Data-Driven Risk Factors and Asset Allocation with Unsupervised Learning

Chapter 6, The Machine Learning Process, introduced how unsupervised learning adds value by uncovering structures in data without the need for an outcome variable to guide the search process. This contrasts with supervised learning, which was the focus of the last several chapters: instead of predicting future outcomes, unsupervised learning aims to learn an informative representation of the data that helps explore new data, discover useful insights, or solve some other task more effectively.

Dimensionality reduction and clustering are the main tasks for unsupervised learning:

• Dimensionality reduction transforms the existing features into a new, smaller set while minimizing the loss of information. Algorithms differ by how they measure the loss of information, whether they apply linear or nonlinear transformations or which constraints they impose on the new feature set.
• Clustering algorithms...

Dimensionality reduction

In linear algebra terms, the features of a dataset create a vector space whose dimensionality corresponds to the number of linearly independent rows or columns, whichever is larger. Two columns are linearly dependent when they are perfectly correlated so that one can be computed from the other using the linear operations of addition and multiplication.

In other words, they are parallel vectors that represent the same direction rather than different ones in the data and thus only constitute a single dimension. Similarly, if one variable is a linear combination of several others, then it is an element of the vector space created by those columns and does not add a new dimension of its own.

The number of dimensions of a dataset matters because each new dimension can add a signal concerning an outcome. However, there is also a downside known as the curse of dimensionality: as the number of independent features grows while the number of observations...

PCA for trading

PCA is useful for algorithmic trading in several respects, including:

• The data-driven derivation of risk factors by applying PCA to asset returns
• The construction of uncorrelated portfolios based on the principal components of the correlation matrix of asset returns

We will illustrate both of these applications in this section.

Data-driven risk factors

In Chapter 7, Linear Models – From Risk Factors to Return Forecasts, we explored risk factor models used in quantitative finance to capture the main drivers of returns. These models explain differences in returns on assets based on their exposure to systematic risk factors and the rewards associated with these factors. In particular, we explored the Fama-French approach, which specifies factors based on prior knowledge about the empirical behavior of average returns, treats these factors as observable, and then estimates risk model coefficients using linear regression...

Clustering

Both clustering and dimensionality reduction summarize the data. As we have just discussed, dimensionality reduction compresses the data by representing it using new, fewer features that capture the most relevant information. Clustering algorithms, in contrast, assign existing observations to subgroups that consist of similar data points.

Clustering can serve to better understand the data through the lens of categories learned from continuous variables. It also permits you to automatically categorize new objects according to the learned criteria. Examples of related applications include hierarchical taxonomies, medical diagnostics, and customer segmentation. Alternatively, clusters can be used to represent groups as prototypes, using, for example, the midpoint of a cluster as the best representatives of learned grouping. An example application includes image compression.

Clustering algorithms differ with respect to their strategy of identifying groupings:

...

Hierarchical clustering for optimal portfolios

In Chapter 5, Portfolio Optimization and Performance Evaluation, we discussed several methods that aim to choose portfolio weights for a given set of assets to optimize the risk and return profile of the resulting portfolio. These included the mean-variance optimization of Markowitz's modern portfolio theory, the Kelly criterion, and risk parity. In this section, we cover hierarchical risk parity (HRP), a more recent innovation (Prado 2016) that leverages hierarchical clustering to assign position sizes to assets based on the risk characteristics of subgroups.

We will first present how HRP works and then compare its performance against alternatives using a long-only strategy driven by the gradient boosting models we developed in the last chapter.

How hierarchical risk parity works

The key ideas of hierarchical risk parity are to do the following:

• Use hierarchical clustering of the covariance matrix to group...

Summary

In this chapter, we explored unsupervised learning methods that allow us to extract valuable signals from our data without relying on the help of outcome information provided by labels.

We learned how to use linear dimensionality reduction methods like PCA and ICA to extract uncorrelated or independent components from data that can serve as risk factors or portfolio weights. We also covered advanced nonlinear manifold learning techniques that produce state-of-the-art visualizations of complex, alternative datasets. In the second part of the chapter, we covered several clustering methods that produce data-driven groupings under various assumptions. These groupings can be useful, for example, to construct portfolios that apply risk-parity principles to assets that have been clustered hierarchically.

In the next three chapters, we will learn about various machine learning techniques for a key source of alternative data, namely natural language processing for text documents...