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Karami, Benichou, Benzaquen & Bouchaud (2019) show that past trends in a futures eigen-factor (≈10 days) raise or cut instantaneous correlations—indexes vs bonds dominate. Risk map. Not investment advice.
Takeaway. Futures correlations are not a fixed matrix. Principal Regression Analysis (PRA) regresses today’s outer-product of returns on lagged predictors: a down eigen-factor (indexes/commodities/FX vs bonds) over about 10 days raises the market-mode eigenvalue—risk-on/off for CTA-style books.
Conditional Correlations and Principal Regression Analysis for Futures (Armine Karami, Raphael Benichou, Michael Benzaquen, Jean-Philippe Bouchaud, 2019; arXiv:1912.12354).
Fit for learners: PRA: past ~10-day futures “eigen-factor” moves shift tomorrow’s correlation matrix—risk intuition beyond a static cov.
This Hub note is a plain-language intro. Not investment advice.
Sample covariance is noisy and non-stationary. Equities all sit in a +1 market mode; futures do not (indexes vs bonds often negative). DCC-type models are heavy; sudden “flight to quality” is hard to predict, but some lagged factors still move tomorrow’s C.
A risk diagnostic—not a timing strategy.
This is the grown-up version of “corr goes to 1 in a crash” with actual linear algebra. If you can do np.outer and np.linalg.eigh, you can prototype PRA on a toy 10-asset matrix.
Tiny evening exercise: two standardised series x,y; print x*y vs yesterday’s -(x+y)/2; say in one line what a negative slope would mean. Learning only.
Landing: arXiv abs
Not investment advice. This Hub note is educational only. CFM/École polytechnique research on futures correlations—not a recommendation to trade correlation regimes.
Single course CTA: SoloQuant Academy’s Introduction to Python Programming—nested lists become matrices; eigenvalues come after you can index them.