Execution Costs in Financial Markets with Several Institutional Investors

We study multi-period trading strategies of institutional investors who plan to trade the same security during some finite time horizons. Investors who trade large volumes face a price impact that depends on their trading volumes simultaneously, and is usually represented as a function, the so called price-impact function. We show through a numerical example that a trading strategy, optimal for trading in isolation, may become suboptimal in the presence of other institutional investors who trade the same security at the same time. Thus, the trading activities of other investors should not be ignored in practice and need to be modeled properly. Under the assumptions that the number of other investors and their trading volumes are known, the problem can be modeled as a simultaneous game. We investigate the properties of the equilibrium trading strategies and prove that, under mild assumptions on the price-impact function, an equilibrium uniquely exists and can be computed efficiently. Particularly, when short selling is allowed, the equilibrium is found by solving a system of linear equations. Finally, we evaluate the expected execution cost of the equilibrium trading strategy through simulations and demonstrate that even when other investors choose their trading strategies at random, the expected execution cost of the equilibrium trading strategy is likely to be less than the expected execution cost of the trading strategy that was optimal in the absence of other investors.