An algorithm for the orthogonal decomposition of financial return data

TL;DR

This paper introduces an algorithm that decomposes financial return data into orthogonal factors, distinguishing between expected return and various risk components, useful for portfolio analysis.

Contribution

The paper presents a novel algorithm for orthogonal decomposition of financial returns into expected return and multiple risk factors, enhancing portfolio risk analysis.

Findings

Decomposition separates expected return from risk factors.

Expected return is an affine function of productive risk when funds ≤ periods.

Algorithm improves understanding of risk structure in financial data.

Abstract

We present an algorithm for the decomposition of periodic financial return data into orthogonal factors of expected return and "systemic", "productive", and "nonproductive" risk. Generally, when the number of funds does not exceed the number of periods, the expected return of a portfolio is an affine function of its productive risk.