b. WorldQuant, Inc.

c. Swiss Finance Institute

The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available strategies over a fixed-length rolling window of prior time-steps. These are the Time Horizon MG/MAJG/$Gs (THMG, THMAJG, TH$G). Their probabilistic dynamics may be completely characterized in Markov-chain formulation. Games of both the standard and TH variants generate time-series that may be understood as arising from a stochastically perturbed determinism because a coin toss is used to break ties. The average over the binomially distributed coin tosses yields the underlying determinism. In order to quantify the degree of this determinism and of higher-order perturbations, we decompose the sign of the time-series they generate (analogous to a market price time-series) into a superposition of weighted Hamiltonian cycles on graphs—exactly in the TH variants and approximately in the standard versions. The cycle decomposition also provides a ‘dissection’ of the internal dynamics of the games and a quantitative measure of the degree of determinism. We discuss how the outperformance of strategies relative to agents in the THMG—the ‘illusion of control’—and the reverse in the THMAJG and TH$G, i.e. genuine control, may be understood on a cycle-by-cycle basis. The decomposition offers a new metric for comparing different game dynamics with real-world financial time-series and a method for generating predictors. We apply the cycle predictor to a real-world market, with significantly positive returns for the latter. Part I provides an overview of the paper and its methodologies with an appendix for the mathematical details of the Markov analysis of the THMG, THMAJG and TH$G. Part I also describes the cycle predictor and applies it to real-world financial series. Part II performs further analyses of the cycle decomposition method as applied to the time-series generated by agent-based models to gain insight into the ‘illusion of control’ that certain of these games demonstrate, i.e. the fact that the strategies outperform the agents that deploy them. Part II also illustrates both numerical and analytic methods for extracting cycles from a given time-series and applies the method to a number of different real-world data sets, in conjunction with an analysis of persistence.

J. B. Satinover

b. WorldQuant, Inc.

c. Swiss Finance Institute

The present article constitutes part II of a series of two reports in which we study the decomposition of synthetic and real financial time-series into a superposition of weighted Hamiltonian cycles on graphs. Part II further analyses the cycle-decomposition method introduced in part I for the Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G), in order to gain insight into the ‘illusion of control’ that certain of these games demonstrate, i.e. the fact that the strategies outperform the agents that deploy them. We also illustrate both numerical and analytical methods for extracting cycles from a given time-series and apply the method to a number of different real-world data sets, in conjunction with an analysis of persistence

Jeffrey Satinover

b. The King's College, NYC

c. Swiss Finance Institute

We consider the recent financial crisis as an overlapping sequence of interdependent financial bubbles followed by their collapse. Governments and regulatory agencies have made it a prime goal to moderate future crises. Many attempts at financial, economic and social engineering are plagued by an “illusion of control” typical of complex systems for which we offer some suggestive mathematical models. The “illusion of control” presents a significant challenge to effective resilience engineering. Furthermore, control may not only yield no benefit, but at times may exact perverse new costs. We argue that some markets almost always; almost all markets sometimes; and economies in general are truly “complex systems” in a technical sense; that as such, they are intrinsically characterized by periods of extremity and by abrupt state-transition; that they spend much time in a largely unpredictable state, but on the other enter periods of pre-crisis when they are predictable. In consequence of a system phase (or regime) transition, we argue that the most extreme events - the most influential ones - are susceptible to (probabilistic) prediction. In light of this analysis, we offer a small number of perhaps counter-intuitive suggestions, for example, that many of the present interventions in the “liquidity crisis” are ill-advised and possibly dangerous - e.g., the widespread attempts to artificially stimulate consumption in the absence of precautionary reserves and in the presence of huge liabilities; as an example of real-world, large-scale resilience engineering we suggest that bubble-prediction should be a mainstay of financial regulation.

J. Wiesinger

b. Swiss Finance Institute Research Paper No. 10-08 (2010)

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.

