Journal of Risk

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General covariance, the spectrum of Riemannium and a stress test calculation formula

Piotr Chmielowski

ABSTRACT

The formula is motivated by some recent and some old developments in random matrix theory and a requirement that it be explicitly invariant under a change of basis of risk factors. It may naturally be interpreted as the standard deviation stressed by two effects: a correlation shear due to uncertainty of estimation from a finite sample and an additional stress due to unobserved market risk factors. An example application for a relative-value portfolio of crude oil futures is presented.