Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and Their Effect on Portfolio Execution

An analysis of intraday volumes for the S&P 500 constituent stocks illustrates that (i) volume surprises (i.e., deviations from forecasted trading volumes) are correlated across stocks and that (ii) this correlation increases during the last few hours of the trading session. These observations can be attributed partly to the prevalence of portfolio trading activity that is implicit in the growth of passive (systematic) investment strategies and partly to the increased trading intensity of such strategies toward the end of the trading session. In this paper, we investigate the consequences of such portfolio liquidity on price impact and portfolio execution. We derive a linear cross-asset market impact from a stylized model that explicitly captures the fact that a certain fraction of natural liquidity providers trade only portfolios of stocks whenever they choose to execute. We find that because of cross-impact and its intraday variation, it is optimal for a risk-neutral cost-minimizing liquidator to execute a portfolio of orders in a coupled manner, as opposed to the separable volume-weighted average price execution schedule that is often assumed. The optimal schedule couples the execution on the individual stocks so as to take advantage of increased portfolio liquidity toward the end of the day. A worst case analysis shows that the potential cost reduction from this optimized execution schedule over the separable approach can be as high as 15% for plausible model parameters. Finally, we discuss how to estimate cross-sectional price impact if one had a data set of realized portfolio transaction records by exploiting the low-rank structure of its coefficient matrix suggested by our analysis.