# Trading Lightly: Cross-Impact and Optimal Portfolio Execution

## TL;DR

This paper extends the linear propagator model to multiple correlated instruments to accurately estimate impact costs, emphasizing the importance of considering cross-impact effects for optimal execution strategies.

## Contribution

It introduces a multivariate impact cost model that accounts for cross-impact effects, improving the accuracy of liquidity estimation and execution strategies.

## Key findings

- Neglecting cross-impact leads to suboptimal execution.
- Synchronizing execution of correlated contracts improves performance.
- The model is calibrated on US stock data and is arbitrage-free.

## Abstract

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.