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

  • Michael I. C. Nwogugu


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.


Risk-weighted indices Index methodology Incomplete markets Index tracking funds Financial stability ETFs Optimization Portfolio management Nonlinear risk 


  1. Adler, T., & Kritzman, M. (2007). Mean-variance versus full-scale optimization: In and out of sample. Journal of Asset Management, 7, 302–311.Google Scholar
  2. Ahn, C., Byoun, S., & Park, H. Y. (2003). Put-call parity: The case of KOSPI200 options in Korea (Working paper).
  3. Ait-Sahalia, Y., Fan, J., & Xiu, D. (2010). High-frequency covariance estimates with noisy and asynchronous data. Journal of the American Statistical Association, 105, 1504–1517.Google Scholar
  4. Aksu, M., & Onder, T. (2003). The size and book-to-market effects and their role as risk proxies in the Istanbul stock exchange (Working paper).
  5. Alexander, C., & Barbosa, A. (2007). Effectiveness of minimum-variance hedging: The impact of electronic trading and exchange-traded funds. Journal of Portfolio Management, 33(2), 46–59.Google Scholar
  6. 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). Paris: EDHEC. html/attachments/Af2iEDHEC indices study.pdf
  7. Amenc, N., Goltz, F., Martellini, L., & Retkowsky, A. (2010). Efficient indexation: An alternative to cap-weighted indices. Journal of Investment Management, 9(4), 1–23.Google Scholar
  8. Amenc, N., Goltz, F., Martellini, L., & Ye, S. (2011). Improved beta? A comparison of index-weighting schemes. Journal of Indexes.Google Scholar
  9. Amigó, J., & Hirata, Y. (2018). Detecting directional couplings from multivariate flows by the joint distance distribution. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075302.Google Scholar
  10. Ang, A., Hodrick, R., Xing, Y., & Zhang, X. (2005). The cross-section of volatility and expected returns. Journal of Finance, 61(1), 259–269.Google Scholar
  11. Arnott, R., Hsu, J., & Moore, P. (2005). Fundamental indexation. Financial Analysts Journal, 61(2), 83–99.Google Scholar
  12. Arnott, R., Kalesnik, B., Moghtader, P., & Scholl, R. (2010). Beyond cap weight: The empirical evidence for a diversified beta. Journal of Indexes, 2010, 16–26.Google Scholar
  13. Aulerich, N., Fisher, R., & Harris, J. (2011). Why do expiring futures and cash prices diverge for grain markets? Journal of Futures Markets, 31, 503–533.Google Scholar
  14. 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
  15. Backus, D., Routledge, B., & Zin, S. (2005). Recursive preferences (NYU working paper no. EC-05-19).
  16. Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2011). Multivariate realized kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. Journal of Econometrics, 162, 149–169.Google Scholar
  17. Becker, R., Clements, A., & White, S. (2007). Does implied volatility provide any information beyond that captured in model-based volatility forecasts? Journal of Banking & Finance, 31(8), 2535–2549.Google Scholar
  18. Berk, J. (1995). A critique of size-related anomalies. Review of Financial Studies, 8, 275–286.Google Scholar
  19. 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
  20. 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
  21. Blitz, D., & Van Vliet, P. (2007). The volatility effect: Lower risk without lower returns. Journal of Portfolio Management, 34(1), 102–113.Google Scholar
  22. Blitzer, D. (2004). Free float adjustment for the S&P (Standard & Poor’s, 2004).Google Scholar
  23. Blume, M., & Stambaugh, R. (1983). Biases in computed returns: An application to the size effect. Journal of Financial Economics, 12, 387–404.Google Scholar
  24. Bollen, N., & Whaley, R. (2004). Does net buying pressure affect the shape of implied volatility functions? Journal of Finance, 59, 711–754.Google Scholar
  25. Broadie, M., Chernov, M., & Johannes, M. (2009). Understanding index option returns. Review of Financial Studies, 22(11), 4493–4529.Google Scholar
  26. 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
  27. Chan, L., 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
  28. Chang, C., Hsieh, P., & Lai, H. (2009). Do informed option investors predict stock returns? Evidence from the Taiwan stock exchange. Journal of Banking & Finance, 33(4), 757–764.Google Scholar
  29. Chen, T. (2012). Nonlinear 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
  30. Chen, H., et al. (2006). Index changes and losses to index fund investors. Financial Analysts Journal, 62, 31–34.Google Scholar
  31. Chng, N. (2004). The trading dynamics of close-substitute futures markets: Evidence of margin policy spillover effects. Journal of Multinational Financial Management, 14(4–5), 463–483.Google Scholar
  32. Choueifaty, Y., & Coignard, Y. (2008). Toward maximum diversification. Journal of Portfolio Management, 35(1), 40–51.Google Scholar
  33. Cochrane, J. (2014). A mean-variance benchmark for intertemporal portfolio theory. Journal of Finance, 69(1), 1–49.Google Scholar
