Fractal Dimension vs. Non-fractal Risk Measures – Correlation Analysis
Fractal Dimension vs. Non-fractal Risk Measures – Correlation Analysis

Author(s): Rafał Buła
Subject(s): Business Economy / Management
Published by: Masarykova univerzita nakladatelství
Keywords: fractal dimension; risk measurement; correlation analysis;
Summary/Abstract: In the presented paper the relationships between fractal dimension and chosen non-fractal measures of risk are analyzed and discussed. The main objective of the study is to reveal the nature of these dependencies. Moreover, the article is aimed at analyzing whether the abovementioned relations are stable independently of the length of investment horizon considered and of period chosen. In the article prices of shares listed on the Warsaw Stock Exchange are studied using methods of correlation analysis (various correlation coefficients). Calculated values and results of various statistical tests enable to draw a few conclusions. First of all, it must be noticed that the main scientific hypothesis in case of risk measures like standard deviation ought to be rejected, while e.g. for the omega or Farinelli-Tibiletti ratio we are unable to do it. Moreover, it must be concluded that this regularity is valid independently of the length of the investment horizon and analyzed period of time.

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