Fuzzy Factors and Asset Allocation

Abstract

In this article, the authors discuss asset allocation through the factor exposure lens. They argue that a factor dimension brings novel challenges, including ambiguity in investor objectives, a multitude of suitable factor definitions, and the time-varying nature of asset/factor correlations. Such new classes of uncertainties do not fit neatly into the probabilistic framework that is at the core of modern portfolio theory. As a remedy, the authors suggest leveraging fuzzy set theory, which has been specifically created to deal with ambiguities in process objectives, component definitions, and relationships. The authors review basics of the theory, illustrate how to apply it to portfolio optimization problems, and discuss practical application of such a fuzzy asset allocation framework.

TOPICS: Factor-based models, portfolio theory, quantitative methods

Key Findings

• ▪ Most existing factor-based asset allocation frameworks imply quasi-deterministic linkage between assets and factors. At the same time, a broad body of evidence supports the existence of a broad-stroke relationship.

• ▪ Introducing factor considerations into portfolio construction also brings genuinely novel challenges, including vagueness of related investor objectives, time-varying asset/factor relationships, and ambiguity of factor definitions.

• ▪ We show that using the so-called fuzzy set theory may serve as a simple and entirely intuitive framework for accommodating such challenges. Fuzzy set theory was originally introduced in the 1960s and since then has grown into a well-developed branch of applied mathematics and artificial intelligence. We illustrate the basics of the theory and the benefits of applying it to both factor asset allocation tasks and portfolio construction problems more generally.