Multi-Factor Models: Could Less Be Better?
Table of Contents
- Factor Models and the Stochastic Discount Factor in Asset Pricing
- The Case for Less: Low-Dimensional Factor Models and Interpretability
- The Case for More: High-Dimensional SDF Learning with Machine Learning
- Could Less Still Be Better in Asset Pricing?
Factor Models and the Stochastic Discount Factor in Asset Pricing
Most readers in finance are already familiar with factor models. They are the workhorses of empirical asset pricing: we regress returns on a small set of systematic risks, extract betas, and see whether they explain the cross-section. For hedge fund and asset manager, this is more than academic: knowing which factors drive returns allows to construct portfolios with targeted exposures, hedge unwanted risks, and forecast performance across different market regimes. Rumors even says factor models are used to do alpha. But at their core, factor models are not just a regression trick, they are deeply connected to the stochastic discount factor (SDF), the central object of modern asset pricing (Cochrane, 2005).
Historically, factor models were designed to be parsimonious. The CAPM is the cleanest example: a single factor, the market portfolio, is enough to generate testable implications. Why the focus on simplicity? Because in the 1970s–1990s, working with too many factors was computationally and statistically intractable. With only a few regressors, the covariance matrix is easy to invert, and betas admit a neat closed-form solution.
Yet, as empirical work expanded, the factor zoo appeared: dozens, then hundreds of characteristics proposed as “priced risks.” Each paper brought new candidates — value, momentum, profitability, investment, and so on. And more recently, the field has pushed even further. The Instrumented Principal Components Approach (IPCA) of Kelly et al. (2019) and related machine learning methods embrace high-dimensional SDF learning, where the discount factor is estimated flexibly from a vast space of predictors.
This evolution leaves us with a natural question: Should asset pricing rely on fewer factors, or embrace more? In this post, we will take a historical perspective, from the early parsimonious models to today’s machine-learning approaches, and compare their strengths and weaknesses. Let’s try together to trace this journey.