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Abstract
The work of Haugen and Baker (1991) and Grinold (1992) has shown that market capitalisation-weighted indices are not mean-variance efficient. Further research by Amenc, Goltz, and Le Sourd (2006) proves that even naive equal weighting can offer a better risk to return trade-off to investors in the developed markets. Based on earlier research findings of Zoricic, Dolinar, and Kozul (2014) and Dolinar, Zoricic and Kozul (2017) for the Croatian market which demonstrated that outperforming the cap-weighted index in an illiquid and undeveloped market is much more challenging the aim of this paper is to assess the efficiency of both CROBEX and CROBEX 10 stock market indices. Efficient frontier was derived based on historical data ("ex post") for 5 revisions for each index. The distance from the efficient frontier was calculated revealing weaker efficiency but also greater diversification opportunities in the case of the broader CROBEX index. However, lower efficiency gains and higher estimation error in emerging market environment reduce significantly the out-of-sample potential for efficient index benchmarks. The analysis conducted in this paper makes it hard to assess if such potential truly exists but provides an insight based on calculation of indifference transaction costs following the work of Amenc et al. (2011).
Keywords: cap-weighted indices, index efficiency.
Jel Classification: G11; G12
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INTRODUCTION
In the 1990's the research of Haugen and Baker (1991) and Grinold (1992) pointed out for the first time that stock market cap-weighted indices offer an inefficient risk to return trade-off. The finding was crucial both for practice and theory of the passive portfolio management as it corroborated a much earlier research of Roll (1977) who addressed the issue of the market portfolio in the Capital Asset Pricing Model (CAPM) being unobservable. Since it is unobservable a proxy has to be used in its place in order to apply the CAPM in practice. Roll argued that such a proxy would not represent a meanvariance efficient portfolio as opposed to the CAPM market portfolio which must be efficient if the CAPM assumptions hold (Amenc et al. 2006, 31).
According to Goltz and Le Sourd (2011) Roll's findings focused on the CAPM but in the broader context of the passive portfolio management they meant that there is no...