Factor Exposure Analysis 116: Residualized Indices

Orthogonalizing independent variables

November 2025. Reading Time: 10 Minutes. Author: Nicolas Rabener.

• Most country and sector indices are highly correlated
• Residualization can be used for a better risk contribution analysis
• However, residualized indices are abstract and counterintuitive

INTRODUCTION

Although artificial intelligence and machine learning have advanced rapidly in finance, most portfolio risk and return analysis still relies on traditional linear regression. The underlying math has not changed much, but the frameworks and factor sets have evolved significantly.

For instance, MSCI’s risk attribution model separates contributions from currency, market timing, and residuals. Within residuals, it further distinguishes between specific and common factors such as industry, country, global, and risk indices – allowing for quite granular analysis.

Other providers, including Bloomberg, Northfield, and Venn by Two Sigma, employ comparable frameworks, but with meaningful differences. Venn, for example, relies on just 18 independent variables, in contrast to MSCI’s 200+ factors. Still, a common thread across these approaches is the residualization of variables used in regression.

We introduced residualization in Factor Exposure Analysis 103: Exploring Residualization, and this article will build on that foundation with a deeper investigation.

COUNTRY AND SECTOR CORRELATIONS

The purpose of linear regression is to explain the behavior of a dependent variable – such as a portfolio – using a set of independent variables. However, when those independent variables are highly correlated, the regression results can lose statistical significance. For instance, country and sector indices often move together because the global economy and financial markets are deeply interconnected. A disruption in Taiwan, for example, can quickly ripple into the U.S. economy through the semiconductor supply chain.