additions and earnings expectations. Journal of Finance, 58, 1821–1840.Google Scholar
  67. DesHarnais, S. I., Forthman, M. T., Homa-Lowry, J. M., & Wooster, L. D. (1997). How to use risk-adjusted quality indicators to assess hospitals. QRC Advisor, 13(5), 6–8.Google Scholar
  68. DesHarnais, S. I., Forthman, M. T., Homa-Lowry, J. M., & Wooster, L. D. (2000). Risk-adjusted clinical quality indicators: Indices for measuring and monitoring rates of mortality, complications, and readmissions. Quality Management in Health Care, 9(1), 14–22.Google Scholar
  69. Devi, S. (2017). Financial market dynamics: Superdiffusive or not? Journal of Statistical Mechanics: Theory and Experiment, 2017(8), 083207.Google Scholar
  70. Diewert, E. (2009). Cost of living indexes and exact index numbers revised. In D. Slottje (Ed.), Quantifying consumer preferences (Contributions to economic analysis, Vol. 288). Bingley: Emerald Publishing Group.Google Scholar
  71. Dorfleitner, G. (2003). Why the return notion matters. International Journal of Theoretical and Applied Finance, 6, 73–86.Google Scholar
  72. Drew, M., Naughton, T., & Veeraraghavan, M. (2003). Firm size, book-to-market equity and security returns: Evidence from the Shanghai Stock Exchange. Australian Journal of Management, 28, 119–139.Google Scholar
  73. Duarte, F., Tenreiro, J., et al. (2010). Dynamics of the Dow Jones and the NASDAQ stock indexes. Nonlinear Dynamics, 61(4), 691–705.Google Scholar
  74. Eggins, J., & Hill, R. J. (2008). Momentum and contrarian stock-market indices (Working paper).Google Scholar
  75. Elton, E. J., Gruber, M. J., & Busse, J. A. (2004). Are investors rational? Choices among index funds. Journal of Finance, 59, 261–288.Google Scholar
  76. Epaulard, A., & Pommeret, A. (2001, January). Recursive utility, endogenous growth and the welfare cost of volatility (IMF working paper WP/01/5).Google Scholar
  77. Falkenstein, E. G. (2009). Risk and return in general: Theory and evidence (Working paper). Available at:
  78. Fan, G., & Zeng, Y. (2012). The timing of portfolio adjustments: A regime switching approach. International Journal of Information Technology & Decision Making, 11, 909–914.Google Scholar
  79. Fenn, D., Porter, M., et al. (2011). Temporal evolution of financial-market correlations. Physical Review E, 84(2), 026109.Google Scholar
  80. Fernholz, R. (1999). On the diversity of equity markets. Journal of Mathematical Economics, 31(3), 393–417.Google Scholar
  81. Fernholz, R., Garvy, R., & Hannon, J. (1998). Diversity-weighted indexing. Journal of Portfolio Management, 4(2), 74–82.Google Scholar
  82. Fisher, L., Weaver, D., & Webb, G. (2010). Removing biases in computed returns. Review of Quantitative Finance and Accounting, 21, 137–160.Google Scholar
  83. Fisher, L., Weaver, D., & Webb, G. (2012). Removing biases in computed returns: An analysis of bias in equally-weighted return indexes of REITs. International Real Estate Review, 15, 43–71.Google Scholar
  84. Fisher, G., Shah, R., & Titman, S. (2015). Decomposing fundamental indexation. The Journal of Index Investing, 6(3), 10–19.Google Scholar
  85. Flam, S. (2010). Portfolio management without probabilities or statistics. Annals of Finance, 6, 357–368.Google Scholar
  86. Forthman, M. T., Gold, R. S., Dove, H. G., & Henderson, R. D. (2010). Risk-adjusted indices for measuring the quality of inpatient care. Quality Management in Health Care, 19(3), 265–277.Google Scholar
  87. Fowler, S., & Hope, C. (2007). A critical review of sustainable business indices and their impact. Journal of Business Ethics, 76(3), 243–252.Google Scholar
  88. Franzen L., Spizman J., & Suh, J. (2014, September). Added pressure to perform: The effect of S&P 500 index inclusion on earnings management.
