Application of Luenberger Shortage Function on the Zagreb Stock Exchange: Analysis of Efficient Market Portfolio
In order to apply the CAPM in practice, the estimation of the market portfolio presents one of the biggest challenges. Even more so after the research in early 1990s pointed out the mean-variance inefficiency of stock market capitalization-weighted indices. In the paper we perform an in-sample optimisation for the CROBEX index constituents to test its efficiency ex post. Selected CROBEX index revisions from the period March 2005 – September 2017 are analysed. We find the index to be inefficient which confirms the results of earlier studies. However, since mean-variance optimisation often yields extreme portfolio weights, thus reducing the effective number of stocks in the portfolio, the focus of this research is on testing if improvement in efficiency over the CROBEX index is possible, with respect to the portfolio deconcentration level. The Luenberger’s shortage function is added to the optimisation algorithm in order to increase the number of efficient portfolios analysed.
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