Target close execution strategies ∗

Be it directly, using DMA services, or intermediated by brokers, investors send their orders to trading platforms using execution algorithms. VWAP algorithms are widely used but they are only part of the menu proposed to investors. POV (also called PVol, for Percentage of Volume) is another instance of execution strategy, in which participation rate to the market is as close as possible to a predetermined constant. IS (Implementation Shortfall) or TWAP (Time weighted average price) algorithms are also proposed to minimize slippage with respect to the arrival price of the order or to the average price over the desired execution period. Numerous investors also use another execution strategy in line with the evaluation of their portfolio: Target Close strategy. When their portfolio is evaluated every day at the closing price of the day, investors’ interest is to be executed as close as possible to the closing price. In this article dedicated to Target Close strategies, we develop several liquidation strategies to execute as close as possible to the closing price, without making the closing price. Risk-liquidity premia are also discussed. Introduction Investors in stocks buy and sell large quantities of shares to build or rebalance their portfolios. Depending on the urgency of their orders and on their incentives, they use different execution algorithms. Algorithms trying to replicate the VWAP over a predetermined time window are the most widely used in practice although, only a few academic papers are dedicated to it (see [12, 13, 14, 16, 23, 28, 29]). IS strategies, rarely used in comparison, have been the topic of most academic works on optimal execution. The most classical framework is the one developed by Almgren and Chriss in their seminal papers [7, 8, 10]. This framework, enriched to account for stochastic volatility and liquidity [6], and generalized to other objective criteria and to more general impact functions (see [9], [15], [18], [27], [32], [33] or [34]) has long been the only reference framework. Today, this framework is challenged by new ∗This research has been conducted with the support of the Research Initiative “Exécution optimale et statistiques de la liquidité haute fréquence” under the aegis of the Europlace Institute of Finance. I would like to thank Nicolas Grandchamp des Raux (HSBC France), Guillaume Royer (Ecole Polytechnique) and Christopher Ulph (HSBC) for the conversations we had on the subject. †Université Paris-Diderot, UFR de Mathématiques, Laboratoire Jacques-Louis Lions. Avenue de France, 75013 Paris, France. [email protected]