  89. Frino, A., Gallagher, D. R., & Oetomo, T. N. (2005). The index tracking strategies of passive and enhanced index equity funds. Australian Journal of Management, 30, 23–55.Google Scholar
  90. Garlappi, L., Shu, T., & Yan, H. (2008). Default risk, shareholder advantage, and stock returns. Review of Financial Studies, 21(6), 2743–2778.Google Scholar
  91. Gharghori, P., Chan, H., & Faff, R. (2007). Are the Fama-French factors proxying default risk? Australian Journal of Management, 32, 223–249.Google Scholar
  92. Goetzmann, W. N., & Massa, M. (2003). Index funds and stock market growth. Journal of Business, 76, 29–38.Google Scholar
  93. Goldman Sachs (2018). S&P GSCI™ commodity index components, weights, index levels and construction.
  94. Goltz, F., & Le Sourd, V. (2010). Does finance theory make the case for capitalization weighted indexing. The Journal of Index Investing, 2(2), 59–75.Google Scholar
  95. Green, R., & Hollifield, B. (1992). When will mean-variance portfolios be well diversified? Journal of Finance, 47(5), 1785–1809.Google Scholar
  96. Groshen, E., Moyer, B., et al. (2017). How government statistics adjust for potential biases from quality change and new goods in an age of digital technologies: A view from the trenches. Journal of Economic Perspectives, 31(2), 187–210.Google Scholar
  97. Guido, R., & Walsh, K. (2001). Equity market valuation: Assessing the adequacy of value measures to predict index returns. Australian Journal of Management, 26, 163–196.Google Scholar
  98. Guo, H. (2004). A rational pricing explanation for the failure of the CAPM. Federal Reserve Bank of St. Louis Review, 86(3), 23–33.Google Scholar
  99. Hajim, C. (2006, October 26). A better way to index? Fortune Magazine.
  100. Haluszczynski, A., Laut, I., et al. (2017). Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization. Physics Review E, 96, 062315.Google Scholar
  101. Harré, M., & Bossomaier, T. (2009). Phase-transition–like behaviour of information measures in financial markets. Europhysics Letters, 87(1), 18009.Google Scholar
  102. Haugen, R. A., & Baker, N. L. (1991). The efficient market inefficiency of capitalization-weighted stock portfolios. Journal of Portfolio Management, 17(3), 35–40.Google Scholar
  103. Hausman, J. (2003). Sources of Bias and solutions to bias in the consumer Price index. Journal of Economic Perspectives, 17(1), 23–44.Google Scholar
  104. Hertzberg, M. (1987). A critique of the dust explosibility index: An alternative for estimating explosion probabilities. U.S. Department of the Interior, Bureau of Mines, Report of Investigations, RI 9095.Google Scholar
  105. Ho, L., & Huang, C. (2015). The nonlinear relationships between stock indexes and exchange rates. Japan and the World Economy, 33, 20–27.Google Scholar
  106. Hoque, A. (2010, January). Econometric modeling for transaction cost-adjusted put-call parity: Evidence from the currency options market (Working paper). Available at:
  107. Hsu, J. (2006). Cap-weighted portfolios are sub-optimal portfolios. Journal of Investment Management, 4(3), 44–53.Google Scholar
  108. Hsu, J. C., & Campollo, C. (2006, January/February 6). New frontiers in index investing. Journal of Indexes.Google Scholar
  109. Hunstad, M. (2016). Choosing factors: Not “which?” but “when?”. The Journal of Index Investing, 7(2), 100–108.Google Scholar
  110. Hunstad, M., & Dekhayser, J. (2015). Evaluating the efficiency of ‘smart beta’ indexes. The Journal of Index Investing, 6(1), 111–121.Google Scholar
  111. Hunstad, M., & Dekhayser, J. (2016). Investors care about the purity of factor indexes: A reply. The Journal of Index Investing, 7(1), 14–16.Google Scholar
  112. Hurlbert, S. (1971). The non-concept of species diversity: A critique and alternative parameters. Ecology, 52(4), 576–580.Google Scholar