J.B. Satinover

b. Department of Management, Technology and Economics, ETH Zurich, CH-8032 Zurich, Switzerland

Both single-player Parrondo games (SPPG) and multi-player Parrondo games (MPPG) display the Parrondo effect (PE) wherein two or more individually fair (or losing) games yield a net winning outcome if alternated periodically or randomly. (There is a more formal, less restrictive definition of the PE.) We illustrate that, when subject to an elementary optimization rule, the PG displays degraded rather than enhanced returns. Optimization provides only the illusion of control, when low-entropy strategies (i.e., which use more information) under-perform random strategies (with maximal entropy). This illusion is unfortunately widespread in many human attempts to manage or predict complex systems. For the PG, the illusion is especially striking in that the optimization rule reverses an already paradoxical-seeming positive gain—the Parrondo effect proper—and turns it negative. While this phenomenon has been previously demonstrated using somewhat artificial conditions in the MPPG [L. Dinis, J.M.R. Parrondo, Europhys. Lett. 63 (2003) 319; J.M.R. Parrondo, L. Dinis, J. Buceta, K. Lindenberg, Advances in Condensed Matter and Statistical Mechanics, E. Korutcheva, R. Cuerno (Eds.), Nova Science Publishers, New York, 2003], we demonstrate it in the natural setting of a history-dependent SPPG.

Keywords: Applications to game theory and mathematical economics; Interacting agent models; Models of financial markets

PACS classification codes: 02.50.Le; 05.40.Jc; 89.65.Gh

J.B. Satinover

b. Department of Management, Technology and Economics, ETH Zurich, 8032 Zurich, Switzerland

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive [J.D. Taylor, S.E. Brown, Psych. Bull. 103, 193 (1988); A. Bandura, Self-efficacy: the exercise of control (WH Freeman, New York, 1997)]. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate [E. Langer, J. Pers. Soc. Psych. 7, 185 (1975)] or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Time-Horizon Minority Game [M.L. Hart, P. Jefferies, N.F. Johnson, Phys. A 311, 275 (2002)] and the Parrondo Game [J.M.R. Parrondo, G.P. Harmer, D. Abbott, Phys. Rev. Lett. 85, 5226 (2000); J.M.R. Parrondo, How to cheat a bad mathematician (ISI, Italy, 1996)], that agents who optimize their strategy based on past information may actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in certain set-ups a priori defined to emphasize the importance of optimization. PACS classification codes: 89.75.-k - Complex systems; 89.65.Gh – Economics, econophysics, financial markets, business and management; 02.50.Le - Decision theory and game theory.

J.B. Satinover

b. Department of Management, Technology and Economics, ETH Zurich, CH-8032 Zurich, Switzerland

jsatinover@ethz.ch and dsornette@ethz.ch

The Minority Game (MG), the Majority Game (MAJG) and the Dollar Game ($G) are important and closely-related versions of market-entry games designed to model different features of real-world financial markets. In a variant of these games, agents measure the performance of their available strategies over a fixed-length rolling window of prior time steps. These are the so-called Time Horizon MG/MAJG/$G (THMG, THMAJG, TH$G). Their probabilistic dynamics may be completely characterized in Markov-chain formulation. Games of both the standard and TH variants generate time-series that may be understood as arising from a stochastically perturbed determinism because a coin toss is used to break ties. The average over the binomially-distributed coin-tosses yields the underlying determinism. In order to quantify the degree of this determinism and of higher-order perturbations, we decompose the sign of the time-series they generate (analogous to a market price time series) into a superposition of weighted Hamiltonian cycles on graphs—exactly in the TH variants and approximately in the standard versions. The cycle decomposition also provides a “dissection” of the internal dynamics of the games and a quantitative measure of the degree of determinism. We discuss how the outperformance of strategies relative to agents in the THMG—the “illusion of control”— and the reverse in the THMAJG and TH$G, i.e., genuine control—may be understood on a cycle-by-cycle basis. The decomposition offers as well a new metric for comparing different game dynamics to real-world financial time-series and a method for generating predictors. We apply the cycle predictor a real-world market, with significantly positive returns for the latter.

