Canonical Portfolios: Optimal Asset and Signal Combination

TL;DR

This paper introduces a new framework for optimal asset and signal combination using canonical correlation analysis, providing scalable solutions and improved performance over benchmarks in large financial applications.

Contribution

It reformulates dynamic portfolio selection into a tractable form and applies canonical correlation analysis to identify uncorrelated managed portfolios, offering new economic insights.

Findings

Closed-form optimal portfolio policy derived

Framework scalable to large applications

Improved performance over benchmarks

Abstract

This paper presents a novel framework for analyzing the optimal asset and signal combination problem. Our approach builds upon the dynamic portfolio selection problem introduced by Brandt and Santa-Clara (2006) and consists of two stages. First, we reformulate their original investment problem into a tractable one that allows us to derive a closed-form expression for the optimal portfolio policy that is scalable to large cross-sectional financial applications. Second, we recast the problem of selecting a portfolio of correlated assets and signals into selecting a set of uncorrelated managed portfolios through the lens of Canonical Correlation Analysis of Hotelling (1936). The new investment environment of uncorrelated managed portfolios offers unique economic insights into the joint correlation structure of our optimal portfolio policy. We also operationalize our theoretical framework to bridge the gap between theory and practice, showcasing the improved performance of our proposed method over natural competing benchmarks.