In the field of portfolio management the focus has been on the out-of-sample estimation of the covariance matrix mainly because the estimation of expected return is much more challenging. However, recent research efforts have not only tried to improve the estimation of risk parameters by expanding the analysis beyond the mean-variance setting but also by testing whether risk measures can be used as proxies for the expected return in the stock market. In this research, we test the standard deviation (measure of total volatility) and the semi-deviation (measure of downside risk) as proxies for the expected market return in the illiquid and undeveloped Croatian stock market in the period from January 2005 until November 2017. In such an environment, the application of the proposed methodology yielded poor results, which helps explain the failure of the out-of-sample estimation of the maximum Sharpe ratio portfolio in earlier research in the Croatian equity market.
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