  We explore the effect of past market movements on the instantaneous
correlations between assets within the futures market. Quantifying this effect
is of interest to estimate and manage the risk associated to portfolios of
futures in a non-stationary context. We apply and extend a previously reported
method called the Principal Regression Analysis (PRA) to a universe of $84$
futures contracts between $2009$ and $2019$. We show that the past up (resp.
down) 10 day trends of a novel predictor -- the eigen-factor -- tend to reduce
(resp. increase) instantaneous correlations. We then carry out a multifactor
PRA on sectorial predictors corresponding to the four futures sectors (indexes,
commodities, bonds and currencies), and show that the effect of past market
movements on the future variations of the instantaneous correlations can be
decomposed into two significant components. The first component is due to the
market movements within the index sector, while the second component is due to
the market movements within the bonds sector.
