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...