
Analyzing global fixed income markets with tensors
Roughly speaking, a tensor is an array (generalization of a matrix) of numbers that transform according to certain rules when the array’s coordinates change. Fixed-income returns across countries can be seen as residing on tensor-like multidimensional data structures. Hence a tensor-valued approach allows identifying common factors behind international yield curves in the same way as principal components analysis identifies key factors behind a local yield curve. Estimated risk factors can be decomposed into two parallel risk domains, the maturity domain, and the country domain. This achieves a significant reduction in the number of parameters required to fully describe the international investment universe.