Analysis of Global Fixed Income Returns Using Multilinear Tensor Algebra

Abstract

Global fixed income returns exhibit highly structured correlations across maturities and economies (data modes), and their modeling therefore requires analysis tools that are capable of directly capturing the inherent multi-way couplings present in such multimodal data. Yet, current analyses typically employ “flat-view” multivariate matrix models and their associated linear algebras; these are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, we first show that global fixed income returns naturally reside on multi-modal lattice data structures, referred to as tensors. This serves as a basis to introduce a multilinear algebraic approach, inherent to tensors, to the modeling of the global term structure underlying multiple interest rate curves. Owing to the enhanced flexibility of multilinear algebra, statistical descriptors, such as correlations, exist between tensor columns and rows (fibers), as opposed to between individual entries in standard matrix analysis. This allows us to express the covariance of global returns as a joint multilinear decomposition of the maturity-domain and country-domain covariances. This not only drastically reduces the number of parameters required to fully capture the global returns covariance structure, but also makes it possible to devise rigorous and tractable global portfolio management strategies; we tailor these specifically to each of the data domains and thereby fully exploit the lattice structure of global fixed income returns. The ability of the proposed multilinear tensor approach to compactly describe the macroeconomic environment through economically meaningful factors is validated via empirical analysis that demonstrates the existence of maturity-domain and country-domain covariances underlying the interest rate curves of eight developed economies.

TOPICS: Fixed income and structured finance, quantitative methods, statistical methods, portfolio construction, global markets

Key Findings

• ▪ We show that global fixed income returns naturally reside on multi-modal lattice data structures, referred to as tensors, which exhibit highly structured correlations across maturities and economies.

• ▪ We introduce a multilinear algebraic approach to the modeling of the global term structure underlying multiple interest rate curves, which allows us to express the covariance of global returns as a joint multilinear decomposition of the maturity-domain and country-domain covariances.

• ▪ This drastically reduces the number of parameters required to fully capture the global returns covariance structure, and makes it possible to devise rigorous and tractable global portfolio management strategies which are tailored to each of the data domains.