Principal Trading Arrangements : Optimality under Temporary and Permanent Price Impact

We study the optimal execution problem in a principal-agent setting. A client contracts to purchase a large position from a dealer at a future point in time. In the interim, the dealer acquires the position from the market, choosing how to split the parent order into smaller child orders. Price impact may have temporary and permanent components. There is hidden action in that the client cannot directly dictate the dealer’s trades. Rather, she chooses a contract with the goal of minimizing her expected payment, given the price process and an understanding of the dealer’s incentives. We characterize explicitly the optimal weighted-average-price contract: it is symmetric and generally U-shaped over the trading periods. This U-shape is accentuated by permanent price impact and moderated by both temporary price impact and dealer risk aversion. In contrast, the first-best solution (which reduces to a classical optimal execution problem) is invariant to these parameters