  113. ICE. (2017, October). Commodity index methodology – The ICE BofAML commodity index eXtra handbook.
  114. Jacob, R., Koschutzki, D., et al. (2013). Algorithms for centrality indices. In Network analysis (Lecture notes in computer science, Vol. 3418, pp. 62–82).Google Scholar
  115. Jahmani, Y., Niranjan, S., & Toney, S. (2014). Earnings management in recession and recovery periods (Working paper). Available at:
  116. Jalbert, T. (2012). The performance of currency value-adjusted stock indices. The Journal of Index Investing, 3(2), 34–48.Google Scholar
  117. Jha, R., Murthy, K., & Bhanu, V. (2003, April). A critique of the environmental sustainability index (Working paper). Australian National University, Division of Economics. Available at SSRN: or
  118. Jianping, L., et al. (2012). Risk integration mechanisms and approaches in the banking industry. International Journal of Information Technology & Decision Making, 11, 1183–1187.Google Scholar
  119. Joyce, J., & Vogel, R. (1970). The uncertainty in risk: Is variance unambiguous? Journal of Finance, 25(1), 127–134.Google Scholar
  120. Jun, D., & Malkiel, B. (2007). New paradigms in stock market indexing. European Financial Management, 14(1), 118–126.Google Scholar
  121. Kaiser, L., Fleisch, M., & Salcher, L. (2018). Bias and misrepresentation revisited: Perspective on major equity indices. Finance Research Letters, forthcoming.Google Scholar
  122. Kang, W., & Ratti, R. (2013). Oil shocks, policy uncertainty and stock market returns. Journal of International Financial Markets, Institutions and Money, 26, 305–318.Google Scholar
  123. Kaplan, P. (2008). Why fundamental indexation might – Or might not – Work. Financial Analysts Journal, 64(1), 32–39.Google Scholar
  124. Karabatsos, G. (2000). A critique of Rasch residual fit statistics. Journal of Applied Measurement, 1(2), 152–176.Google Scholar
  125. Kassimatis, K. (2008). Size, book to market and momentum effects in the Australian stock market. Australian Journal of Management, 33, 145–168.Google Scholar
  126. Keim, D. B. (1999). An analysis of mutual fund design: The case of investing in small-cap stocks. Journal of Financial Economics, 51, 173–194.Google Scholar
  127. Kim, J., Kim, S. H., & Levin, A. (2003). Patience, persistence and welfare costs of incomplete markets in open economies. Journal of International Economics, 61(2), 385–396.Google Scholar
  128. Klibanoff, P., Marinacci, M., & Mukerji, S. (2009). Recursive smooth ambiguity preferences. Journal of Economic Theory, 144(3), 930–976.Google Scholar
  129. Kliesen, K. (1997, July). Critiquing the consumer price index. Federal Reserve Bank of St. Louis – Regional Economist.
  130. Kovacevic, M. (2011, February). Review of HDI critiques and potential improvements. Human Development Research Paper 2010/33; Human Development Report Office of the United Nations Development Programme (UNDP).
