The Time Diversification Monitoring of a Stock Portfolio: An Approach Based on the Fractal Dimension

摘要

Diversification is a technique used to reduce the risk of investment and is accomplished by including uncorrelated and independent stocks in one's portfolio. By diversifying, the investor aims to reduce the risk of an entire portfolio depreciating in value, if a few of the assets within the portfolio are depreciated. In the past, the correlation coefficient has been used as a basis for diversification. However, the correlation coefficient is problematic since it can not capture nonlinear dependency, and analyzing pair-by-pair stocks in the portfolio does not always give the best estimation of diversification for the entire portfolio. In this paper we present a simple, but efficient methodology for monitoring portfolio diversification, which can capture most of the nonlinear phenomena in a portfolio. We propose a measurement of portfolio diversification through the fractal dimension parameter. Monitoring this parameter in a time domain represents the basis for automatic detection of significant changes in portfolio diversification. When the fractal dimension is significantly reduced, the algorithm eliminates stocks that are highly correlated and adds new uncorrelated stocks to the portfolio. We tested our method using real historical stock data and obtained significant improvements in the time diversification of selected stock portfolios.