Complex signals generated by economic systems are non-trivial structures which can be characterized in terms of the theory of multifractals. What is surprising is that these structures are to some degree universal in real-world signals coming not only from finance but also from diverse fields of science like physics, chemistry or biology. The concept of "fractal world" was proposed by Mandelbrot in 1970s and was based on scale-invariant statistics with power law correlations. It allows us to study the global and local behavior of singular measure, or, in other words, the mono- and multifractal properties of complex systems. Investigating the signals using WTMM or MF-DFA methods we assume that positive and negative fluctuations have the same fractal or scaling properties, but this may not apply to some particular cases. In order to apprehend the studied process completely we have to investigate the fluctuations with taking into consideration also their sign. We therefore generalize MF-DFA algorithm to analyze positive and negative changes separately such that the natural scale and the length of possible temporal correlations is preserved. Such an analysis of financial time series shows that both the positive and negative fluctuations reveal multiscaling which can be quantified by the spectrum f($\alpha$). Curiously the multifractal spectra indicate a significant difference in the scaling properties of returns with opposite sign. We may say that the negative price changes are ruled by richer dynamics and stronger temporal correlations than the positive ones which is manifested by wider multifractal spectra and larger Holder exponents. For the declining market trends the singularity spectra for both signs indicate strong linear correlations with a diverse dynamics for the negative changes.  These results are independent of the considered region of the world (US, Europe) or of the epoch. The difference in scaling behavior depending on the direction of price changes gives some new information about the financial systems. We believe that asymmetric fractal properties can give us opportunity of better understanding the mechanism that governs the system's dynamics. From a practical point of view this fact can have applications in modeling and forecasting the stock market data and may have crucial meaning in risk evaluation.