Abstract
Since the introduction of CAPM in the 1960s, the asset pricing literature has documented hundreds of characteristics that capture the cross-sectional variation in stock returns. Traditionally, multifactor models seek a multidimensional representation of common risks; this approach entails selecting a small number of representative characteristics from a set of candidate characteristics that, together, explain most of the cross-sectional variation in stock returns. Characteristics-based long-short portfolios are partially loaded on the true underlying risk factors and are at best noisy proxies for true latent factors. However, the expansive list of potential characteristics, along with developments in the field of dimensionality reduction, offers us an opportunity to seek better approximations of the unobservable latent risk factors. A recent stream of literature has investigated how to appropriately extract relevant features from the “factor zoo” while incorporating information from the expansive list of factors. This chapter aims to summarize this novel paradigm in factor modeling.
TopIntroduction
The essence of asset pricing boils down to one central question: Why do different assets earn different returns? Much of the investment literature produced over the last four decades has been dedicated to addressing this question. The risk-return tradeoff applied by investors and academics alike has proven to be a good starting point to understanding this issue. Synonymous to the English phrase “there is no such thing as a free lunch”, this fundamental assumption has been extensively explored and is widely accepted in investment circles. In order to make higher returns, investors must take risky positions and to avoid risky investments, they must settle for lower expected returns. However, measuring risk is an extremely challenging problem empirically and is still very much an issue of debate in asset pricing.
Key Terms in this Chapter
Dimensionality Reduction: Dimensionality reduction is the process of reducing the number of random variables under consideration into fewer principal variables.
Multifactor Model: Multifactor models in finance are models that use characteristics sorted portfolios or information extracted from such portfolios as risk factors that explain expected returns of financial assets.
Capital Asset Pricing Model: The capital asset pricing model models the expected returns on financial assets as a linear function of the market returns.
Autoencoder: An autoencoder is a type of artificial neural network that is used to encode the data in lower dimensional representations.
Feature Extraction: Feature extraction is a procedure in dimensionality reduction of extracting principal variables (features) from some random variables under consideration, usually achieved by extracting one principal variable (feature) as mapping from multiple random variables.
Principal Component Analysis: Principal component analysis is a dimensionality reduction technique that reduces multiple (correlated) random variables into smaller number of (uncorrelated and orthogonal) random variables such the explained variance is maximized.
Deep Learning: Deep learning is a subfield of machine learning that uses artificial neural networks to predict, classify, and generate data.
Feature Selection: Feature selection is the process of selecting important principal variables (features) from some random variables under consideration, usually achieved by selecting a principal variable (feature) as one of the random variables.
Arbitrage Pricing Theory: Arbitrage pricing theory is a general theory in finance that suggests that, expected returns on any asset can be modelled as a linear function of some underlying risk factors.