Philip Genetic Programming In Statistical Arbitrage

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  • 1. Genetic Programming in Statistical Arbitrage Philip Saks PhD Seminar 17.10.2007
  • 2. Contents
    • Introduction
    • Genetic Programming
    • Clustering of Financial Data
    • Data
    • Framework
    • Results
    • Conclusion
  • 3. Introduction
    • To develop an automated framework for trading strategy design, by employing evolutionary computation in conjunction with other machine learning paradigms
    • The present framework utilize genetic programming
    • Much of the existing financial forecasting using GP has focused on high-frequency FX [Jonsson, 1997][Dempster and Jones, 2001][Bhattacharyya et al, 2002] and the general consencus is that there is predictability, and excess return is achievable in the pressence of transaction costs
    • For stocks, the results are mixed [Allen and Karjalainen, 1999] do not significantly out-perform the buy-and-hold on S&P500 daily data, but [Becker and Sheshadri, 2003] do on monthly.
  • 4. GP I
    • EC is a concept inspired by the Darwinian survival of the fittest principle – The rationale being, that natural evolution has proved succesfull in solving a wide range of problems throughout time, hence an algorithm that mimics this behavior, might solve a wide range of artificial problems
    • The concept was pioneered by Holland (1975) in the form of Genetic Algorithms (GA)
    • A GA is essentially a population based search method, where each candidate solution is incoded in a fixed length binary string.
    • The population evolves, via mainly three operators, selection, reproduction and mutation.
    • The selection process is based on the survival of the fittest principle.
  • 5. GP II
    • GP’s are basically GA’s in which the genome contitutes hierachical computer programs
    • Using this representation, we can solve problems in a wide range of fields such as, symbolic or ordinary regression, classification, optimal control theory etc. since each of these areas “can be viewed as requiring discovery of a computer program that produces some desired output for particular inputs” (Koza, 1992)
    • Tree representation of programs, function & terminal Set
    • Evolutionary operators: selection, cross-over & mutation
  • 6. Clustering of Financial Data
  • 7. Data
    • Hourly VWAP prices and volume for banking stocks within the Euro Stoxx Universe, covering the period from 01-Apr-2003 to 29-Jun-2007 (8648 oberservations).
  • 8. Framework
    • Evolve trading rules with binary decisions
    • We consider the classical single tree setup, but also a dual tree framework, where buy and sell rules are co-evolved.
    • The training set comprises 6000 samples, while the remaining 2647 are used for out-of-sample testing
    • 10 runs are performed for each experiment.
  • 9. Results
    • Trading on VWAP, assuming 1bp market impact
  • 10. Sensitivity Analysis
  • 11. Stress Testing I
  • 12. Turnover Analysis
  • 13. Transaction Cost Implications
  • 14. Conclusion
    • It is possible to discover profitable arbitrage trading rules on the Euro Stoxx banking sector.
    • A cooperative co-evolution of buy and sell rules are beneficial to the classical single tree structure.
    • Optimizing in the pressence of transaction costs makes a difference – There should be correspondence between assumption and application for optimal performance.