  131. Kumar, V., & Ziemba, W. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2), 6–11.Google Scholar
  132. Kwon, O., & Yang, J. (2008). Information flow between stock indices. Europhysics Letters, 82(6), 68003.Google Scholar
  133. Lee, Y. (2003). Indexation of momentum effects. Journal of Investment Management, 1(4).Google Scholar
  134. Levell, P. (2015). Is the Carli index flawed? Assessing the case for the new retail price index RPIJ. Journal of the Royal Statistical Society: Series A (Statistics in Society), 178, 303–336.Google Scholar
  135. Lewellen, J., & Nagel, S. (2006). The conditional CAPM does not explain asset-pricing anomalies. Journal of Financial Economics, 82, 289–314.Google Scholar
  136. Li, D. (2009). Relative ratio method for multiple attribute decision making problems. International Journal of Information Technology & Decision Making, 8(2), 289–311.Google Scholar
  137. Li, X., & Peng, L. (2017). US economic policy uncertainty and co-movements between Chinese and US stock markets. Economic Modelling, 61, 27–39.Google Scholar
  138. Li, X., Zhang, B., & Gao, R. (2015). Economic policy uncertainty shocks and stock-bond correlations: Evidence from the US market. Economics Letters, 132, 91–96.Google Scholar
  139. Li, X., Balcilar, M., Gupta, M., & Chang, T. (2016). The causal relationship between economic policy uncertainty and stock returns in China and India: Evidence from a bootstrap rolling-window approach. Emerging Markets Finance and Trade, 52(3), 674–689.Google Scholar
  140. Liu, L., & Zhang, T. (2015). Economic policy uncertainty and stock market volatility. Finance Research Letters, 15, 99–105.Google Scholar
  141. Loayza, N., Ranciere, R., Serven, L., & Ventura, J. (2007). Macroeconomic volatility and welfare in developing countries: An introduction. World Bank Economic Review, 21(3), 343–357.Google Scholar
  142. Madhavan, A., & Ming, K. (2002). The hidden costs of index rebalancing: A case study of the S&P 500 composition changes of July 19, 2002 (ITG working paper).Google Scholar
  143. Madhavan, A., Sobczyk, A., & Ang, A. (2018). What’s in your benchmark? A factor analysis of major market indexes. The Journal of Index Investing, 9(2), 66–79.Google Scholar
  144. Maillard S., Roncalli T., & Teiletche J. (2008). On the properties of equally-weighted risk contributions portfolios (Working paper).Google Scholar
  145. Maillard, S., Roncalli, T., & Teiletche, J. (2010). The properties of equally-weighted risk contributions portfolios. Journal of Portfolio Management, 36(4), 60–70.Google Scholar
  146. Malevergne, Y., Santa-Clara, P., & Sornette, D. (2009). Professor Zipf goes to Wall Street (Working paper). National Bureau of Economic Research.Google Scholar
  147. Mar, J., Bird, R., Casavecchia, L., & Yeung, D. (2009). Fundamental indexation: An Australian investigation. Australian Journal of Management, 34, 1–20
  148. Martellini, L. (2008). Towards the Design of better equity benchmarks: Rehabilitating the Tangency portfolio from modern portfolio theory. Journal of Portfolio Management, 34(4), 26–33.Google Scholar
  149. Martin, G., Thomas W., & Wieland M. (2013). S&P 500 membership and managers’ supply of conservative financial reports (Working paper). Indiana University.Google Scholar
  150. Martyn, I., Kuhn, T., et al. (2012). Computing evolutionary distinctiveness indices in large scale analysis. Algorithms for Molecular Biology, 7, 6.
  151. McCulloch, J. H. (1997). Measuring tail thickness to estimate the stable index α: A critique. Journal of Business & Economic Statistics, 15(1), 74–81.Google Scholar
  152. McLaughlin, T. (2008). Eyes wide shut: Exchange traded funds, index arbitrage and the need for change. Annual Review of Banking and Financial Law, 27, 597–608.
  153. Mensi, W., Hammoudeh, S., Reboredo, J., & Nguyen, D. (2014). Do global factors impact BRICS stock markets? A quantile regression approach. Emerging Markets Review, 19, 1–17.Google Scholar