  34. Conrad, J., & Kaul, G. (1993). Long-term market overreaction or biases in computed returns. Journal of Finance, 48(1), 39–63.Google Scholar
  35. 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
  36. Corrado, C. J., & Miller, T. W. (2005). The forecast quality of CBOE implied volatility indexes. Journal of Futures Markets, 25, 339–373.Google Scholar
  37. CXO Advisory Group. (2008). Extinction of the predictive power of futures? Available at:
  38. Daniel, K., & Titman, S. (1997). Evidence on the characteristics of cross sectional variation in stock returns. Journal of Finance, 52, 1–33.Google Scholar
  39. 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
  40. de Silva, R., Clarke, H., & Thorley, S. (2006). Minimum-variance portfolios in the U.S. equity market. Journal of Portfolio Management, 33(1), 1–14.Google Scholar
  41. DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915–1953.Google Scholar
  42. DesHarnais, S., Forthman, M., Homa-Lowry, J., & Wooster, L. D. (1997). How to use risk-adjusted quality indicators to assess hospitals. QRC Advisor, 13(5), 6–8.Google Scholar
  43. DesHarnais, S., Forthman, M., Homa-Lowry, J., & 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
  44. Dorfleitner, G. (2003). Why the return notion matters. International Journal of Theoretical and Applied Finance, 6, 73–86.Google Scholar
  45. Dotsis, G., Psychoyios, D., & Skiadopoulos, G. (2007). An empirical comparison of continuous-time models of implied volatility indices. Journal of Banking & Finance, 31, 3584–3603.Google Scholar
  46. 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
  47. EDHEC Risk Institute. (2010, October). Methodologies for the management of the FTSE EDHEC-RISK efficient index series. EDHEC. EDHEC-Risk Efficient Index Series Rules.pdf
  48. Eggins, J., & Hill, R. J. (2008). Momentum and contrarian stock-market indices (Working paper).Google Scholar
  49. Elton, E. J., Gruber, M., & Busse, J. A. (2004). Are investors rational? Choices among index funds. Journal of Finance, 59, 261–288.Google Scholar
  50. Epaulard, A., & Pommeret, A. (2009). Recursive utility, endogenous growth and the welfare cost of volatility (IMF working paper No. 1/5).Google Scholar
  51. Falkenstein, E. G. (2009). Risk and return in general: Theory and evidence (Working paper).
  52. Fenn, D. J., et al. (2011). Temporal evolution of financial-market correlations. Physics Review E, 84, 61–65.Google Scholar
  53. Fernholz, R. (1999a). Diversity-weighted equity indexes. Journal of Indexes.
  54. Fernholz, R. (1999b). On the diversity of equity markets. Journal of Mathematical Economics, 31(3), 393–417.Google Scholar
  55. Fernholz, R., Garvy, R., & Hannon, J. (1998). Diversity-weighted indexing. Journal of Portfolio Management, 4(2), 74–82.Google Scholar
  56. 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, 1, 43–71.Google Scholar
  57. Flam, S. D. (2010). Portfolio management without probabilities or statistics. Annals of Finance, 6(3), 357–368.Google Scholar
  58. Forthman, M., Gold, R., Dove, H., & 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
  59. Frino, A., Gallagher, D., & Oetomo, T. (2005). The index tracking strategies of passive and enhanced index equity funds. Australian Journal of Management, 30, 23–55.Google Scholar
  60. Garlappi, L., Shu, T., & Yan, H. (2008). Default risk, shareholder advantage and stock returns. Review of Financial Studies, 21(6), 2743–2778.Google Scholar
  61. Gharghori, P., Chan, H., & Faff, R. (2007). Are the Fama-French factors proxying default risk? Australian Journal of Management, 32, 223–249.Google Scholar
  62. Giot, P. (2005a). Relationships between implied volatility indexes and stock index returns. Journal of Portfolio Management, 31, 92–100.Google Scholar
  63. Giot, P. (2005b). Implied volatility indexes and daily value at risk models. The Journal of Derivatives, 12(4), 54–64.Google Scholar
  64. Goyal, A., & Santa-Clara, P. (2003). Idiosyncratic risk matters. Journal of Finance, 58, 975–1007.Google Scholar
  65. Green, R., & Hollifield, B. (1992). When will mean-variance portfolios be well diversified? Journal of Finance, 47(5), 1785–1809.Google Scholar
  66. Guo, H. (2004). A rational pricing explanation for the failure of the CAPM. Federal Reserve Bank of St. Louis Review, 86(3), 23–34.Google Scholar
  67. Haugen, R., & Baker, N. L. (1991). The efficient market inefficiency of capitalization weighted stock portfolios. Journal of Portfolio Management, 17(3), 35–40.Google Scholar
  68. Hertzberg, M. (1987). A critique of the dust explosibility index: An alternative for estimating explosion probabilities, Report of Investigations. U.S. Department of the Interior, Bureau of Mines, RI 9095.Google Scholar
  69. Hoque, A. (2010). Econometric modeling for transaction cost-adjusted put-call parity: Evidence from the currency options market (Working paper).
