Factor Exposure Analysis 117: Risk Contribution Analysis

Intuitive vs quant risk reports

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

SUMMARY

• The choice of indices and regression type leads to different risk contributions
• Technically, most risk of equity funds can be attributed to a single variable
• Elastic net is advantageous over linear and lasso regressions

INTRODUCTION

In our recent research article Factor Exposure Analysis 116: Residualized Indices, we explored a method to reduce correlations among independent variables, such as country stock market indices, in regression analyses. Practically, this involved a two-step process: first, removing the global stock market effect, and second, residualizing country indices against other countries and sector indices against other sectors. The result is a set of indices that are “purer” than the raw indices.

Theoretically, these residualized indices are better suited for return and risk contribution analysis, though they can become more abstract. For example, the CAGR of the MSCI Japan Index dropped from 6.3% to 0.6% between 2018 and 2025 when fully residualized.

In this article, we compare the use of raw versus residualized indices in a risk contribution analysis across a selection of funds.

REGRESSION ANALYSIS

We randomly selected 15 equity funds trading in the U.S. that provide exposure to broad stock markets, individual countries, and sectors. We then ran three types of regressions – linear, lasso, and elastic net – using 17 country indices, 7 equity factor indices, and 11 sector indices. As independent variables, we used three sets of indices: raw indices, ACWI-residualized indices, and fully residualized indices (with ACWI, country, and sector exposures removed). This resulted in a total of nine regressions.

We compared the average R2 across these nine regressions. Using raw or ACWI-adj