  154. Morris, S. (2006, December 12). What’s the right way to index?
  155. MSCI. (2007, March). MSCI US equity indices: Index construction objectives and methodology the MSCI equity indices. MSCI.Google Scholar
  156. Murphy, E., & Garvey, E. (2005). Cost of living indices and flexible consumption behaviour: A partial critique (Working paper).Google Scholar
  157. Nayebi, H., & Abdollahyan, H. (2006). Social stratification and its indices: A critique. Critique: Critical Middle Eastern Studies, 15(3), 249–263.Google Scholar
  158. Neher, D., & Darby, B. (2006). Computation and application of nematode community indices: General guidelines (Working paper). Available at:
  159. Nobi, A., Lee, S., et al. (2014). Correlation and network topologies in global and local stock indices. Physics Letters A, 378(34), 2482–2489.Google Scholar
  160. Nwogugu, M. (2003). Decision-making under uncertainty: A critique of options pricing models. Derivatives Use, Trading and Regulation (now Journal of Derivatives & Hedge Funds), 9(2), 164–178.Google Scholar
  161. Nwogugu, M. (2005a). Further critique of GARCH/ARMA/VAR/SV models. Applied Mathematics and Computation, 182(2), 1735–1748.Google Scholar
  162. Nwogugu, M. (2005b). Towards multifactor models of decision making and risk: Critique of prospect theory and related approaches, part three. Journal of Risk Finance, 6(3), 267–276.Google Scholar
  163. Nwogugu, M. (2006). Regret minimization, willingness-to-accept-losses and framing. Applied Mathematics and Computation, 179(2), 440–450.Google Scholar
  164. Nwogugu, M. (2010). CML, ICAPM/CAPM and APT/IAPT are inaccurate in incomplete markets with dynamic un-aggregated preferences (Working paper).Google Scholar
  165. Nwogugu, M. (2013). Decision-making, sub-additive recursive “matching” noise and biases in risk-weighted index calculation methods in in-complete markets with partially observable multi-attribute preferences. Discrete Mathematics, Algorithms and Applications, 5, 1350020.
  166. Nwogugu, M. (2015). The ‘popular-index ecosystems’: Managerial psychology, corporate governance and risk. Available at SSRN: or
  167. Nwogugu, M. (2017a). Some biases and evolutionary homomorphisms implicit in the calculation of returns. In M. Nwogugu, Anomalies in net present value, returns and polynomials, and regret theory in decision making (Chapter 8). London: Palgrave Macmillan.Google Scholar
  168. Nwogugu, M. (2017b). Spatio-temporal framing anomalies in the NPV-MIRR-IRR model and related approaches; and regret theory. In M. Nwogugu, Anomalies in net present value, returns and polynomials, and regret theory in decision making (Chapter 2). London: Palgrave Macmillan.Google Scholar
  169. Nwogugu, M. (2017c). The historical and current concepts of “plain” interest rates, forward rates and discount rates can be misleading. In M. Nwogugu, Anomalies in net present value, returns and polynomials, and regret theory in decision making (Chapter 6). London: Palgrave Macmillan.Google Scholar
  170. Nwogugu, M. (2017d). Regret theory and asset pricing anomalies in incomplete markets with dynamic un-aggregated preferences. In M. Nwogugu, Anomalies in net present value, returns and polynomials, and regret theory in decision making (Chapter 3). London: Palgrave Macmillan.Google Scholar
  171. Ongan, E., & Gocer, I. (2017). Testing the causalities between economic policy uncertainty and the US stock indices: Applications of linear and nonlinear approaches. Annals of Financial Economics, 12, 1750016.Google Scholar
  172. Onnela, J., Chakraborti, A., et al. (2003). Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E, 68(5), 056110.Google Scholar
  173. Ozer, G., & Ertokatli, C. (2010). Chaotic processes of common stock index returns: An empirical examination on Istanbul stock exchange (ISE) market. African Journal of Business Management, 4(6), 1140–1148.Google Scholar
  174. Pallage, S., & Robe, M. (2003). On the welfare cost of economic fluctuations in developing countries. International Economic Review, 44(2), 677–698.Google Scholar
  175. Perold, A. (2007). Fundamentally flawed indexing. Financial Analysts Journal, 6(6), 31–37.Google Scholar
  176. Platt, H., Cai, L., & Platt, M. (2014). Is the DJIA index biased? The Journal of Index Investing, 4(4), 43–52.Google Scholar
  177. Plerou, V., Gopikrishnan, P., et al. (1999). Universal and nonuniversal properties of cross correlations in financial time series. Physical Review Letters, 83(7), 1471.Google Scholar
  178. Poitras, G., Veld, C., & Zabolotnyuk, Y. (2009). European put-call parity and the early exercise premium for American currency options. Multinational Finance Journal, 13(1/2), 39–54.Google Scholar
  179. Pope, B. (2008). Insights on market capitalization and fundamental weighted indexes (Working paper).
  180. Powell, P., Roa, R., Shi, J., & Xayavong, V. (2007). A test for long-term cyclical clustering of stock market regimes. Australian Journal of Management, 32, 205–221.Google Scholar
  181. Preis, T., Schneider, J., & Stanley, H. (2011). Switching processes in financial markets. Proceedings of the National Academy of Sciences (USA), 108(19), 7674–7678.Google Scholar
  182. Prono, T. (2007, June). GARCH-based identification of triangular systems with an application to the CAPM: Still living with the roll critique (Working papers #07-1). Federal Reserve Bank of Boston.
