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Evolution of trading strategies in a market with heterogeneously informed agents

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Abstract

We present an agent-based simulation of an asset market with heterogeneously informed agents. Genetic programming is applied to optimize the agents’ trading strategies. After optimization, insiders are the only agents able to generate small systematic above-average returns. For all other agents, genetic programming finds a rich variety of trading strategies that are predominantly based on exclusive subsets of their information. This limits their price impact and prevents them from making systematic losses. The resulting low noise renders market prices as largely informationally efficient.

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Notes

  1. Meaning situations where no agent can enhance his payoff by changing his trading strategy.

  2. With 10 signals ϵ i and two possible states for each signal, there are r = 210 = 1,024 possible states of the information system.

  3. An exception are cases where CVo 50 = CVo 51. In those cases we follow Schredelseker (2001) by adjusting P to CVo 50 − 0.05 or CVo 50 + 0.05 if this increases the number of shares traded. I.e., when CVo 50 = CVo 51 = CVo 52, the median price would leave us with three neutral agents and a market volume of 48 shares. Instead, P = CVo 50 − 0.05 will allow for a market volume of 49 shares with 51 buyers facing 49 sellers. in this case, scale selling is used and buyers will only receive \(s= \frac{49}{51}\) shares.

  4. As an agent in I = 0 gets no information at all, he will submit a reservation price of CV 0 = 5 when applying a fundamental strategy.

  5. E.g., if an agent decides to buy the security, he will realize gains if the security is undervalued, and he will make losses if it is overvalued. If his decision does not influence the market price, he will have a 50% chance for gains and losses, leaving him with an average performance of 0.

  6. The ramped half-and-half method proposed by Koza (1992) is used to ensure a rich diversity of trees.

  7. As reservation prices smaller than zero or greater than ten make no sense in this model, fitness in such cases is set to the minimal possible value which corresponds to a return of −1.

  8. This means that there is a 10% chance for reproduction, so that the selected strategy will be inherited by the new generation without any modification. This assures that successful strategies can survive.

  9. See http://jgap.sourceforge.net/ for a documentation on this package.

  10. The 100 agents are sorted in ascending order by their gains and one of the first agents is chosen using a log-normally distributed variable.

  11. For a detailed discussion of this effect see Lawrenz (2008).

  12. Note that every simulation of this kind is unique, so results on the development during optimization cannot be generalized. However, results after optimization do not change qualitatively when repeating the simulation or carrying out more runs. A robustness check where the simulation starts with different initial strategies supports this.

  13. As indicated by the grey bars in Fig. 26, some of them have already been optimized, but the optimization did not derive a superior strategy for them.

  14. Note that this is no equilibrium situation as described in Schredelseker (2001). In his model with three possible strategies, only 4 of 10 traders change strategies.

  15. Note the different scaling of the chart when comparing it to Fig. 3.

  16. The examples for trading strategies mentioned here are the simplest to be found after optimization. The formulas for the vast majority of optimized strategies are too complex to interpret.

  17. Two strategies are considered to be identical if they derive identical returns in all 1,024 runs.

  18. Note that in this optimization, the fundamental strategy of the insiders emerges endogenously. On average, genetic programming generates this strategy 520 times in each optimization step.

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Acknowledgements

We thank Michael Hanke, Jürgen Huber, Klaus Schredelseker, all discussants at the workshop “Evolution and Market Behavior in Economics and Finance”, and three anonymous referees for very helpful comments on this paper. We also acknowledge the FNR (Fonds National de la Recherche Luxembourg) for financial support on this project.

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Authors and Affiliations

  1. Department of Banking and Finance, Innsbruck University School of Management, Universitaetsstrasse 15, 6020, Innsbruck, Austria

    Florian Hauser & Bob Kaempff

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  1. Florian Hauser
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  2. Bob Kaempff
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Correspondence to Florian Hauser.

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Appendix

Appendix

Fig. 17
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Distribution of returns for all 100 agents after 10 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 18
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Distribution of returns for all 100 agents after 20 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 19
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Distribution of returns for all 100 agents after 30 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 20
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Distribution of returns for all 100 agents after 40 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 21
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Distribution of returns for all 100 agents after 50 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 22
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Distribution of returns for all 100 agents after 60 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 23
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Distribution of returns for all 100 agents after 70 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 24
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Distribution of returns for all 100 agents after 80 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 25
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Distribution of returns for all 100 agents after 90 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 26
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Distribution of returns for all 100 agents after 100 optimizations. Grey bars denote that an agent has already been optimized

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Fig. 27
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Distribution of returns for all 100 agents after 250 optimizations. Grey bars denote that an agent has already been optimized

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Hauser, F., Kaempff, B. Evolution of trading strategies in a market with heterogeneously informed agents. J Evol Econ 23, 575–607 (2013). https://doi.org/10.1007/s00191-011-0232-6

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