It is well-known that trading a security has an impact on that security’s price. But the impact of trading one security on the price of another, called cross-impact, has been much less studied. Cross-impact is very important in accurate assessment of portfolio trading cost. Ignoring it will certainly introduce biases in evaluating performance of portfolio-level trading strategies. In this paper, we aim to develop a cross-impact model that can be assessed using market variables.
Our research aims to provide convincing evidence of price cross-impact and to formulate a cross-impact model that can be used to predict the cost of trading multiple securities simultaneously. We propose linear and nonlinear cross-impact models, with their model parameters calibrated using Bloomberg client-reported trade data for global developed markets. Finally, dynamic arbitrage analysis is performed for both the linear- and nonlinear-aggregating models, which shows that no dynamic arbitrage is possible under normal scenarios.
Actual trade data
Many studies of cross-impact have worked only with publicly available data such as the trade and quote (TAQ) record from the New York Stock Exchange. However, as has been pointed out in academic research, that dataset has several shortcomings.
For this research, we use a large proprietary dataset compiled from anonymized Bloomberg client-reported trade data to analyze trade costs at the level of large orders. The market coverage of this dataset is extensive, and we can treat it as a proxy for the whole market.
Specialized models
We begin by extending a well-known form of a single-security price impact function to multiple concurrently traded securities. We then investigate a linear aggregating function as well as a shifted logistic function to allow for the nonlinear aggregation of cross-impacts from multiple securities simultaneously. We calibrate our model parameters separately for each developed market using a nonlinear least-squares algorithm.
Dynamic arbitrage analysis
After developing the models, we apply them to investigate the possibility of dynamic arbitrage. We find that it is theoretically possible for market conditions to be such that they allow dynamic arbitrage given our cross-impact model. Nevertheless, the parameter values that define the market “state” that would allow the arbitrage are so far from what we observe that we conclude that dynamic arbitrage is not possible under normal market conditions.
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