  183. Prono, T. (2009, June). Market proxies, correlation and relative mean-variance efficiency: Still living with the roll critique (Working paper # QAU09-3). Federal Reserve Bank of Boston.Google Scholar
  184. Raddant, K., Zatlavi, M., et al. (2012). Correlations in the global financial village. International Journal of Modern Physics: Conference Series, 16(1), 13–28.Google Scholar
  185. Ramsden, J. J. (2009). Impact factors: A critique. Journal of Biological Physics & Chemistry, 9, 139–140.Google Scholar
  186. Rauterberg, G., & Verstein, A. (2013). Index theory: The law, promise and failure of financial indices. Yale Journal on Regulation, 30(1), 1–10.Google Scholar
  187. Ronalds, N., & Anderson, C. (2006, November/December). The Synthetic EAFE index. Journal of Indexes.Google Scholar
  188. Russell. (2008). US equity style methodology – Comments. Russell Investments.Google Scholar
  189. S&P Dow Jones Indices. (2018a). S&P global carbon efficient indices: Our approach.
  190. S&P Dow Jones Indices. (2018b). S&P GSCI methodology.
  191. S&P Dow Jones Indices. (2018c). S&P global carbon efficient index series methodology.
  192. S&P Dow Jones Indices. (2018d). Fixed income index mathematics methodology.Google Scholar
  193. S&P Dow Jones Indices. (2018e). S&P green bond indices methodology.
  194. Schultz, M. T. (2001). A critique of EPA’s index of watershed indicators. Journal of Environmental Management, 62(4), 429–442.Google Scholar
  195. Serrano, R., & Aumann, R. J. (2008). An economic index of riskiness. Journal of Political Economy, 116(5), 810–836.Google Scholar
  196. Shapira, Y., Kenett, D., & Ben-Jacob, E. (2009). Index cohesive effect on the market. European Physical Journal B, 72(4), 657–669.Google Scholar
  197. Siegel, J. J., Schwartz, J. D., & Siracusano, L. (2007). The unique risk and return characteristics of dividend-weighted stock indexes (Working paper).Google Scholar
  198. Sims, C. (1980). Macroeconomics and reality. Econometrica, 48(1), 1–48.Google Scholar
  199. Staines, J. (2016). Component risk parity: Using traditionally weighted indexes in an equal risk fashion. The Journal of Index Investing, 6(4), 82–87.Google Scholar
  200. Steel, M., Mimoto, A., & Mooers, A. (2007). Hedging our bets: The expected contribution of species to future phylogenetic diversity. Evolutionary Bioinformatics, 3, 237–244.Google Scholar
  201. Su, Z. (2011). A hybrid fuzzy approach to fuzzy multi attribute group decision making. International Journal of Information Technology & Decision Making, 10, 695–700.Google Scholar
  202. Sum, V. (2012). The effect of economic policy uncertainty in the US on the stock market performance in Canada and Mexico. International Journal of Economics and Finance, 4(11), 165–171.Google Scholar
  203. Suryanarayanan, R., Varga, K., Gupta, A., & Kassam, A. (2014). Index performance in changing economic environments. MSCI Research Insight, MSCI.Google Scholar
  204. Tabner, I. (2007). Benchmark concentration: Capitalisation weights versus equal weights in the FTSE 100 index (Working paper). University of Stirling.Google Scholar
  205. Takahashi, H. (2012). An analysis of the influence of dispersion of valuations on financial markets through agent-based modeling. International Journal of Information Technology & Decision Making, 11, 143–148.Google Scholar
  206. Taleb, N. (2008). Finiteness of variance is irrelevant in the practice of quantitative finance. Complexity, 14(3), 66–76.Google Scholar
  207. Theiler, J., Eubank, S., et al. (1992). Testing for nonlinearity in time series: The method of surrogate data. Physica D: Nonlinear Phenomena, 58(1–4), 77–94.Google Scholar
