{'fraction_non_alphanumeric': 0.012345679012345678, 'fraction_numerical': 0.0, 'mean_word_length': 4.9, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
General Covariance, the Spectrum of Riemannium and a Stress Test Calculation Formula

This article proposes a formula for a market stress-test of a portfolio. The formula is motivated by some recent and old developments in random matrix theory and a requirement that it be explicitly invariant under a change of basis of risk factors. It has a natural interpretation 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 the unobserved market risk factors. An example application for a relative-value portfolio of crude oil futures is presented.