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We perform an analysis of fractal properties of the positive and the negativechanges of the German DAX30 index separately using Multifractal DetrendedFluctuation Analysis (MFDFA). By calculating the singularity spectra$f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously,these spectra display a significant difference in the scaling properties ofreturns with opposite sign. The negative price changes are ruled by strongertemporal correlations than the positive ones, what is manifested by largervalues of the corresponding H\"{o}lder exponents. As regards the properties ofdominant trends, a bear market is more persistent than the bull marketirrespective of the sign of fluctuations.

Different fractal properties of positive and negative returns