  208. Thomson Reuters. (2009, November). Thomson Reuters business classification methodology.Google Scholar
  209. Thomson Reuters. (2010, February). Thomson Reuters country and regional index methodology.
  210. Thurston, M. (2011). Expansion of the Russell stability indexes: The global series. Russell Investments.
  211. Tofallis, C. (2008). Investment volatility: A critique of standard beta estimation and a simple way forward. European Journal of Operational Research, 187, 1358–1367.Google Scholar
  212. Tower, E., & Yang, C. (2013). Is traditional indexation Passé? Vanguard versus the enhanced indexers: DFA, RAFI, and WisdomTree. The Journal of Index Investing, 4(1), 70–81.Google Scholar
  213. Tumminello, M., Di Matteo, T., Aste, T., & Mantegna, R. (2007). Correlation based networks of equity returns sampled at different time horizons. The European Physical Journal B, 55(2), 209–217.Google Scholar
  214. U.S. Department of Commerce/National Oceanic and Atmospheric Administration. (2003). Report on wind chill temperature and extreme heat indices: Evaluation and improvement projects (Working paper). US Government.
  215. Van Dijk, M. (2007, July). The size effect paradox (Working paper).Google Scholar
  216. Van Dijk, M., Karolyi, G. A., & Lee, K. (2009, June). Commonality in returns, liquidity, and turnover around the world (Working paper).Google Scholar
  217. Vassalou, M., & Xing, Y. (2004). Default risk in equity returns. Journal of Finance, 59, 831–868.Google Scholar
  218. Von Der Lippe, P. (1999). A critique of international recommendations concerning price index formulas. Journal of Economics and Statistics, 218(3+4), 385–414.Google Scholar
  219. Von der Lippe, P., & Diewert, E. (2010). Notes on unit value index Bias. Journal of Economics and Statistics, 230(6), 690–708.Google Scholar
  220. Vortelinos, D., Gkillas, K., et al. (2018). Asymmetric and nonlinear inter-relations of US stock indices. International Journal of Managerial Finance, 14(1), 78–129.Google Scholar
  221. Wagner, N., & Stocker, E. (2009). A new family of equity style indices (Working paper).Google Scholar
  222. Wagner, D., Ellis, D., & Dubofsky, D. (1996). The factors behind put-call parity violations of S&P 100 index options. Financial Review, 31, 535–552.Google Scholar
  223. Walkshäusl, C., & Lobe, S. (2010). Fundamental indexing around the world. Review of Financial Economics, 19(3), 117–127.Google Scholar
  224. Walsh, D. (1997). Orders vs trades: Price effects and size measures. Australian Journal of Management, 22(1), 47–69.Google Scholar
  225. White, A. (2007). Biases in consumer price indexes. International Statistical Review, (3), 67.Google Scholar
  226. Willey, T. (1992). Testing for nonlinear dependence in daily stock indices. Journal of Economics and Business, 44, 63–76.Google Scholar
  227. Zang, A. (2012). Evidence on the trade-off between real activities manipulation and accrual-based earnings management. The Accounting Review, 87(2), 675–703.Google Scholar
  228. Zatlavi, L., Kenett, D., & Ben-Jacob, E. (2014). The design and performance of the adaptive stock market index. Algorithmic Finance, 3, 189–207.
  229. Zinkevich, M., Bowling, M., Johanson, M., & Piccione, C. (2009). Regret minimization in games with incomplete information. Advances in Neural Information Processing Systems, 20(NIPS), 905–912.Google Scholar
  230. Zitzewitz, E. (2003). Who cares about shareholders? Arbitrage-proofing mutual funds. Journal of Law, Economics, and Organization, 19(2), 245–280.Google Scholar

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Authors and Affiliations

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

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