engleski

Application of Luenberger shortage function on the Zagreb Stock Exchange: analysis of efficient market portfolio

In order to apply the Capital Asset Pricing Model (CAPM) in practice, the estimation of the market portfolio presents one of the biggest challenges. Even more so after the work of Haugen and Baker (1991) and Grinold (1992), who pointed out that the stock market capitalisation-weighted indices are mean- variance inefficient. In the paper we perform in-sample optimisation for the CROBEX index constituents in order to test its efficiency ex post. Selected CROBEX index revisions in the period 2005-2017 are analysed. We find the index to be inefficient just as its’ developed market counterparts ; and as suggested in earlier research for the Croatian equity market by Zoričić et al. (2014). Based on the results we calculate indifference level of transaction costs for selected efficient portfolios in order to compare improvement in efficiency to increase in turnover in relation to the cap-weighted benchmark index. Instead of limiting research efforts to maximum Sharpe ratio and minimum variance portfolios, we further test other efficient portfolios obtained by using the Luenberger shortage function in order to provide a more detailed assessment of the efficient frontier portfolios for the analysed data samples. Also, since mean-variance optimisation often yields extreme portfolio weights thus reducing the effective number of stocks in portfolio, the possibility of improving the efficiency while maintaining the diversification level was tested. Results show that imposing the required constraints significantly reducesin-sample efficiency which has considerable implications regarding the attempts to estimate efficient portfolios out-of-sample in an undeveloped market.

efficient market portfolio, Croatian stock market, shortage function, efficient frontier

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