33-58

• Andreu, Jordi
• Torra, Salvador

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM arefulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz’s efficient frontier, andpassive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biasessuffered by passive investors: the sample, construction, efficiency and active biases and tracking error arepresented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, andto provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities.MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock marketsachieving interesting results. Our indices are less risky and more profitable than current Market Indices in theArgentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must beoutlined: an error dimension has been included in the backtesting and the Sharpe’s Ratio has been used to selectthe ‘best’ MRI.

• Economics and Business

• Διοίκηση επιχειρήσεων
• risk management
• Business management
• Οικονομία

index biases, passive investing, market indices, VaR, portfolio optimization, minimum risk indices

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