Deconstructing the Gerber statistic

The Gerber Statistic is a recently proposed co-movement measure. The measure is a conditional statistic and due to conditioning bias, will naturally differ from full-sample measures. This contribution makes use of an intuitive two-asset simulation framework to better elucidate the statistical behaviour of the Gerber Statistic, across its three proposed forms. Using graphical correlation profiles, we explore the measure's behaviour across return conditioning threshold, sample size and market distribution, detailing its mechanisms of performance but also demonstrating several caveats around its understanding and use. We conclude that while interesting, the Gerber Statistic is best viewed as an imperfect conditional dependence metric.

Automated summary

The Gerber Statistic is a conditional co-movement measure that differs from full-sample measures due to conditioning bias. This study uses a two-asset simulation framework to analyze the statistical behavior of the Gerber Statistic and explores its performance across various factors. The findings highlight the limitations and caveats of using the Gerber Statistic as a conditional dependence metric.