  This paper goes beyond the optimal trading Mean Field Game model introduced
by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and
Lehalle, C.-A., Mean field game of controls and an application to trade
crowding, Mathematics and Financial Economics (2018)]. It starts by extending
it to portfolios of correlated instruments. This leads to several original
contributions: first that hedging strategies naturally stem from optimal
liquidation schemes on portfolios. Second we show the influence of trading
flows on naive estimates of intraday volatility and correlations. Focussing on
this important relation, we exhibit a closed form formula expressing standard
estimates of correlations as a function of the underlying correlations and the
initial imbalance of large orders, via the optimal flows of our mean field game
between traders. To support our theoretical findings, we use a real dataset of
176 US stocks from January to December 2014 sampled every 5 minutes to analyze
the influence of the daily flows on the observed correlations. Finally, we
propose a toy model based approach to calibrate our MFG model on data.
