Tensor Analysis of Global Fixed-Income Returns

Global fixed income returns span across multiple maturities and economies, that is, they naturally reside on multi-dimensional data structures referred to as tensors. In contrast to standard “flat-view” multivariate models that are agnostic to data structure and only describe linear pairwise relationships, we introduced a tensor-valued approach to model the global risks shared by multiple interest rate curves. In this way, the estimated risk factors can be analytically decomposed into maturity-domain and country-domain constituents, which allows the investor to devise rigorous and tractable global portfolio management and hedging strategies tailored to each risk domain.

Global fixed income returns reside on regular multi-dimensional data structures referred to as tensors. Therefore, it is only through tensor analysis that we have the opportunity to develop sophisticated models capturing the interactions between the entirety of interest rate curves. We proposed methods for estimating the 'tensor variance' parameters by introducing a statistically identifiable re-parameterisation of the covariance parameters. The proposed method benefits from its high economic interpretation and explanatory power of the variance. Furthermore, we conducted an empirical analysis that confirms the existence of global risk factors shared by eight developed economies.

By applying the proposed method to the global risk factors shared by eight developed economies, we identified three leading global factors in the maturity-domain and eight leading global factors in the country-domain. The resulting maturity-domain and country-domain factors are shown to provide compact and physically meaningful insight into the global macroeconomic environment. The following two tables show the explanatory power of the identified factors and their corresponding economic interpretations.

The framework we developed employs the structure-aware multilinear algebra to rigorously model the risk factors shared by an international universe of fixed-income returns. In this way, the estimated risk factors can be analytically decomposed into two parallel domains of risk: (i) maturity-domain factors which are shared by all countries; and (ii) country-domain factors which are shared by all maturities. By operating within each domain in parallel, the investor can devise rigorous and tractable global portfolio management and hedging strategies, with fewer decision parameters, that are simultaneously tailored to each risk domain, as a consequence and natural extension of the proposed multilinear framework.

For a detailed read of the paper, please see: https://www.pm-research.com/content/iijfixinc/30/4/32