Explanatory power of risk measures in long term by diversification.

<p><i>Note</i>: This figure shows the explanatory power (<i>R</i>²) of portfolios with different number of securities involved and different risk estimate methods. We generate 10 million random equally weighted portfolios with different number of securities involved (at most 100,000 for each size) using daily risk premiums of 150 randomly selected securities. The risk of portfolios is estimated by standard deviation (light gray curve), CAPM beta (black dotted curve), Shannon- (gray) and Rényi entropy (black). 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.