Factor Exposure Analysis 101

Testing the effectiveness and sensitivity of linear regressions

October 2020. Reading Time: 10 Minutes. Author: Nicolas Rabener.

SUMMARY

  • Linear regression is widely used for factor exposure analysis
  • However, a high R2 and low p-value can be misleading
  • Unsurprisingly the data quality matters

INTRODUCTION

Some fields of science like math or statistics seem to be too dry to be joking about, but a quick Google search for jokes on statisticians reveals that even this area is a fertile ground for humor. Sample these for a quick laugh: 

  • A statistician is a person whose life-time ambition is to be wrong 5% of the time.
  • I asked a statistician for her phone number… and she gave me an estimate.
  • Regression is a powerful tool for forecasting. Economists using it successfully predicted ten out of the last two recessions.

Thinking about the approximately 27,000 statisticians working in the US today throws up some odd questions. At what age did they decide to pursue this career path? What is at university where the professor of statistics whispered that by choosing his subject they would never have to be right about anything ever again?

Regardless of how these people ended up in their jobs, we should be thankful for them. Especially finance would be a lot less exciting without frequent reports about GDP growth, the unemployment rate, and revisions to GDP growth and the unemployment rate. 

Without statistics, it would also be challenging for investors to analyze their portfolios and determine what they are actually holding. Naturally, investors know what stocks they bought and are frequently able to explain in excruciating detail what the company is doing, but that often fails to satisfy clients and risk managers who want risk reports and factor exposure analysis.

Despite a significant increase in the use of machine learning and artificial intelligence in finance, simple regression analysis is still the most used tool for portfolio analysis. We are not the first ones to point this anachronism. For instance, Marcos Lopez de Prado has pointed repeatedly the reliance of financial analysis on techniques developed over two hundred years ago. In this short research note, we will explore the nuances and challenges of regression-based factor exposure analysis (read