  We model the impact costs of a strategy that trades a basket of correlated
instruments, by extending to the multivariate case the linear propagator model
previously used for single instruments. Our specification allows us to
calibrate a cost model that is free of arbitrage and price manipulation. We
illustrate our results using a pool of US stocks and show that neglecting
cross-impact effects leads to an incorrect estimation of the liquidity and
suboptimal execution strategies. We show in particular the importance of
synchronizing the execution of correlated contracts.