PACS classification numbers: 02.50 Le, 05.40 Je

J.B. Satinover and D. Sornette , Illusory versus genuine control in agent-based games. Eur. Phys. J. B 67, 357-367 (2009)

In the Minority, Majority and Dollar Games (MG, MAJG, $G) agents compete for rewards, acting in accord with the previously best-performing of their strategies. Different aspects/kinds of real-world markets are modelled by these games. In the MG, agents compete for scarce resources; in the MAJG agents imitate the group to exploit a trend; in the $G agents attempt to predict and benefit both from trends and changes in the direction of a market. It has been previously shown that in the MG for a reasonable number of preliminary time steps preceding equilibrium (Time Horizon MG, THMG), agents' attempt to optimize their gains by active strategy selection is “illusory”: the hypothetical gains of their strategies is greater on average than agents' actual average gains. Furthermore, if a small proportion of agents deliberately choose and act in accord with their seemingly worst performing strategy, these outperform all other agents on average, and even attain mean positive gain, otherwise rare for agents in the MG. This latter phenomenon raises the question as to how well the optimization procedure works in the THMAJG and TH$G. We demonstrate that the illusion of control is absent in THMAJG and TH$G. This provides further clarification of the kinds of situations subject to genuine control, and those not, in set-ups a priori defined to emphasize the importance of optimization.

PACS classification codes: 89.75.-k - Complex systems. 89.65.Gh - Economics; econophysics, financial markets, business and management. 02.50.Le - Decision theory and game theory.

J.B. Satinover and D. Sornette, Anomalous Returns in a Neural Network Equity-Ranking Predictor, Swiss Finance Institute Research Paper No. 08-15 (2008)

selected in PinHawk NewzDigest, Economic Research and News, Thursday, July 10, 2008, Vol. 1, No. 298

Using an artificial neural network (ANN), a fixed universe of ~1500 equities from the Value Line index are rank-ordered by their predicted price changes over the next quarter. Inputs to the network consist only of the ten prior quarterly percentage changes in price and in earnings for each equity (by quarter, not accumulated), converted to a relative rank scaled around zero. Thirty simulated portfolios are constructed respectively of the 10, 20, ..., and 100 top ranking equities (long portfolios), the 10, 20, ..., 100 bottom ranking equities (short portfolios) and their hedged sets (long-short portfolios). In a 29-quarter simulation from the end of the third quarter of 1994 through the fourth quarter of 2001 that duplicates real-world trading of the same method employed during 2002, all portfolios are held fixed for one quarter. Results are compared to the S&P 500, the Value Line universe itself, trading the universe of equities using the proprietary Value Line Ranking System (to which this method is in some ways similar), and to a Martingale method of ranking the same equities. The cumulative returns generated by the network predictor significantly exceed those generated by the S&P 500, the overall universe, the Martingale and Value Line prediction methods and are not eroded by trading costs. The ANN shows significantly positive Jensen's alpha. All three active trading methods result in very high levels of volatility. But the network method exhibits a distinct kind of volatility: Though overall it does the best job of segregating equities in advance into those that will rise and those that will fall relative to one another, there are many quarters when it does not merely fail, but rather inverts: It disproportionately predicts an inverse rank ordering and therefore generates unusually large losses in those quarters. The same phenomenon occurs, but to a greater degree, with the VL system itself and with a one-step Martingale predictor. An examination of the quarter to quarter performance of the actual and predicted rankings of the change in equity prices suggests while the network is capturing, after a delay, changes in the market sampled by the equities in the Value Line index (enough to generate substantial gains), it also fails in large measure to keep up with the fluctuating data, leading the predictor to be often out of phase with the market. A time series of its global performance thus shows antipersistence. However, its performance is significantly better than a simple one-step Martingale predictor, than the Value Line system itself and than a simple buy and hold strategy, even when transaction costs are accounted for.

Keywords: Neural networks, Value Line ranking, anomalous returns, anti-persistence

JEL Classifications: G11, C15, C45

J.B. Satinover, Decoherence-Free Subspaces in Supersymmetric Oscillator Networks. arXiv:quant-ph/0211172v2 (2003)

Keck Center for Quantum Information and Processing and Theoretical Condensed Matter Physics Group, Dept. of Physics, Yale University, New Haven, Connecticut, USA

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

J.B. Satinover, The Quantum Brain, Wiley (Book, 2001)