Calibrating emergent phenomena in stock markets with agent based models.

Since the 2008 financial crisis, agent-based models (ABMs), which account for out-of-equilibrium dynamics, heterogeneous preferences, time horizons and strategies, have often been envisioned as the new frontier that could revolutionise and displace the more standard models and tools in economics. However, their adoption and generalisation is drastically hindered by the absence of general reliable operational calibration methods. Here, we start with a different calibration angle that qualifies an ABM for its ability to achieve abnormal trading performance with respect to the buy-and-hold strategy when fed with real financial data. Starting from the common definition of standard minority and majority agents with binary strategies, we prove their equivalence to optimal decision trees. This efficient representation allows us to exhaustively test all meaningful single agent models for their potential anomalous investment performance, which we apply to the NASDAQ Composite index over the last 20 years. We uncover large significant predictive power, with anomalous Sharpe ratio and directional accuracy, in particular during the dotcom bubble and crash and the 2008 financial crisis. A principal component analysis reveals transient convergence between the anomalous minority and majority models. A novel combination of the optimal single-agent models of both classes into a two-agents model leads to remarkable superior investment performance, especially during the periods of bubbles and crashes. Our design opens the field of ABMs to construct novel types of advanced warning systems of market crises, based on the emergent collective intelligence of ABMs built on carefully designed optimal decision trees that can be reversed engineered from real financial data.