  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
introduce 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. An empirical
analysis confirms the existence of global risk factors shared by eight
developed economies, and demonstrates their ability to compactly describe the
global macroeconomic environment.
