  We reconsider the multivariate Kyle model in a risk-neutral setting with a
single, perfectly informed rational insider and a rational competitive market
maker, setting the price of n correlated securities. We prove the unicity of a
symmetric, positive definite solution for the impact matrix and provide
insights on its interpretation. We explore its implications from the
perspective of empirical market microstructure, and argue that it provides a
sensible inference procedure to cure some pathologies encountered in recent
attempts to calibrate cross-impact matrices. As an illustration, we determine
the empirical cross impact matrix of US. Treasuries, and compare the results
with recent alternative calibration methods.
