An enhanced Gerber statistic for portfolio optimization

The purpose of this letter is to introduce a modified version of the Gerber statistic resulting in the enhancement of its function as a measure of statistical co-movement. The modification centres around the redefinition of zones and thresholds, alongside the use of finite real-valued contributions rather than discrete binary counts in assigning value to individual co-movements. Arguments for the former are based on the statistical alignment of data series for the purposes of more effectively delineating concordant and discordant co-movement. Arguments for the latter are based on attributing greater weight to better information. Collectively this approach simultaneously incorporates the merits of Gerber-like thresholds and zoning, and conventional correlation-like co-movement measurement.

Automated summary

This article introduces a modified version of the Gerber statistic that enhances its function as a measure of statistical co-movement by redefining zones and thresholds, and using finite real-valued contributions. This approach combines the merits of Gerber-like thresholds and zoning, and conventional correlation-like co-movement measurement.