Using virtual stock markets with artificial interacting software investors, aka agent-based models (ABMs), we present a method to reverse engineer real-world financial time series. We model financial markets as made of a large number of interacting boundedly rational agents. By optimizing the similarity between the actual data and that generated by the reconstructed virtual stock market, we obtain parameters and strategies, which reveal some of the inner workings of the target stock market. We validate our approach by out-of-sample predictions of directional moves of the Nasdaq Composite Index.
The prediction of financial markets has long been the object of keen interest among both financial professionals and academics. The widely, -if not universally -, accepted Efficient Market Hypothesis (EMH) (Fama, 1970), (Fama, 1991) provides a powerful argument that markets are inherently unpredictable, in particular on the basis of prior price data: Because all information about the future is incorporated into the current price (for all practical purposes immediately), price changes must follow a random walk (Malkiel, 2003). There is considerable evidence however that prices do not perfectly follow a random walk and that some price inefficiency is present, varying over time, perhaps enough at times to be exploitable (Dahlquist and Bauer, 1998). However, recent assessments of the performance of hedge-funds (Barras, Scaillet, and Wermers, 2008) and of mutual funds (Fama and French, 2009) cast doubt on the reality of the gains resulting from the practical implementation of these inefficiencies, if they exist. As illustrated in the approaches of Barras, Scaillet, and Wermers (2008) and Fama and French (2009), deviations from the EMH are searched in the form of anomalous performance, beyond what can be explained by risk premia associated with exposures to a few dominating risk factors.
The near-absence of predictability in financial markets, or more precisely of risk-adjusted arbitrage opportunities, is truly remarkable. A rich academic literature has clarified the zen-like nature of the EMH in the sense that, the more intelligent are the investors and the harder are their efforts to gather information to make the best possible investment decisions, the fewer trading opportunities there are, and the more efficient is the market. The fact that markets are close to efficient can thus be understood as a macroscopic organization that result from the collective actions of the active investors. Borrowing from the jargon of complex system theory, market efficiency is an emergent phenomenon. Emergence, the existence of qualitatively new properties exhibited by collections of interacting individuals, is often taken to be the defining characteristic of complex adaptive systems.
Reciprocally, we ask here how the observation of the large scale behavior of a macroscopic system can (i) uncover the internal properties of a system and the organization among its constituents and (ii) be used for its prediction. Following Richard Feynman, we argue that, in order to really understand a system, we need to be able to strip things down, then rebuild them in order to play with the reconstructed simplified system and analyze variants, from which understanding can emerge. We address this question of “reverse engineering” in the context of one-dimensional financial (market) time-series. The challenge consists in building a virtual stock market with artificial interacting software investors. The method presumes that real-world discrete market price changes may be in principle modeled as the aggregated output of a large number of interacting boundedly rational agents. These agents have limited knowledge of the detailed properties of the markets they participate in and create, have access to a finite set of strategies to take only a small number of actions at each time-step and have restricted adaptation abilities. Given the time series data, our method of reverse engineering determines what set of agents, with which parameters and strategies, optimizes (in the sense of various robust metrics) the similarity between the actual data and that generated by an ensemble of virtual stock markets peopled by software investors. We provide a validation step by testing the performance of the reverse engineered artificial market in predicting out-ofsample directional moves of the real-world time series. Using only some of the simplest strategies and agents, the p-value for the statistical significance of the prediction of the directional moves for more than 600 trading days of the Nasdaq Composite Index is smaller than 0.02. The results are robust with changes of the styles of agents’ strategies and for different market regimes.
Our work uses the extensive literature on agent-based models that has been developing at least since the 1960s (see LeBaron (2000) and references therein). In ABMs, a system is modeled as a collection of autonomous decision-making entities, called agents. Repetitive competitive interactions among agents generate complex behavioral patterns. Due to the evolutionary switching among strategies, ABMs are highly nonlinear. The aggregation of simple interactions at the micro level may generate sophisticated structures at the macro level which provide valuable information about the dynamics of the real-world system which the ABM emulates. The main benefits of ABMs are that they (i) capture emergent phenomena; (ii) provide a natural description of a system; (iii) are flexible. ABMs have already been successfully applied in real-wo
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