Market impact for large institutional investors: empirical evidences and theoretical models

Advances in technology have deeply changed the way how securities are traded. The introduction of new technologies has enabled exchanges to automate the majority of their trading operations, leading on one side to a considerable cost reductions and on the other side oering a full set of new possibilities for market participants. In parallel to this automation, also brokers, hedge funds, proprietary trading forms, and other market participants have profitted from these new technology approaches for automating a variety of tasks, from optimization of order execution to whole trading strategies. In particular, with this progressive market automation a large amount of data becomes available, representing a unique laboratory where to discover new stylized facts and where to test new financial theories proposed in literature. This possibility has opened new challenges finalized to exploit this information for quantitative research and trading purposes, with a particular focus in market microstructure. For example, it is commonly accepted that market price moves during the execution of a trade - in average it increases for a buy order and vice versa it decreases for a sell order. This phenomenon, coined as market impact, is clearly a question of great relevance when studying the price formation process and it has also become a major practical issue for brokers, market makers and institutional investors in the design of their optimal trading strategies. Indeed, in order to know whether a trade will be profitable, it is essential to monitor transactions costs, which are directly related to market impact. Measuring and modelling market impact has therefore become a central question of interest both for finance researchers and practitioners with ongoing effort to generate trading model ideas and cost modelling improvements that help with portfolio construction techniques. In this research strand, one of the most surprising stylized facts is that the market impact of a so called metaorder - a long sequence of orders executed sequentially in the same direction and originated by the same trading decision - is approximately described by a square-root law of the order size, and not linearly as one may have naively expected. In general, public transaction data are not sufficient to perform market impact analysis since from the available information it is not possible to clearly identify the metaorders. This is why much of the work in both the academic and the industrial communities has been done using proprietary datasets. However, from these datasets focusing singularly on a single financial institution at the time it follows that i) the results are specific of the strategy and execution style of the institution, ii) it is not possible to have insights on how the metaorders executed from several institutions interact. For these reasons, one of the principal aims of this thesis is to investigate the interaction effects on market impact using a data-driven approach based on a rich dataset of metaorders originated by an heterogeneous set of investors in the U.S. equity market. The thesis is organized as follows. Chapter 1 provides an overview of the most relevant contributions in this thesis. Chapter 2 introduces the themes and research questions that we address for a general audience. A reader already familiar with the concepts related to the market impact and more in general with the market microstructure field could skip this part. Chapter 3 presents the ANcerno dataset used through this thesis for the several empirical analysis. It is represented by a rich dataset of heterogeneous institutional investors metaorders traded in the U.S. equity market. We describe some summary statistics of these metaorders introducing the parameters used to characterize their execution. Chapter 4 describes the first empirical study meant to validate a recent model of market impact based on a dynamical theory of liquidity. We find that the theoretical predictions, based on reaction-diffusion equations in a multiple-time scales framework, are remarkably well borne out by data: a transition from a linear to a square root market impact is observed, as predicted by the theory. Chapter 5 is devoted to the study of how the square-root law emerges from the interaction between different agents executing metaorders on the same asset. The crowding effects on market impact are investigated and special care is devoted to construct statistical models, which calibrated on data allow us to reproduce very well the different regimes of the empirical market impact curves. Chapter 6 is focused to shed light on what happens to the price dynamics after the metaorder execution. This is coined as price relaxation and we use several approaches in such a way to clarify the role of the order ow correlation on how the price relaxes after the end of the metaorder both at the intraday and at the multi-day levels. We find that relaxation takes place as soon as the metaorder ends and it continues in the following days with no apparent saturation at any predictable plateau. Chapter 7 concerns the trading cost associated with the execution of a metaorder which allows to define a natural dimensionless invariant in agreement with the trading invariance principle recently postulated in financial literature. From our empirical evidences it emerges that the trading invariance can be justified from the validity of the square-root law for market impact and from the proportionality between spread and volatility. Appendix A is devoted to underline that market impact should not be miscontrued as volatility. In particular, the square-root market impact has nothing to do with price diffusion, i.e. that typical price changes grow as the square-root of time. We therefore rationalise empirical findings on market impact and volatility by introducing a simple scaling argument in agreement with data. Chapters 4 through 7 and Appendix A contain the original contributions of this thesis. Each of them is self-contained and in principle can be read separately.