Inversions distribution and testing correlation changes for rates of return

Abstract

PURPOSE: The paper presents the application of a test based on the inversions number distribution. The purpose of the work is to examine the stability of dependence measures between rates of return for financial instruments.

DESIGN/METHODOLOGY/APPROACH: The issue plays a vital role in portfolio analysis because dependence measures are an essential factor affecting the portfolio risk of financial instruments. Direct application of the classic measure of dependence, such as Pearson's correlation coefficient, requires several additional assumptions regarding the existence of moments or the normality of the distribution of random variables analyzed. Therefore, the choice falls on the tau Kendall coefficient.

FINDINGS: First of all, it is suitable for testing distributions for which variance does not exist (e.g., stable distributions). Secondly, we present a new way of testing the hypothesis about the equality of the Kendall coefficient over two separate periods. A miniature sample version was introduced in the article. An essential feature of the proposed test is the ability to calculate its power analytically.