Calibration of optimal execution of financial transactions in the presence of transient market impact

Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud et al., 2004), which has the property of describing both the volume and the temporal dependence of price change due to trading. We show how this model can be used to describe price impact also in aggregated trade time or in real time. We then solve analytically and calibrate with real data the optimal execution problem both for risk neutral and for risk averse investors and we derive an efficient frontier of optimal execution. When we include spread costs the problem must be solved numerically and we show that the introduction of such costs regularizes the solution.Comment: 31 pages, 8 figure

Size and investment performance: a research note

This article examines the performance of actively managed Australian equity funds and the extent to which both fund size and manager size are related to risk-adjusted returns. Larger investment managers, by definition, engage in higher trade volume. The literature documents that transaction costs and trade difficulty increase with trade size, given difficulties associated with`large trades and their potential market impact on security prices. Therefore, ceteris paribus, large orders are consistent with lower levels of efficiency in trade execution and higher transaction costs. While larger investment managers may experience material disadvantages relative to their smaller counterparts, the Australian literature to date has largely ignored the issues of asset size and the long run performance of investment offerings. This article, employing returns and fund size data that control for survivorship bias, documents that while large retail active equity funds earn higher risk-adjusted returns (after expenses) than small funds, the difference in mean performance is not significantly different. In the institutional sphere, the study also finds no statistically significant performance differences (net of expenses) between funds on the basis of portfolio size. These findings suggest the hypothesis that performance declines with fund size is not supported empirically