  70. Hsu, J. (2006). Cap-weighted portfolios are sub-optimal portfolios. Journal of Investment Management, 4(3), 1–10.Google Scholar
  71. Hsu, J. C., & Campollo, C. (2006). New frontiers in index investing. Journal of Indexes, 58, 32–37.Google Scholar
  72. Huberman, G., & Kandel, S. (1987). Mean-variance spanning. Journal of Finance, 42(4), 873–888.Google Scholar
  73. Hurlbert, S. (1971). The non-concept of species diversity: A critique and alternative parameters. Ecology, 52(4), 576–580.Google Scholar
  74. Jensen, M. (1968). The performance of mutual funds in the period 1945–1964. Journal of Finance, 23(2), 389–416.Google Scholar
  75. Jha, R., Murthy, K., & Bhanu, V. (2003, April). A critique of the environmental sustainability index (Australian National University Division of Economics working paper). or
  76. Joyce, J., & Vogel, R. (1970). The uncertainty in risk: Is variance unambiguous? Journal of Finance, 25(1), 127–134.Google Scholar
  77. Juttner, J., & Leung, W. (2009). Towards decoding currency volatilities. Multinational Finance Journal, 13(1/2), 103–134.Google Scholar
  78. Karabatsos, G. (2000). A critique of rasch residual fit statistics. Journal of Applied Measurement, 1(2), 152–176.∼georgek/HomePage/Karabatsos2000JAM.pdfGoogle Scholar
  79. 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
  80. 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
  81. Kinnebrock, S., & Podolskij, M. (2008). Estimation of the quadratic covariation matrix in noisy diffusion models (Unpublished working paper). University of Oxford and Heidelberg University.Google Scholar
  82. Klibanoff, P., Marinacci, M., & Mukerji, S. (2009). Recursive smooth ambiguity preferences. Journal of Economic Theory, 144(3), 930–976.Google Scholar
  83. Klitgaard, T., & Weir, L. (2004). Exchange rate changes and net positions of speculators in futures markets. Economic Policy Review — Federal Reserve Bank of New York, 10(1), 17–28.Google Scholar
  84. Konstantinidi, E., & Skiadopoulos, G. (2011). Are VIX futures prices predictable? An empirical investigation. International Journal of Forecasting, 27(2), 543–560.Google Scholar
  85. Konstantinidi, E., Skiadopoulos, G., & Tzagkaraki, E. (2008). Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices. Journal of Banking & Finance, 32(11), 2401–2411.Google Scholar
  86. Kriener, B., Helias, M., Rotter, S., et al. (2014). How pattern formation in ring networks of excitatory and inhibitory spiking neurons depends on the input current regime. Frontiers of Computational Neuroscience, 7, 187–191.Google Scholar
  87. Kroll, Y., Levy, H., & Markowitz, H. (1984). Mean-variance versus direct utility maximization. Journal of Finance, 39(1), 47–61.Google Scholar
  88. 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
  89. Lee, Y. (2004). Indexation of momentum effects. EFMA 2004 Basel Meetings Paper. Available at SSRN: or
  90. Lewellen, J., & Nagel, S. (2006). The conditional CAPM does not explain asset-pricing anomalies. Journal of Financial Economics, 82(2), 289–314.Google Scholar
  91. Liang, S. (2018). Causation and information flow with respect to relative entropy. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075311.Google Scholar
  92. 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
  93. Madhavan, A., & Ming, K. (2002). The hidden costs of index re-balancing: A case study of the S&P 500 composition changes of July 19, 2002 (ITG working paper).Google Scholar
  94. Maillard, S., Roncalli, T., & Teiletche, J. (2008, September). On the properties of equally-weighted risk contributions portfolios (SSRN working paper).Google Scholar
  95. Mar, J., Bird, R., Casavecchia, L., & Yeung, D. (2010). Fundamental indexation: An Australian investigation. Australian Journal of Management, 34(1), 1–20.Google Scholar
  96. Martellini, L. (2008). Towards the design of better equity benchmarks: Rehabilitating the tangency portfolio from modern portfolio theory. Journal of Portfolio Management, 34(4), 34–41.Google Scholar
  97. Martellini, L., & Urosevic, B. (2006). Static mean-variance analysis with uncertain time horizon. Management Science, 52(6), 955–964.Google Scholar
