Bayesian Hierarchical Models for Market Impact

Every day, portfolio managers at Robeco generate orders that are sent to the equity trading desk and executed by traders. The main goal of traders is to minimize market impact—that is, the change in price caused by a trade or order. This research aims to develop a model that predicts market impact using economic factors for specific trades, such as relative order size (defined as the absolute volume of the trade divided by the 25-day Average Daily Volume for the specific stock), stock volatility, and bid-ask spread. The goal is to ensure that, at a regional level (America, Asia, and Europe), the mean prediction falls within the 95% confidence intervals derived from the data. Three different approaches are explored. First, the formula for computing the relative order size is modified by using the number of shares bought or sold instead of the volume in milion of euros. This adjustment ensures that the Average Daily Volume is not affected by fluctuations in exchange rates between the euro and local currencies. However, this change resulted in almost no variation in prediction accuracy. Secondly, new models from the literature are implemented, incorporating additional predictors. Lastly, the research focuses on Bayesian Hierarchical Models with an emphasis on partial pooling. This technique provides a structured framework for the model—in our case, a linear spline. Initially, the model is estimated globally, and this estimate is then used as a prior for the next step. In the second step, the model is re-trained, allowing for differences at the regional level or any other specified data segment. If the data for a specific segment shows a significantly different trend from the global one, the model parameters at the regional level are estimated accordingly. However, if the data is sparse or noisy, the estimates will tend toward the global model; this effect is known as shrinkage. This model demonstrates a balanced trade-off between regional fit and parameter stability over time. In the last chapter, we investigate whether Linear Mixed-Effects Models (LMMs) can yield similar results to partial pooling models without the need for Bayesian estimation. The conclusion is that LMMs produce estimates that are less stable over time compared to partial pooling.