A Mean Field Game of Portfolio Trading and Its Consequences On Perceived Correlations

TL;DR

This paper extends a mean field game model to portfolios of correlated assets, revealing how trading flows influence perceived correlations and providing formulas to estimate true correlations from observed data.

Contribution

It introduces a novel extension of the mean field game framework to portfolios, linking trading strategies with correlation estimates and offering calibration methods.

Findings

Hedging strategies emerge from optimal liquidation in portfolios.

Trading flows significantly affect naive correlation estimates.

A closed-form formula relates observed and true correlations.

Abstract

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.