  98. 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 Scholar
  99. Morris, S. (2006, December). What’s the right way to index? (Working paper).
  100. MSCI. (2011, May). MSCI factor indices methodology. USA: MSCI. docs/MSCI Factor Index Methodology May11.pdf
  101. MSCI Barra. (2009, November). MSCI minimum volatility indices methodology. USA: MSCI Barra. and strategy/minimum volatility/MSCI Minimum Volatility Methodology.pdf
  102. Murphy, E., & Garvey, E. (2005). Cost of living indices and flexible consumption behavior: A partial critique (Department of Economics National University of Ireland working paper no. 0103).Google Scholar
  103. Nayebi, H., & Abdollahyan, H. (2006). Social stratification and its indices: A critique. Critique: Critical Middle Eastern Studies, 15(3), 249–263.Google Scholar
  104. Neely, C. J. (2009). Forecasting foreign exchange volatility: Why is implied volatility biased and inefficient? And does it matter? Journal of International Financial Markets, Institutions and Money, 19(1), 188–205.Google Scholar
  105. Neher, D., & Darby, B. (2006). Computation and application of nematode community indices: General guidelines. In E. Abebe, W. Traunspurger, & I. Andrassy (Eds.), Freshwater nematodes: Ecology and taxonomy (pp. 211–222). Oxfordshire: CABI Publishing.Google Scholar
  106. Neukirch, T. (2008). Alternative indexing with the MSCI World Index (Working paper).Google Scholar
  107. Nossman, N., & Wilhelmsson, A. (2009). Is the VIX futures market able to predict the VDC index? A test of the expectation hypothesis. The Journal of Alternative Investments, 12(2), 54–67.Google Scholar
  108. Nwogugu, M. (2003). Decision-making under uncertainty: A critique of options pricing models. Journal of Derivatives & Hedge Funds, 9(2), 164–178.Google Scholar
  109. Nwogugu, M. (2005a). Towards multifactor models of decision making and risk: Critique of prospect theory and related approaches, part two. Journal of Risk Finance, 6(2), 163–173.Google Scholar
  110. 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
  111. Nwogugu, M. (2006). Further critique of GARCH/ARMA/VAR/SV models. Applied Mathematics and Computation, 182(2), 1735–1748.Google Scholar
  112. Nwogugu, M. (2010a). Correlation, variance, co-variance and semi-variance are irrelevant in Risk Analysis and Portfolio Management (Working paper).Google Scholar
  113. Nwogugu, M. (2010b). CML, ICAPM/CAPM and APT/IAPT are inaccurate in incomplete markets with dynamic unaggregated preferences (Working paper).Google Scholar
  114. Nwogugu, M. (2010c). Sub-additive recursive ‘matching’ noise and biases in risk-weighted index calculation methods in incomplete markets with partially observable multi-attribute preferences (March 10, 2012). Available at SSRN: or
  115. 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
  116. Nwogugu, M. (2017b). 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
  117. Pallage, S., & Robe, M. (2003). On the welfare cost of economic fluctuations in developing countries. International Economic Review, 44(2), 677–698.Google Scholar
  118. Paluš, M., Krakovská, A., et al. (2018). Causality, dynamical systems and the arrow of time. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075307.Google Scholar
  119. Pearson, K. (1895). Contributions to the mathematical theory of evolution II: skew variations in homogeneous material. Philosophical Transactions of the Royal Society London A, 186, 343–414.Google Scholar
  120. Perdue, W. C. (1987). Manipulation of futures markets: Redefining the offense. Fordham Law Review, 56(3), 345–355.Google Scholar
  121. 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
  122. 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(2), 205–221.Google Scholar
  123. Prono, T. (2007, June). GARCH-based identification of triangular systems with an application to the CAPM: Still living with the roll critique (Federal Reserve Bank of Boston working paper #07-1).
