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Some New Index-Calculation Methods and Their Mathematical Properties

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Indices, Index Funds And ETFs

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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.

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Notes

  1. 1.

    See: Zitzewitz (2003), Haslem (2008), Donnelly and Tower (2007), IFA (2002), Birdthistle (2008), Boudoukh et al. (2002), Houge and Wellman (2005), Greene and Hodges (2002), Turkington and Walsh (1999), Heaney (1995), and Stoll and Whaley (1997).

  2. 2.

    See Balk (1995, 2016), Van Veelen and Vander Weide (2008), Diewert (1978, 2005), Malaney (1996), Vartia (1976a, b, 1978, 1983, 2010), Lintunen et al. (2009), Pursiainen (2005), Törnqvist et al. (1985), Vartia and Vartia (1984), Bleecker (2013), Hosseiny (Jan. 2017), Barnett and Chauvet (2011), Von Der Lippe and Diewert (2010), Silver (1982), Bai and Ng (2002), Onatski (2009), White (2007), Afriat (2012), Elliott et al. (2013), Jazari (2013), Ivancic et al. (2011), Levell (2015), Clements et al. (2006), Vartia and Weymark (1981), Hausman (2003), Sabourin (2012), Groshen et al. (2017), Akem (2018) and Kaiser et al. (2018).

  3. 3.

    See https://www.eurexchange.com/blob/934090/f6266dfd6baed0afb34e6068181adf2a/data/2014_06_11_cs_1_history_en.pdf.pdf

  4. 4.

    See: http://www.indexfunds.com/PFarticles/20000224_etfwhite_adv_veh_JN.htm See: Disclosure Regarding Market Timing and Selective Disclosure of Portfolio Holdings, 68 Fed. Reg. 70402, 70408 (proposed Dec. 17, 2003) (to be codified at 17 C.F.R. pt. 239). See generally, iShares, http://www.ishares.com/home.htm (last visited Apr. 15, 2008). See: http://www.sec.gov/news/speech/1987/100687ruder.pdf

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Nwogugu, M.I.C. (2018). Some New Index-Calculation Methods and Their Mathematical Properties. In: Indices, Index Funds And ETFs. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-44701-2_10

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