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. 2014 Dec 29;9(12):e115742. doi: 10.1371/journal.pone.0115742

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© 2014 Ormos, Zibriczky

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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Note: The panels show the expected risk premium of the portfolios (calculated by the average of daily risk premiums) versus the estimated risk using different methods; the number of securities involved is indicated by the different markers. We generate a sample of 750 random portfolios by using 150 randomly selected securities and 200-200 random equally weighted portfolios with 2, 5 and 10 securities. The risk of portfolios is estimated by standard deviation, CAPM beta, Shannon- and Rényi entropy by using daily returns in the period from 1985 to the end of 2011. Both types of entropy functions are calculated by histogram based density function estimation, with 175 bins for Shannon entropy and 50 bins for Rényi entropy.