  124. Prono, T. (2009, June). Market proxies, correlation and relative mean-variance efficiency: Still living with the roll critique (Federal Reserve Bank of Boston working paper #QAU09-3).Google Scholar
  125. Qian, E. (2005, September). Risk parity portfolios: Efficient portfolios through true diversification. Panagora Asset Management, USA.Google Scholar
  126. Qian, E. (2006). On the financial interpretation of risk contributions: Risk budgets to add up. Journal of Investment Management, 4(4), 41–51.Google Scholar
  127. Ramsden, J. J. (2009). Impact factors: A critique. Journal of Biological Physics & Chemistry, 9, 139–140. factors-a critique2009.pdfGoogle Scholar
  128. 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
  129. Ronalds, N., & Anderson, C. (2008). The synthetic EAFE index. Journal of Indexes, 8(6), 30–35.Google Scholar
  130. Roy, S., & Jantzen, B. (2018). Detecting causality using symmetry transformations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075305.Google Scholar
  131. Runge, J. (2018). Causal network reconstruction from time series: From theoretical assumptions to practical estimation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075310.Google Scholar
  132. Rupea, A., & Crutchfield, J. (2018). Local causal states and discrete coherent structures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28, 075312.Google Scholar
  133. Russell. (2008). US equity style methodology, comments. USA: Russell.Google Scholar
  134. S&P Dow Jones Indices. (2011, August). S&P index mathematics methodology. USA: Standard & Poor’s.Google Scholar
  135. Sault, S. (2005). Movements in Australian stock volatility: A disaggregated approach. Australian Journal of Management, 30(2), 303–320.Google Scholar
  136. Scherer, B. (2011). A new look at minimum variance investing. Journal of Empirical Finance, 18(4), 652–660.Google Scholar
  137. Schultz, M. T. (2001). A critique of EPA’s index of watershed indicators. Journal of Environmental Management, 62(4), 429–442.Google Scholar
  138. Serrano, R., & Aumann, R. J. (2008). An economic index of riskiness. Journal of Political Economy, 116(5), 810–836.Google Scholar
  139. Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119–138.Google Scholar
  140. Siegel, J. J., Schwartz, J. D., & Siracusano, L. (2007). The unique risk and return characteristics of dividend weighted stock indexes (Working paper).Google Scholar
  141. Szakmary, A., Ors, E., Kim, J. K., & Davidson, W. N. (2003). The predictive power of implied volatility: Evidence from thirty five futures markets. Journal of Banking & Finance, 27, 2151–2175.Google Scholar
  142. Taleb, N. (2009). Finiteness of variance is irrelevant in the practice of quantitative finance. Complexity, 14(3), 66–76.Google Scholar
  143. Thomson Reuters. (2007). Lipper optimal indices. Thomson Reuters.
  144. 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
  145. Treynor, J. (1965). How to rate management of investment funds. Harvard Business Review, 43(1), 63–75.Google Scholar
  146. Tucker, T. (1997). Rethinking rigor in calculus: The role of the mean value theorem. American Mathematical Monthly, 104(3), 231–240.Google Scholar
  147. Tzang, S., Hung, C., Wang, C., & Shyu, D. (2011). Do liquidity and sampling methods matter in constructing volatility indices? Empirical evidence from Taiwan. International Review of Economics & Finance, 20(2), 312–324.Google Scholar
  148. U.S. Department of Commerce/National Oceanic and Atmospheric Administration. (2003). Report on wind chill temperature and extreme heat indices: Evaluation and improvement projects. opening.pdf
  149. Varadi, D., Kapler M., Bee H., & Rittenhouse, C. (2012). The minimum correlation algorithm: A practical diversification tool (Working paper).Google Scholar
  150. 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
  151. Wagner, N., & Stocker, E. (2009). A new family of equity style indices (Working paper).Google Scholar
  152. Walsh, D. (1997). Orders vs trades: Price effects and size measures. Australian Journal of Management, 22(1), 47–69.Google Scholar
  153. Zitzewitz, E. (2003). Who cares about shareholders? Arbitrage-proofing mutual funds. Journal of Law, Economics and Organization, 19(2), 245–280.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

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

Personalised recommendations