This study investigates the performance of the naive 1/N portfolios relative to the mean-variance efficient portfolios and index replicating portfolios. We use the Sharpe ratio to measure the portfolio efficiency applied on sample and out-of sample portfolios from two capital markets, one developed (German) and one underdeveloped (Bosnian) in the pre- and post-crisis periods. We answer the question whether the active portfolio strategies are also more efficient. Our research heavy rely on the research from DeMiguel, Garlappi and Uppal (2009), who found that naive 1/N diversification outperform other optimizing portfolio models in the US stock market. Methods of determining efficient portfolios are mathematical and statistical problems, solved by applying convex, square or linear programming. According to the chosen methodology we applied our own software to solve optimization problems. We use Monte Carlo simulation to generate returns data in order to examine the persistence of the outperforming strategy in different periods. Keywords: Risk, Naive Diversification, Efficient Diversification. JEL Classification: G11

The first index funds appeared in capital markets during the 1970s. Their investment strategy was based on replicating the fluctuations of some of the world's well-known stock market indexes. Legislation and regulation in Bosnia and Herzegovina, as in other neighboring countries, provides the possibility of establishing index funds, with no concrete initiatives at the moment. One of the better-known asset valuation models, the capital asset pricing model (CAPM), determines the required rate of return on risky assets if the assets are to be added to an already well-diversified portfolio. Since a market portfolio is a theoretical concept, wide stock market indexes are used as proxies for the market. These stock market indexes have to obtain mean-variance efficiency for the CAPM tests. In this paper, we apply a mean-variance optimization model to a basket of securities from the Bosnia and Herzegovina stock market. We explore the efficiency of these indexes as securities portfolios. The possible efficiency of these indexes would encourage the creation of index funds in Bosnia and Herzegovina. Furthermore, we investigate the possible use of these indexes in CAPM tests. Our research shows that the analyzed indexes are not mean-variance efficient. For the purpose of efficient portfolio determination, we use our own software in the application section of the paper. Using this software, we propose indexes that obtain mean-variance efficiency.