Financial ratios and stock returns reappraised through a topological data analysis lens

TL;DR

This paper uses topological data analysis, specifically the TDA Ball Mapper algorithm, to visualize and explore the complex relationships between financial ratios and stock returns, revealing non-monotonic interdependencies that could be exploited for profit.

Contribution

It introduces a novel application of topological data analysis to financial ratios, providing new insights into their associations with stock returns beyond traditional methods.

Findings

Financial ratios exhibit complex, non-monotonic relationships with stock returns.

TDA Ball Mapper effectively visualizes interdependencies among financial factors.

Potential for investors to exploit these relationships for profit.

Abstract

Firm financials are well established as return predictors, being the inspiration for a large set of anomalies in the asset pricing literature. Employing topological data analysis we revisit the question of association between seven of the most commonly studied financial ratios and stock returns. Specifically the TDA Ball Mapper algorithm is applied to visualise the point cloud of financial ratios as an abstract two-dimensional graph readily allowing for identification of interdependencies between factors. These relationships are seldom monotonic, opportunities for investors to profitably exploit this knowledge provided by TDA abound. Clear potential offered by the tools of TDA to shed new light on asset pricing models is demonstrated. Scope for benefit is limited only by the availability of information to the analyst.