Portfolios and the market geometry

TL;DR

This paper uses geometric analysis of market return time series to identify portfolio performance patterns, revealing that portfolios aligned with small eigenvalue subspaces outperform those in dominant directions over nearly two decades.

Contribution

It introduces a novel geometric approach to analyze market data, highlighting the significance of small eigenvalue subspaces in portfolio performance.

Findings

Portfolios in small eigenvalue subspaces outperform others.

Systematic performance pattern observed from 1990 to 2008.

Small eigenvalue subspaces contain critical systematic information.

Abstract

A geometric analysis of the time series of returns has been performed in the past and it implied that the most of the systematic information of the market is contained in a space of small dimension. Here we have explored subspaces of this space to find out the relative performance of portfolios formed from the companies that have the largest projections in each one of the subspaces. It was found that the best performance portfolios are associated to some of the small eigenvalue subspaces and not to the dominant directions in the distances matrix. This occurs in such a systematic fashion over an extended period (1990-2008) that it may not be a statistical accident.