Visibility of the compass rose in financial asset returns: A quantitative study

The compass rose phenomenon is studied based on the random walk model of stock prices. It is found that the structure is inherently present in any financial data having a finite precision, but becomes visible only under some conditions. A quantitative description of the pattern visibility condition is given, providing a method for the interpretation of pattern appearance and a more comprehensive understanding of the compass rose phenomenon. This is achieved by defining a measure of pattern quality. The arguments and the proposed method are supported by numerical examples. One such example is the presentation of patterns in portfolios with some specific weights. (C) 2002 Elsevier Science B.V. All rights reserved.