Incremental Sharpe and other performance ratios

TL;DR

This paper introduces a novel method to decompose and analyze incremental contributions to portfolio performance ratios like Sharpe and Treynor, enhancing understanding of asset impact.

Contribution

It proposes a new decomposition technique using Euler's theorem for performance ratios, enabling better insight into asset contributions and incremental performance.

Findings

Decomposition of performance ratios into linear combinations.

Conditions for assets to provide incremental performance.

Numerical examples demonstrating the methodology.

Abstract

We present a new methodology of computing incremental contribution for performance ratios for portfolio like Sharpe, Treynor, Calmar or Sterling ratios. Using Euler's homogeneous function theorem, we are able to decompose these performance ratios as a linear combination of individual modified performance ratios. This allows understanding the drivers of these performance ratios as well as deriving a condition for a new asset to provide incremental performance for the portfolio. We provide various numerical examples of this performance ratio decomposition.